Vehicle speed optimization method, device and vehicle

Abstract

The application provides a vehicle speed optimization method and device and a vehicle. The method comprises the following steps: acquiring vehicle parameters, road parameters and environmental parameters where the vehicle is located; determining tire force circle constraints and relaxation variables based on the vehicle parameters, the road parameters and the environmental parameters, and introducing a preset safety threshold for the relaxation variables to obtain an obstacle cost term; determining a power constraint corresponding to the vehicle, a reference speed cost term and a smoothness cost term according to the vehicle parameters, and obtaining a total cost function based on weighted summation of the obstacle cost term, the reference speed cost term and the smoothness cost term; performing analytical derivation processing on the obstacle cost term based on the vehicle parameters to obtain convergence information of the obstacle cost term; and constructing an optimization target and iteratively solving based on the convergence information and the total cost function to obtain a speed optimization parameter of the vehicle. The constraint accuracy, solution stability and dynamic adaptability of the vehicle speed planning in a low adhesion coefficient road surface scenario are improved.

Description

Technical Field

[0001] This application relates to the field of autonomous vehicle control, and in particular to vehicle speed optimization methods, devices, and vehicles. Background Technology

[0002] On roads with low adhesion coefficients, autonomous vehicles typically employ speed planning and trajectory control methods based on dynamic constraints, combining information such as vehicle status, road curvature, and slope to generate a driving speed sequence.

[0003] However, existing solutions often treat longitudinal and lateral constraints separately and frequently use fixed parameters for optimization, which makes it difficult to accurately reflect the dynamic changes in tire force coupling and road conditions. This can easily lead to conservative planning, reduced efficiency, or constraint overruns under extreme conditions, thus affecting the stability and adaptability of real-time optimization.

[0004] Therefore, how to achieve the constraint accuracy, solution stability and dynamic adaptability of speed planning under low adhesion coefficient road surfaces has become an urgent technical problem to be solved. Summary of the Invention

[0005] The vehicle speed optimization method, apparatus, and vehicle provided in this application address the aforementioned technical problems. This method addresses the speed optimization needs of vehicles in autonomous driving mode. It uniformly models the constraints affecting vehicle driving safety and speed decisions, considering the vehicle's own state, road conditions, and external environmental information. Based on this, it forms a comprehensive cost description for speed optimization, achieving coordinated optimization of vehicle speed and thus improving the constraint accuracy, solution stability, and dynamic adaptability of speed planning in low-adhesion road surface scenarios.

[0006] In a first aspect, embodiments of this application provide a vehicle speed optimization method, applied to a vehicle in an autonomous driving state, the method comprising:

[0007] Obtain vehicle parameters, road parameters, and environmental parameters.

[0008] Based on vehicle parameters, road parameters, and environmental parameters, tire force circle constraints and relaxation variables are determined, and a preset safety threshold is introduced for the relaxation variables to obtain the obstacle cost term.

[0009] Based on the vehicle parameters, the corresponding dynamic constraints, reference speed cost term, and ride comfort cost term are determined. The total cost function is obtained by weighted summation of the obstacle cost term, reference speed cost term, and ride comfort cost term.

[0010] Based on vehicle parameters, the obstacle cost term is analytically derived to obtain the convergence information of the obstacle cost term;

[0011] Based on convergence information and the total cost function, an optimization objective is constructed and solved iteratively to obtain the vehicle speed optimization parameters.

[0012] In one possible embodiment, the vehicle parameters include at least: vehicle speed, vehicle mass, drag coefficient, frontal area, and rolling resistance coefficient;

[0013] Road parameters should include at least: path curvature and road slope;

[0014] Environmental parameters include at least: road surface adhesion coefficient and air density.

[0015] In one possible embodiment, tire force circle constraints and relaxation variables are determined based on vehicle parameters, road parameters, and environmental parameters, including:

[0016] Based on vehicle parameters, road parameters, and environmental parameters, determine the longitudinal and lateral forces of the vehicle.

[0017] Based on longitudinal and lateral forces, tire force circle constraints and relaxation variables are determined.

[0018] In one possible embodiment, determining the longitudinal force of the vehicle based on vehicle parameters, road parameters, and environmental parameters includes:

[0019] The longitudinal resistance term of the vehicle is determined based on vehicle speed, vehicle mass, drag coefficient, frontal area, rolling resistance coefficient, road gradient, and air density.

[0020] The longitudinal force is determined based on the vehicle body mass, vehicle speed, and longitudinal resistance term.

[0021] In one possible embodiment, the longitudinal resistance term includes: wind resistance, rolling resistance, and slope resistance;

[0022] Wind resistance is determined based on the drag coefficient, frontal area, air density, and vehicle speed; rolling resistance is determined based on the rolling resistance coefficient and vehicle mass; and gradient resistance is determined based on the road gradient and vehicle mass.

[0023] In one possible embodiment, determining the tire force circle constraint based on longitudinal and lateral forces includes:

[0024] The resultant force is constructed based on longitudinal and lateral forces, and the resultant force is compared with the adhesion limit corresponding to the road adhesion coefficient to determine the tire force circle constraint.

[0025] In one possible embodiment, the step of determining the slack variable includes:

[0026] The tire force circle constraint is transformed into an inequality relationship between vehicle speed and the corresponding acceleration, and the margin parameter of the inequality relationship is determined.

[0027] The margin parameter is defined as a slack variable.

[0028] In one possible embodiment, a preset safety threshold is introduced for the slack variable to obtain the barrier cost term, including:

[0029] Determine the obstacle factor based on the road surface adhesion coefficient;

[0030] When the slack variable is greater than the preset safety threshold, the barrier cost term is calculated using the logarithmic barrier function based on the barrier factor and the slack variable.

[0031] In one possible embodiment, when the slack variable is less than or equal to a preset safety threshold, the obstacle cost term is obtained by a quadratic approximation calculation based on the obstacle factor, the preset safety threshold, and the slack variable.

[0032] In one possible embodiment, the step of obtaining convergence information for the barrier cost term includes:

[0033] Based on the vehicle speed and the corresponding acceleration, the first derivative of the obstacle cost term is calculated to obtain the gradient information, and the second derivative is calculated based on the first derivative to obtain the Hessian matrix information;

[0034] Gradient information and Hessian matrix information are used as convergence information.

[0035] In one possible embodiment, the step of obtaining the vehicle speed optimization parameters includes:

[0036] A decision vector is constructed by combining vehicle speed, acceleration, and vehicle jerk.

[0037] Based on convergence information and the total cost function, an optimization objective is constructed, and the decision vector is iteratively solved using the optimization objective to obtain the speed optimization parameters.

[0038] In one possible embodiment, a decision vector is constructed based on vehicle speed, acceleration, and vehicle jerk, including:

[0039] Vehicle speed and acceleration are used as state variables, and vehicle jerk is used as a control variable. The state variables and control variables are combined into a decision vector.

[0040] In one possible embodiment, iteratively solving for the decision vector includes:

[0041] In each iteration, the convergence direction and step size are determined based on gradient information and Hessian matrix information;

[0042] If the change in the total cost function is less than the convergence tolerance, and / or the number of iterations reaches the preset upper limit, the iteration is terminated and the speed optimization parameters are output.

[0043] In one possible embodiment, the method further includes:

[0044] Update the vehicle's road and environmental parameters at each discrete time step within the preset planning time domain;

[0045] The updated road and environmental parameters are used to update the time-varying parameters in the tire force circle constraint, the obstacle factor in the obstacle cost term, and the preset safety threshold.

[0046] In one possible embodiment, after updating the time-varying parameters in the tire force circle constraint, the obstacle factor in the obstacle cost term, and the preset safety threshold, the method further includes:

[0047] Based on the updated time-varying parameters, barrier factors, and preset safety thresholds, the convergence information and total cost function are redefined.

[0048] Secondly, embodiments of this application provide a vehicle speed optimization device applied to a vehicle in an autonomous driving state. The device includes:

[0049] The acquisition module is used to acquire vehicle parameters, road parameters, and environmental parameters.

[0050] The determination module is used to determine the tire force circle constraint and relaxation variables based on vehicle parameters, road parameters and environmental parameters, and to introduce a preset safety threshold for the relaxation variables to obtain the obstacle cost term;

[0051] The determination module is also used to determine the corresponding dynamic constraints, reference speed cost terms and ride comfort cost terms of the vehicle based on the vehicle parameters, and to obtain the total cost function based on the obstacle cost terms, reference speed cost terms and ride comfort cost terms.

[0052] The parsing module is used to perform analytical derivation of the obstacle cost term based on vehicle parameters to obtain the convergence information of the obstacle cost term;

[0053] The determination module is also used to construct an optimization objective and iteratively solve it based on convergence information and the total cost function to obtain the vehicle speed optimization parameters.

[0054] In one possible embodiment, the vehicle parameters include at least: vehicle speed, vehicle mass, drag coefficient, frontal area, and rolling resistance coefficient;

[0055] Road parameters should include at least: path curvature and road slope;

[0056] Environmental parameters include at least: road surface adhesion coefficient and air density.

[0057] In one possible embodiment, the determining module is further configured to:

[0058] Based on vehicle parameters, road parameters, and environmental parameters, determine the longitudinal and lateral forces of the vehicle.

[0059] Based on longitudinal and lateral forces, tire force circle constraints and relaxation variables are determined.

[0060] In one possible embodiment, the determining module is further configured to:

[0061] The longitudinal resistance term of the vehicle is determined based on vehicle speed, vehicle mass, drag coefficient, frontal area, rolling resistance coefficient, road gradient, and air density.

[0062] The longitudinal force is determined based on the vehicle body mass, vehicle speed, and longitudinal resistance term.

[0063] In one possible embodiment, the longitudinal resistance term includes: wind resistance, rolling resistance, and slope resistance;

[0064] Wind resistance is determined based on the drag coefficient, frontal area, air density, and vehicle speed; rolling resistance is determined based on the rolling resistance coefficient and vehicle mass; and gradient resistance is determined based on the road gradient and vehicle mass.

[0065] In one possible embodiment, the determining module is further configured to:

[0066] The resultant force is constructed based on longitudinal and lateral forces, and the resultant force is compared with the adhesion limit corresponding to the road adhesion coefficient to determine the tire force circle constraint.

[0067] In one possible embodiment, the determining module is further configured to:

[0068] The tire force circle constraint is transformed into an inequality relationship between vehicle speed and the corresponding acceleration, and the margin parameter of the inequality relationship is determined.

[0069] The margin parameter is defined as a slack variable.

[0070] In one possible embodiment, the determining module is further configured to:

[0071] Determine the obstacle factor based on the road surface adhesion coefficient;

[0072] When the slack variable is greater than the preset safety threshold, the barrier cost term is calculated using the logarithmic barrier function based on the barrier factor and the slack variable.

[0073] In one possible embodiment, the determining module is further configured to:

[0074] When the slack variable is less than or equal to the preset safety threshold, the obstacle cost term is obtained by a quadratic approximation based on the obstacle factor, the preset safety threshold, and the slack variable.

[0075] In one possible embodiment, the parsing module is further configured to:

[0076] Based on the vehicle speed and the corresponding acceleration, the first derivative of the obstacle cost term is calculated to obtain the gradient information, and the second derivative is calculated based on the first derivative to obtain the Hessian matrix information;

[0077] Gradient information and Hessian matrix information are used as convergence information.

[0078] In one possible embodiment, the determining module is further configured to:

[0079] A decision vector is constructed by combining vehicle speed, acceleration, and vehicle jerk.

[0080] Based on convergence information and the total cost function, an optimization objective is constructed, and the decision vector is iteratively solved using the optimization objective to obtain the speed optimization parameters.

[0081] In one possible embodiment, the determining module is further configured to:

[0082] Vehicle speed and acceleration are used as state variables, and vehicle jerk is used as a control variable. The state variables and control variables are combined into a decision vector.

[0083] In one possible embodiment, the determining module is further configured to:

[0084] In each iteration, the convergence direction and step size are determined based on gradient information and Hessian matrix information;

[0085] If the change in the total cost function is less than the convergence tolerance, and / or the number of iterations reaches the preset upper limit, the iteration is terminated and the speed optimization parameters are output.

[0086] In one possible embodiment, the vehicle speed optimization device is further used for:

[0087] Update the vehicle's road and environmental parameters at each discrete time step within the preset planning time domain;

[0088] The updated road and environmental parameters are used to update the time-varying parameters in the tire force circle constraint, the obstacle factor in the obstacle cost term, and the preset safety threshold.

[0089] In one possible embodiment, the vehicle speed optimization device is further used for:

[0090] Based on the updated time-varying parameters, barrier factors, and preset safety thresholds, the convergence information and total cost function are redefined.

[0091] Thirdly, this application provides a vehicle equipped with a control unit, which is used to optimize vehicle speed using the method provided above.

[0092] The control unit includes: a processor and memory;

[0093] The memory stores instructions that the computer executes;

[0094] The processor executes computer execution instructions stored in memory, causing the processor to perform the method provided by the first aspect of the invention.

[0095] Fourthly, this application provides a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, are used to implement the vehicle speed optimization method of the first aspect of the invention.

[0096] Fifthly, this application provides a computer program product, including a computer program, which, when executed by a processor, is used to implement the vehicle speed optimization method described in the first aspect of the invention.

[0097] Based on the implementation methods provided in the above aspects, this application can be further combined to provide more implementation methods.

[0098] The vehicle speed optimization method, apparatus, and vehicle provided in this application acquire vehicle parameters, road parameters, and environmental parameters, and comprehensively determine tire force circle constraints and relaxation variables based on these parameters. This allows the vehicle's longitudinal and lateral coupling constraints to be incorporated into a unified optimization framework, thereby improving the accuracy of characterizing the vehicle's feasible driving range under extreme conditions. By introducing a preset safety threshold for the relaxation variables and weighting and summing the obstacle cost, reference speed cost, and ride comfort cost, the method can balance safety margin, target speed tracking, and driving ride comfort, thereby reducing the risk of overly conservative speed planning or excessive constraints. By analytically deriving the obstacle cost and combining it with convergence information to solve for speed optimization parameters, the method can improve the convergence of the optimization process and the stability of real-time calculation, thereby enhancing the adaptability and execution reliability of vehicle speed optimization on low-adhesion road surfaces. Attached Figure Description

[0099] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0100] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0101] Figure 1 A flowchart illustrating the vehicle speed optimization method provided in this application embodiment. Figure 1 ;

[0102] Figure 2 A flowchart illustrating the vehicle speed optimization method provided in this application embodiment. Figure 2 ;

[0103] Figure 3 A flowchart illustrating the vehicle speed optimization method provided in this application embodiment. Figure 3 ;

[0104] Figure 4 A flowchart illustrating the vehicle speed optimization method provided in this application embodiment. Figure 4 ;

[0105] Figure 5 A flowchart illustrating the vehicle speed optimization method provided in this application embodiment. Figure 5 ;

[0106] Figure 6 A flowchart illustrating the vehicle speed optimization method provided in this application embodiment. Figure 6 ;

[0107] Figure 7 This is a schematic diagram of the vehicle speed optimization device provided in the embodiments of this application;

[0108] Figure 8 This is a schematic diagram of a control unit provided in an embodiment of this application. Detailed Implementation

[0109] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.

[0110] In the embodiments of this application, the terms "first" and "second" are used to distinguish identical or similar items with substantially the same function and effect. Those skilled in the art will understand that the terms "first" and "second" do not limit the quantity or execution order, and that "first" and "second" do not necessarily imply difference. It should be noted that in the embodiments of this application, the words "exemplary" or "for example" are used to indicate that something is being used as an example, illustration, or description. Any embodiment or design scheme described as "exemplary" or "for example" in this application should not be construed as being better or more advantageous than other embodiments or design schemes. Specifically, the use of "exemplary" or "for example" is intended to present the relevant concepts in a concrete manner. In the embodiments of this application, "at least one" refers to one or more, and "more than one" refers to two or more.

[0111] It should be noted that the phrase "at...time" in the embodiments of this application can refer to the instant at which a certain situation occurs, or to a period of time after the occurrence of a certain situation; the embodiments of this application do not specifically limit this. Furthermore, the vehicle speed optimization method provided in the embodiments of this application is merely an example, and the vehicle speed optimization method may include more or less content.

[0112] Vehicle speed optimization on low-friction surfaces falls under the field of autonomous vehicle motion control and trajectory planning, typically consisting of a closed-loop control architecture comprised of onboard sensors, high-precision maps, and environmental perception modules. When a vehicle travels on icy, slippery, or gravelly surfaces, it needs to generate an executable speed trajectory based on information such as speed, acceleration, road curvature, gradient, and friction coefficient, and then output the optimization results to the underlying controller for tracking control.

[0113] Existing technologies mostly rely on vehicle dynamics constraints for speed planning, typically modeling longitudinal and lateral forces separately, and then combining fixed adhesion limits or empirical thresholds to impose speed restrictions, thereby solving for the optimal trajectory under reference speed, ride comfort, and safety constraints. This type of method struggles to accurately reflect tire force coupling on low-adhesion surfaces. When encountering curves, changes in gradient, and fluctuations in the adhesion coefficient, it is prone to problems such as inaccurate constraint representation, oscillations in optimization boundaries, and overly conservative results. Some solutions may even produce out-of-limit trajectories under extreme conditions, causing sideslip, skidding, or a significant decrease in traffic efficiency.

[0114] Based on the aforementioned technical issues, vehicle parameters, road parameters, and environmental parameters are used to jointly characterize the tire force circle boundary. Then, a safety threshold is introduced around the relaxation variables, and an obstacle cost term is constructed, allowing tire force constraints to participate in the speed solution process in an optimization-compatible form. Since the longitudinal and lateral forces of the tire have a strong coupling relationship under low-adhesion conditions, if they are transformed into a cost expression with convergence information and weighted together with dynamic constraints, reference speed costs, and ride comfort costs, it is possible to continuously select speed trajectories that meet the grip limit under complex road condition changes, while simultaneously considering solution stability and ride comfort.

[0115] This application addresses the problems of difficulty in accurately modeling the longitudinal and lateral force coupling constraints of tires on roads with low adhesion coefficients, instability in optimization solutions caused by direct hard constraints, and easy exceedance of planning results when road parameters change dynamically. It proposes a speed optimization framework with tire force circle constraints as the core, logarithmic obstacle functions as soft constraint bridges, and analytical gradient Hessian as efficient solution support.

[0116] Specifically, firstly, longitudinal forces (including wind resistance, rolling resistance, and slope resistance) and lateral forces (including curvature centrifugal force) are uniformly incorporated into the tire force circle constraint and expanded into a quadratic inequality concerning vehicle speed and acceleration, thus transforming the physical adhesion limit into a mathematically calculable constraint. Secondly, slack variables are introduced to quantify the degree of constraint satisfaction, and a logarithmic barrier function is used to smoothly integrate the inequality constraint into the cost function. Simultaneously, in the dangerous region where the slack variables approach the boundary, a quadratic approximation is used to avoid numerical instability caused by the infinite derivative of the logarithmic function, achieving a "constraint..." The system achieves the effect of "hard, soft cost, and stable boundary"; furthermore, it analyzes the derivative of the obstacle cost term with respect to vehicle speed and acceleration to obtain closed expressions for the gradient and Hessian matrix, providing accurate direction and curvature information for optimization solutions, thus significantly improving the iterative convergence speed compared to numerical difference methods; finally, by allowing the constraint parameters to be dynamically updated with discrete time steps, the speed trajectory in the planning time domain can respond in real time to changes in road slope, curvature, and road surface adhesion coefficient, thereby maximizing tire grip while ensuring safety, and balancing traffic efficiency and driving smoothness.

[0117] The technical solution of this application and how the technical solution of this application solves the above-mentioned technical problems are described in detail below with specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of this application will now be described with reference to the accompanying drawings.

[0118] Figure 1 A flowchart illustrating the vehicle speed optimization method provided in this application embodiment. Figure 1 To facilitate understanding, the following will combine... Figure 1The vehicle speed optimization method provided in the embodiments of this application is described below. The method includes:

[0119] S101. Obtain vehicle parameters, road parameters, and environmental parameters.

[0120] Vehicle parameters are parameters that characterize the vehicle's own state and dynamic characteristics. These parameters may include vehicle speed, vehicle mass, drag coefficient, frontal area, and rolling resistance coefficient. Vehicle parameters can be provided by onboard sensors (wheel speed sensors, inertial navigation, fusion positioning), vehicle calibration parameters, or load estimation modules.

[0121] Road parameters are parameters that characterize the geometric features of the road the vehicle is currently traveling on, such as path curvature and road slope. Road parameters can be obtained from high-precision maps, trajectory planning results, or environmental perception modules.

[0122] Environmental parameters characterize road surface adhesion conditions and external medium conditions, including the road surface adhesion coefficient and air density. The road surface adhesion coefficient can be provided by road surface sensing results, historical estimates, or online identification modules; air density can be calculated from environmental sensors using temperature, air pressure, and altitude information. For example, the road surface adhesion coefficient can be derived by using wheel speed difference and yaw rate response, combined with Kalman filter to identify tire lateral stiffness online, and then back-calculating the adhesion coefficient; or it can be obtained by looking up pre-stored road surface attribute labels (asphalt / concrete / ice and snow) in a high-precision map; or it can be obtained by identifying road surface texture features through a camera and mapping them to an adhesion coefficient estimate through a classification model.

[0123] Understandably, vehicle parameters can be updated within each control cycle (typically 100ms). Vehicle mass can be estimated by the load estimation module based on suspension travel sensors or tire pressure monitoring systems. The road adhesion coefficient can be identified online using signals such as wheel speed difference, yaw rate response, and lateral acceleration, combined with a Kalman filter. Air density can be calculated using the ideal gas law based on ambient temperature, air pressure, and altitude information.

[0124] In practice, vehicle parameters, road parameters, and environmental parameters all use real-time data from when the vehicle is in autonomous driving mode as input. Vehicle parameters are used to characterize the vehicle's own state and serve as input for subsequent modeling. Road parameters are used to characterize the geometric features of the road the vehicle is currently traveling on, and environmental parameters are used to characterize road surface adhesion and external medium conditions.

[0125] Optionally, vehicle parameters, road parameters, and environmental parameters can be used for subsequent optimization modeling. These parameters can be configured according to the actual application scenario and together form the input basis for tire force constraints, dynamic constraints, and cost functions.

[0126] S102. Based on vehicle parameters, road parameters, and environmental parameters, determine tire force circle constraints and relaxation variables, and introduce a preset safety threshold for the relaxation variables to obtain the obstacle cost term.

[0127] The tire force circle constraint characterizes the boundary of the total grip force that the tire can provide. Its physical meaning is that the resultant force of the tire's longitudinal force and lateral force does not exceed the adhesion limit corresponding to the road adhesion coefficient. This constraint reflects the coupling relationship between longitudinal force and lateral force, that is, when the vehicle accelerates / brakes (longitudinal force) and turns (lateral force), the two share a limited tire grip force.

[0128] Slack variables are used to quantify the margin of the current speed planning distance from the tire force circle constraint boundary. A positive and larger slack variable indicates that the constraint is satisfied with a margin of error, a value close to zero indicates that the constraint is close to the boundary (dangerous), and a negative value indicates that the constraint is violated (slippage).

[0129] A preset safety threshold is used to define the calculation interval for the barrier cost term. When the slack variable is greater than this threshold, a logarithmic barrier function is used; when it is less than or equal to this threshold, a quadratic approximation is used to avoid numerical instability caused by the infinite derivative of the logarithmic function when the slack variable approaches zero.

[0130] The obstacle cost term transforms the hard constraint of the tire force circle constraint into a cost expression of the soft constraint, so that the optimizer guides the solution to move into the feasible region by the principle that "the closer the constraint is violated, the greater the cost", rather than directly dealing with the nonlinear hard constraint.

[0131] In practice, a tire force constraint model is established based on vehicle parameters, road parameters, and environmental parameters, thereby obtaining the tire force circle constraint. The tire force circle constraint is used to characterize the boundary of the total grip force that the tire can provide, and its expression can be limited by the road surface adhesion conditions.

[0132] Furthermore, a slack variable is defined to reflect the margin of the current velocity planning distance from the constraint boundary. The smaller the slack variable, the closer the planning result is to the constraint boundary. After introducing a preset safety threshold for this slack variable, the obstacle cost term can be constructed in a piecewise form: when the slack variable is greater than the preset safety threshold, the obstacle function is used to penalize the degree of constraint proximity; when the slack variable is less than or equal to the preset safety threshold, an approximate form is used to replace the obstacle function to avoid numerical instability caused by the slack variable approaching zero.

[0133] The obstacle cost term thus transforms the tire force circle constraint, which was originally difficult to directly participate in optimization, into a weighted summable cost expression, allowing constraint information to enter the speed optimization process in a continuous and differentiable form. A preset safety threshold is used here to divide the safety interval and the boundary interval; its value can be preset according to actual optimization needs, thereby maintaining stable numerical performance near the constraint boundary.

[0134] S103. Based on the vehicle parameters, determine the corresponding dynamic constraints, reference speed cost term, and ride comfort cost term for the vehicle, and obtain the total cost function by weighted summation of the obstacle cost term, reference speed cost term, and ride comfort cost term.

[0135] Among them, dynamic constraints are used to describe the range of longitudinal driving force and braking force that the vehicle can achieve in the current state, including speed boundary constraints ( ), acceleration boundary constraints ( ) and jerk boundary constraints ( ).

[0136] The reference speed cost term represents the deviation between the optimized speed and the reference speed. The reference speed is set comprehensively based on the road speed limit, curvature, and coefficient of friction. For example, the upper speed limit is first determined based on the road speed limit, then the upper speed limit for cornering is calculated based on the curvature, and then further reduced based on the coefficient of friction. The minimum value of the three is taken as the final reference speed. The ride comfort cost term describes the smoothness of the speed change process, by penalizing the jerk ( The magnitude of the rate of change of acceleration is used to ensure passenger comfort. The total cost function is a unified optimization criterion that weights and integrates three types of objectives: safety (obstacle cost), efficiency (reference speed cost), and comfort (smoothness cost).

[0137] In practice, the vehicle's dynamic constraints are directly determined by the vehicle parameters, describing the range of longitudinal driving and braking forces achievable by the vehicle in the current state, and forming the constraint conditions. The reference speed cost term is used to characterize the deviation between the optimized speed and the reference speed, which can come from speed limit information, the expected speed of path planning, or the output of the upper-level decision module; the ride comfort cost term is used to characterize the smoothness of the speed change process, penalizing excessively rapid speed changes or sudden changes in trajectory curvature.

[0138] Furthermore, the obstacle cost, reference speed cost, and ride comfort cost are assigned preset weight coefficients and then summed in a weighted manner to form a unified total cost function. Each weight coefficient reflects the relative effects of safety, tracking, and ride comfort under the current operating conditions. The total cost function can be written in the form of an objective function in a discrete-time optimal control problem, accumulating the costs at each time step to provide a unified optimization criterion for subsequent solutions. Optionally, the weight coefficients can be adjusted according to the driving mode.

[0139] By unifying the obstacle expression of tire force constraints with dynamic constraints, speed tracking, and speed change smoothness into the same objective function, the optimization solution can simultaneously consider the actual power capability of the vehicle and the continuity of the speed trajectory, avoiding the problem of overly conservative or out-of-limit results caused by relying on a single constraint model.

[0140] S104. Based on vehicle parameters, the obstacle cost term is analyzed and derived to obtain the convergence information of the obstacle cost term.

[0141] The convergence information includes gradient information (i.e., the first derivative of the obstacle cost term) and Hessian matrix information (i.e., the second derivative of the first derivative), which are used to indicate the search direction and step size in the optimization process. The gradient indicates the direction of the fastest cost descent, and the Hessian matrix indicates the curvature of the cost function to determine the optimization step size.

[0142] In the specific implementation, the relationship between the obstacle cost term and the vehicle parameters is analytically derived. This involves mathematically differentiating the obstacle cost term with respect to state variables (vehicle speed and acceleration) to obtain analytical expressions for its first and second derivatives. This yields convergence information for the obstacle cost term during the optimization iteration process. This convergence information characterizes the search direction, local curvature, and trend towards the optimal solution for the obstacle cost term at the current iteration point.

[0143] Specifically, taking the obstacle cost term as the object and vehicle speed and acceleration as independent variables, the first-order and second-order relationships of the cost function as a function of the state variables are obtained through analytical differentiation. These first-order and second-order relationships are then output as convergence information to the subsequent optimization solution stage. The entire process does not rely on any numerical difference or trial-and-error calculations, but rather obtains a closed-form expression of the derivative through mathematical derivation, thereby significantly reducing the computational load while ensuring the accuracy of the derivative.

[0144] For example, the value of the obstacle cost term is determined by slack variables, which in turn are determined by the constraint function, which is a function of vehicle speed and acceleration. Therefore, the obstacle cost term has both direct and indirect dependencies on vehicle speed and acceleration. Direct dependencies are manifested in the constraint function where the portion explicitly containing acceleration changes with acceleration, and the constraint function where explicitly containing vehicle speed changes with vehicle speed.

[0145] In the specific implementation, the relationship between the obstacle cost term and vehicle parameters is analytically derived. Taking the obstacle cost term as the object and vehicle speed and acceleration as independent variables, the analytical expressions for its first and second derivatives are obtained through the chain rule and sign differentiation. It should be noted that when identifying dependencies, indirect dependency paths must be fully considered: the wind resistance in the longitudinal drag term is proportional to the square of the vehicle speed, and the coefficient of the cross term in the constraint function is indirectly mapped to the vehicle speed through this wind resistance term. If only direct dependencies are considered and this indirect path is ignored, the gradient calculation will be incomplete.

[0146] Therefore, this step explicitly incorporates the indirectly dependent path during differentiation. The chain rule is used to calculate the first-order partial derivatives of the obstacle cost term with respect to acceleration and vehicle speed, which are then combined to form the gradient vector. Subsequently, the derivatives are further differentiated, and combined with the product rule and the nonlinear structure of the constraint function, the second-order partial derivatives are obtained and combined to form the Hessian matrix. The gradient information indicates the direction of the fastest cost descent, and the Hessian matrix indicates the local curvature of the cost surface. This analytical differentiation process is entirely based on closed-form mathematical expressions and does not rely on numerical differencing. The resulting gradient information and Hessian matrix are output as convergence information in subsequent optimization solutions.

[0147] The first-order partial derivative with respect to acceleration indicates that as acceleration increases, the longitudinal force increases accordingly, the net tire force approaches the adhesion limit, the constraint function increases, the relaxation variable decreases, and the obstacle cost term increases. The sign and value of the first-order partial derivative indicate the rate of this change.

[0148] The first-order partial derivative with respect to vehicle speed indicates that as vehicle speed increases, on the one hand, the fourth-order term of the lateral force increases with the fourth power of the vehicle speed, directly increasing the constraint function; on the other hand, wind resistance increases with the square of the vehicle speed, indirectly changing the constraint function through the cross-term coefficient and boundary terms. The sum of these two parts constitutes the total rate of change in the direction of vehicle speed.

[0149] Each of the aforementioned first-order partial derivatives includes a first-order coefficient, which is determined piecewise based on the relationship between the slack variable and the preset safety threshold. When the slack variable is greater than the safety threshold, the vehicle is in a normal driving range far from the boundary. The first-order coefficient is small, the gradient signal is weak, and the obstacle cost term has limited influence on the optimization direction. The optimizer mainly focuses on speed tracking and ride comfort. When the slack variable is less than or equal to the safety threshold, the vehicle enters a near-boundary danger range. The first-order coefficient switches to an expression related to the safety threshold, its value increases significantly, the gradient signal strengthens, and the optimizer is forced to prioritize adjusting vehicle speed and acceleration to increase the slack variable margin. Through this piecewise mechanism, the same set of gradient calculations can adaptively cover the entire driving condition from safe to dangerous, without needing to switch between different gradient calculation logics between different driving conditions.

[0150] Based on the gradient information, the product rule and chain rule are further used to differentiate the first derivative to obtain the second partial derivative, which forms the Hessian matrix. The Hessian matrix describes the curvature of the cost surface at the current point, that is, the rate of change of the gradient itself with the state variable.

[0151] The Hessian matrix of the obstacle cost term can be formed by the superposition of two types of contributions. The first type of contribution comes from the change of the constraint function gradient with respect to the state variables, which is represented by the outer product of the gradient vectors multiplied by a second-order coefficient. This indicates that when the vehicle approaches the adhesion limit, the gradient of the constraint function itself increases sharply, causing the cost surface to form a steep curve near the boundary. In the dangerous region where the relaxation variables approach zero, this type of contribution dominates, causing the optimizer to abruptly change its search direction and drastically reduce its step size when approaching the slippage limit, thus achieving rapid convergence to the safe region.

[0152] The second type of contribution comes from the nonlinear structure of the constraint function itself, manifested as the Hessian matrix of the constraint function multiplied by first-order coefficients. This indicates that even when the vehicle is far from the boundary, the constraint function still exhibits nonlinear characteristics, and the cost surface shows a gentle curvature even far from the boundary. In the safe interval where the relaxation variables are large, this type of contribution dominates, providing the optimizer with a reasonable curvature reference, enabling it to move with an appropriate step size without being overly conservative or skipping the optimal point with an excessively large step size.

[0153] The second-order coefficients are also determined piecewise based on the relationship between the slack variable and the safety threshold. In the logarithmic barrier function interval, the second-order coefficients are inversely proportional to the square of the slack variable and increase as the slack variable decreases. In the quadratic approximation interval, the second-order coefficients are constants inversely proportional to the square of the safety threshold, ensuring that the second derivative is bounded. Understandably, if the quadratic approximation switch is not introduced in the logarithmic interval, the second-order coefficients will tend to infinity when the slack variable approaches zero, leading to a singular Hessian matrix and optimization failure. By piecewise switching of the safety threshold, the second-order coefficients maintain a reasonable magnitude in both intervals, ensuring that the Hessian matrix is ​​stable and invertible under all operating conditions.

[0154] The purpose of this step is to provide a derivative basis for subsequent iterations, enabling the optimization algorithm to quickly correct the search direction and reduce iterative oscillations based on local changes in the obstacle cost term, thereby improving the solution stability near the constraint boundary.

[0155] S105. Based on the convergence information and the total cost function, construct the optimization objective and solve iteratively to obtain the vehicle speed optimization parameters.

[0156] In practice, convergence information is used as the derivative input in the iterative solution, and the total cost function is used as the optimization objective input. The decision variables are iteratively updated to finally obtain the speed optimization parameters. The speed optimization parameters can correspond to the optimal speed sequence in discrete time, or they can correspond to control increments, acceleration sequences, or braking command parameters related to the speed sequence. The specific form depends on the definition of the upper-level planning and lower-level control interfaces.

[0157] Understandably, the obtained speed optimization parameters can be directly output to the vehicle's longitudinal controller to generate throttle, braking, or torque control commands. They can also be used as speed inputs for subsequent trajectory tracking modules, enabling the vehicle to travel along an executable speed trajectory in autonomous driving mode.

[0158] In one specific implementation, vehicle parameters (vehicle speed v, vehicle mass m, drag coefficient) are obtained. Frontal area A, rolling resistance coefficient ), Road parameters (slope) curvature ) and environmental parameters (road adhesion coefficient) air density ).

[0159] Based on the above parameters, dynamic modeling is performed to determine the tire force circle constraint. First, the longitudinal force is calculated: (where 'a' represents vehicle acceleration, which can be determined in real time based on vehicle speed 'v'), where (g is the acceleration due to gravity); secondly, calculate the lateral force based on the path curvature: .

[0160] Constraints can be established based on longitudinal and lateral forces to ensure that the tire force does not exceed the adhesion limit, that is... Expanding and rearranging the tire force circle constraint, we obtain a quadratic inequality regarding the vehicle's acceleration *a* and velocity *v*: By defining the parameters, we can obtain , , , Furthermore, the inequality can be simplified to .

[0161] Therefore, the slack variables can be determined, i.e. Furthermore, a preset safety threshold is introduced for the slack variables to obtain the obstacle cost term. Specifically, a logarithmic barrier function is used to incorporate constraints into the cost function: and introduce a safety threshold. ,when A quadratic approximation is used to avoid numerical instability: .

[0162] Next, based on the vehicle parameters, the corresponding dynamic constraints, reference speed cost term, and ride comfort cost term are determined. Then, the total cost function is obtained by weighted summation of the obstacle cost term, reference speed cost term, and ride comfort cost term. For example, the dynamic constraints include speed boundary constraints (…). ), acceleration boundary constraints ( ) and jerk boundary constraints ( Using velocity v and acceleration a as state variables and jerk as control variables, the time steps are discretized to construct a total cost function (including tracking reference velocity cost, ride comfort cost, and obstacle cost) and dynamic constraints, forming a nonlinear optimal control problem.

[0163] The first derivative (gradient information) and second derivative (Hessian matrix information) of the cost function (obstacle cost term) with respect to the state variables are derived analytically. The gradient information and Hessian matrix information together constitute the convergence information, which is used to determine the search direction and step size in subsequent optimization solutions.

[0164] Subsequently, using the analytical gradient information mentioned above, gradient-based optimization algorithms (such as sequential quadratic programming and interior point method) are used to iteratively solve the problem and obtain the optimal velocity trajectory and acceleration trajectory.

[0165] Based on the above analysis, this application uses vehicle parameters, road parameters, and environmental parameters together for tire force circle constraint modeling. It transforms hard constraints into optimizable cost forms through relaxation variables, preset safety thresholds, and obstacle cost terms. Then, it constructs a total cost function by combining dynamic constraints, reference speed cost terms, and ride comfort cost terms. Simultaneously, it performs analytical derivation of the obstacle cost term to obtain convergence information, thereby generating speed optimization parameters in the iterative solution. This implementation allows the speed optimization process to adapt to tire force coupling relationships under fluctuating adhesion conditions and forms a consistent optimization framework across constraint expression, numerical stability, and trajectory continuity.

[0166] By inputting vehicle parameters, road parameters, and environmental parameters into the dynamic constraint module, a coupled boundary for tire longitudinal and lateral forces is constructed, and relaxation variables are introduced to quantify the safety margin of this boundary. A preset safety threshold is set for the relaxation variables, and the obstacle cost term is used to transform the physical hard constraints into mathematically relaxable constraints. Then, the obstacle cost term is analytically differentiated to obtain convergence information composed of the gradient and Hessian matrix. Finally, the convergence information is used as a local curvature guide for optimizer iteration, combined with the total cost function for nonlinear solution. This approach changes the traditional modeling method of treating longitudinal and lateral forces independently or using fixed empirical thresholds, allowing the tire force coupling relationship to enter the optimization framework in a continuously differentiable cost form. The application of analytical convergence information effectively avoids the truncation error and computational delay caused by numerical difference, significantly improving the constraint accuracy and iterative solution stability of speed planning near physical limits on low-adhesion surfaces. It should be understood that the above example is for demonstration purposes only and is not a limitation.

[0167] Figure 2 A flowchart illustrating the vehicle speed optimization method provided in this application embodiment. Figure 2 .like Figure 2As shown, in step S102, tire force circle constraints and relaxation variables are determined based on vehicle parameters, road parameters and environmental parameters, and a preset safety threshold is introduced for the relaxation variables to obtain the obstacle cost term.

[0168] Among them, vehicle parameters include at least: vehicle speed, vehicle mass, drag coefficient, frontal area, and rolling resistance coefficient;

[0169] Road parameters should include at least: path curvature and road slope;

[0170] Environmental parameters include at least: road surface adhesion coefficient and air density.

[0171] Understandably, vehicle speed characterizes the vehicle's current operating speed and serves as the fundamental input for solving longitudinal forces, lateral forces, and constraints. Vehicle mass characterizes vehicle inertia and participates in the calculation of rolling resistance, gradient drag, and adhesion limits. The drag coefficient and frontal area together characterize air resistance characteristics, while air density determines the magnitude of wind resistance. The rolling resistance coefficient characterizes the rolling resistance characteristics between the wheels and the road surface, path curvature characterizes the degree of road curvature, road gradient characterizes the uphill and downhill variations of the road, and the road adhesion coefficient characterizes the adhesion between the tires and the road surface.

[0172] In practical implementation, the vehicle controller or domain controller acquires vehicle speed, vehicle mass, drag coefficient, frontal area, rolling resistance coefficient, path curvature, road slope, road adhesion coefficient, and air density. It then combines vehicle speed with drag coefficient, frontal area, and air density to calculate air resistance, and combines vehicle speed with vehicle mass and rolling resistance coefficient to calculate rolling resistance. Simultaneously, it calculates slope resistance based on road slope and vehicle mass. These three factors together constitute the vehicle's longitudinal force. Lateral force is calculated based on path curvature and vehicle speed, typically represented by the force value corresponding to the vehicle's lateral acceleration at the current radius of curvature. Subsequently, the longitudinal and lateral forces are substituted into the tire force circle constraint formula, and the adhesion limit is determined by combining the road adhesion coefficient. Then, the relationship between vehicle speed and acceleration is algebraically rearranged to obtain a quadratic inequality regarding speed and acceleration, allowing this constraint to directly participate in subsequent speed optimization solutions.

[0173] In practical applications, vehicle speed can be output from wheel speed sensors, inertial navigation, or fusion positioning results; vehicle mass can be provided by vehicle calibration parameters or load estimation modules; drag coefficient, frontal area, rolling resistance coefficient, and road gradient can be determined jointly by vehicle static parameters and high-precision maps; path curvature can be obtained from trajectory planning results or map curvature information; road surface adhesion coefficient can be given by road surface perception results, historical estimates, or online identification modules; and air density can be calculated from environmental sensors combined with temperature, air pressure, and altitude information. All of the above parameters are uniformly entered into the constraint calculation module within the controller, forming an analytical constraint expression that can be used for optimization. If a specific onboard processor model is used, it can complete multi-source parameter fusion and quadratic inequality solving in a relatively short period. In practical applications, other models of this component can also be selected, and this application does not limit this selection.

[0174] In this structure, the vehicle's longitudinal force, lateral force, and adhesion limit are uniformly mapped into the same constraint expression. The controller can then output speed optimization results that satisfy the grip boundary, maintaining consistency in constraint calculations on low-adhesion, curved, or gradient-changing road sections. Therefore, the speed optimization process can analytically reflect the tire force coupling relationship, ensuring the output speed trajectory matches the current road environment and vehicle state, thus improving the stability and executability of the optimization results.

[0175] Step S102 specifically includes:

[0176] S201. Determine the longitudinal and lateral forces of the vehicle based on vehicle parameters, road parameters, and environmental parameters.

[0177] S202. Based on longitudinal and lateral forces, determine the tire force circle constraints and relaxation variables.

[0178] Among them, longitudinal force is used to characterize the force state of the vehicle in the direction of travel, and lateral force is used to characterize the lateral force state of the vehicle during turning. Together, they reflect the force coupling relationship of the tire on a low-adhesion road surface. Relaxation variable is used to characterize the margin of tire force circle constraint. Its value corresponds to the resultant force formed by longitudinal force and lateral force. The closer the resultant force is to the adhesion limit, the smaller the relaxation variable is.

[0179] In practical implementation, vehicle parameters include at least vehicle speed, vehicle mass, drag coefficient, frontal area, and rolling resistance coefficient; road parameters include at least path curvature and road slope; and environmental parameters include at least road surface adhesion coefficient and air density. Longitudinal forces can be determined by wind resistance, rolling resistance, and slope resistance. Wind resistance is related to air density, drag coefficient, frontal area, and vehicle speed; rolling resistance is related to vehicle mass and rolling resistance coefficient; and slope resistance is related to vehicle mass, gravitational acceleration, and road slope. Lateral forces can be calculated by path curvature and vehicle speed, corresponding to the centrifugal force of the vehicle in a curve. Based on longitudinal and lateral forces, tire force circle constraints are constructed according to tire adhesion limits. Typically, the sum of the squares of the longitudinal and lateral forces is compared with the limit value corresponding to the road surface adhesion coefficient, and the surplus in this comparison result is defined as a relaxation variable.

[0180] In this implementation, the tire force circle constraint is used to express whether the current force on the vehicle exceeds the road surface adhesion capacity, and the relaxation variable is used to quantify the proximity of the constraint boundary, providing a numerical basis for subsequently incorporating the constraint into the cost function. Since both longitudinal and lateral forces are jointly determined by vehicle, road, and environmental parameters, this constraint can be updated synchronously with changes in road surface adhesion, road curvature, and slope, thus forming a force boundary expression suitable for speed optimization calculations. This approach allows the tire force constraint to participate in optimization modeling with a clear margin, and enables subsequent obstacle cost terms to continuously penalize states approaching the adhesion limit, thereby improving the stability and constraint consistency of speed solutions under low-adhesion road conditions.

[0181] S203. Determine the obstacle factor based on the road surface adhesion coefficient.

[0182] S204. When the slack variable is greater than the preset safety threshold, the obstacle cost term is calculated using the logarithmic obstacle function based on the obstacle factor and the slack variable.

[0183] The road surface adhesion coefficient characterizes the adhesion capability between the tire and the road surface. Its value is estimated by the onboard perception module in combination with wheel speed, longitudinal slip ratio, yaw response characteristics, and road surface attributes from a high-precision map, and is mapped to an obstacle factor. The obstacle factor adjusts the penalty intensity of the logarithmic obstacle function; the lower the road surface adhesion coefficient, the larger the obstacle factor value, thus making the penalty more significant when the slack variable approaches the safety boundary. The preset safety threshold is used to define the activation interval of the obstacle cost term, and its value can be preset according to the vehicle's longitudinal control cycle, speed change amplitude, and constraint convergence margin.

[0184] In its implementation, after calculating the tire force circle constraint and relaxation variables, the system compares the relaxation variables with a preset safety threshold. When the relaxation variable exceeds the threshold, a logarithmic barrier function is used to map the relaxation variable into a continuous penalty, and the barrier factor is introduced as a weighting coefficient into the calculation expression, causing the barrier cost term to increase monotonically with the relaxation variable. This logarithmic barrier function can be written as a logarithmic expression related to the difference in relaxation variables, and its input domain is limited to the feasible interval above the threshold to ensure that the cost term has a large gradient response near the boundary. The obtained barrier cost term is then incorporated into the overall objective function to participate in the velocity optimization solution.

[0185] This implementation maps adhesion capability to a barrier factor under low-adhesion road conditions and controls the effective range of the logarithmic barrier function through a threshold, thus penalizing the slack variables more strongly when they approach the constraint boundary, thereby ensuring that the optimization solution process remains within the adhesion limit. Since the barrier cost term is adaptively adjusted by the road adhesion coefficient, it has a consistent ability to express the constraint convergence characteristics under different adhesion conditions, enabling the speed optimization results to maintain relatively stable feasibility and boundary control capability in complex road conditions.

[0186] In another optional embodiment, when the slack variable is less than or equal to a preset safety threshold, the obstacle cost term is obtained by a quadratic approximation calculation based on the obstacle factor, the preset safety threshold, and the slack variable.

[0187] The slack variable characterizes the inequality margin corresponding to the tire force circle constraint. When this margin enters the near-boundary region below the preset safety threshold, the system no longer directly calls the logarithmic barrier function, but switches to a quadratic approximation. The barrier factor is used to adjust the penalty intensity in the near-boundary region, the preset safety threshold is used to limit the trigger boundary of the quadratic approximation, and the slack variable participates in the calculation as the current constraint margin.

[0188] In practice, after acquiring the current slack variable, the controller compares it with a preset safety threshold. When the slack variable is less than or equal to the threshold, a quadratic function with continuous derivatives is constructed based on the barrier factor, the preset safety threshold, and the slack variable. This quadratic function is then output as the barrier cost term. The coefficients of this quadratic function can be determined by matching the function value at the threshold with the first derivative, ensuring a smooth transition between the barrier cost term and the logarithmic barrier function at the threshold boundary, thereby maintaining numerical stability as the slack variable approaches the boundary.

[0189] In this embodiment, the obstacle factor can be obtained by mapping the road surface adhesion coefficient and pre-stored in the controller through a calibration table or functional relationship. The preset safety threshold can be set as a fixed constant or a piecewise constant based on the vehicle dynamics model, solver accuracy, and adhesion coefficient fluctuation range. The quadratic approximation used is completed by the on-board controller during real-time solving. The controller can be an on-board domain control unit or an independent computing module, whose built-in processor executes the corresponding calculation program and outputs the obstacle cost term. This application does not limit this aspect.

[0190] By using a quadratic approximation to replace the logarithmic obstacle function when the slack variable is less than or equal to a preset safety threshold, the obstacle cost term remains continuous and differentiable near the constraint boundary, and the gradient change during the optimization process is smoother. This allows the speed optimization results to remain stable and convergent in low-adhesion road curves or adhesion fluctuation scenarios, and improves the computability of tire force circle constraints and the consistency of trajectory output.

[0191] The obstacle factor is dynamically calibrated based on the road adhesion coefficient to adjust the penalty intensity of the cost function. When the slack variable is greater than a preset safety threshold, the logarithmic obstacle function is used to calculate the obstacle cost term, achieving a weak penalty when far from the boundary. When the slack variable is less than or equal to the preset safety threshold, the algorithm switches to a quadratic approximation expression based on the obstacle factor, safety threshold, and slack variable to achieve a smooth transition near the boundary. This processing of the logarithmic obstacle function maintains the optimizer's focus on speed tracking and ride comfort within the safe interval, avoiding excessive intervention. In the dangerous interval approaching the adhesion limit, the quadratic approximation mechanism effectively avoids the numerical instability caused by the divergence of the derivative of the logarithmic function when the independent variable approaches zero, ensuring the positive definiteness of the Hessian matrix and the controllability of the optimization step size, enabling the algorithm to maintain stable convergence even under extreme conditions.

[0192] Figure 3 A flowchart illustrating the vehicle speed optimization method provided in this application embodiment. Figure 3 .like Figure 3 As shown, step S201 determines the longitudinal force of the vehicle based on vehicle parameters, road parameters, and environmental parameters, and step S202 determines the tire force circle constraint and relaxation variables based on the longitudinal force and lateral force, including:

[0193] S301. Determine the longitudinal resistance term of the vehicle based on vehicle speed, vehicle mass, drag coefficient, frontal area, rolling resistance coefficient, road slope, and air density.

[0194] S302. Determine the longitudinal force based on the vehicle body mass, vehicle speed, and longitudinal resistance term.

[0195] The longitudinal drag term aggregates various drag sources along the vehicle's longitudinal direction and consists of wind drag, rolling drag, and slope drag. The longitudinal force characterizes the actual force acting on the vehicle in its direction of travel and serves as input in the tire force circle constraint modeling. Air density characterizes the impact of the environment on aerodynamic drag, while vehicle speed, vehicle mass, drag coefficient, frontal area, rolling drag coefficient, and road slope are used to determine the magnitude of each drag component.

[0196] In actual implementation, the controller first obtains the current vehicle speed, vehicle mass, drag coefficient, frontal area, rolling resistance coefficient, road slope, and air density, and converts the vehicle speed into units consistent with the mechanical calculations. Then, it calculates the wind resistance based on the aerodynamic drag expression, the rolling resistance based on the tire-road contact conditions, and the slope resistance based on the slope angle or slope percentage. Finally, it combines all the resistance components into a longitudinal resistance term.

[0197] Next, the controller normalizes or mechanically maps the longitudinal resistance term based on the vehicle's mass and current speed to obtain the vehicle's longitudinal force output at the current moment. This output is used for subsequent speed optimization solutions. If an onboard domain controller is used, the longitudinal resistance term calculation module can be jointly completed by the processor and the program in memory. In practical applications, other models of this component can also be selected, and this application does not limit this.

[0198] This approach integrates wind resistance, rolling resistance, and slope resistance into the longitudinal resistance term, and then determines the longitudinal force accordingly. This allows the longitudinal force to be updated synchronously with changes in road conditions and the environment, and provides a mechanical quantity that can be directly involved in the optimization of the tire force circle constraint. As a result, the speed optimization process has a more consistent response to changes in slope, air density, and resistance under low adhesion conditions, which improves the accuracy of constraint modeling and the stability of optimization results.

[0199] In one possible embodiment, the longitudinal resistance term includes: wind resistance, rolling resistance, and slope resistance;

[0200] Wind resistance is determined based on the drag coefficient, frontal area, air density, and vehicle speed; rolling resistance is determined based on the rolling resistance coefficient and vehicle mass; and gradient resistance is determined based on the road gradient and vehicle mass.

[0201] Among them, wind resistance is used to describe the resistance generated by air acting on the vehicle. In this application, it can be determined by the drag coefficient, frontal area, air density and vehicle speed. It can usually be modeled according to the relationship related to the square of the vehicle speed. Rolling resistance is used to describe the continuous resistance formed when the wheel rolls in contact with the road surface. In this application, it can be determined by the rolling resistance coefficient and the vehicle mass. Slope resistance is used to describe the resistance generated by the gravity component when the vehicle is driving on a slope. In this application, it can be determined by the road slope and the vehicle mass.

[0202] The drag coefficient, rolling resistance coefficient, and road slope can be obtained from vehicle parameters, map parameters, and environmental perception results, respectively. Vehicle speed and vehicle mass can be output in real time by the on-board state estimation module, and air density can be calculated based on the results collected by environmental sensors or a preset environmental model.

[0203] In practical implementation, the longitudinal resistance term serves as the fundamental input for calculating the vehicle's longitudinal force. It is formed by the superposition of wind resistance, rolling resistance, and gradient resistance under the current driving conditions. As vehicle speed increases, the corresponding value of wind resistance increases accordingly; as vehicle mass increases, the corresponding values ​​of rolling resistance and gradient resistance change, thus enabling the longitudinal resistance term to reflect the force differences under different speed ranges, load conditions, and different road slopes. These parameters can be updated within each control cycle and input into the speed optimization model to form longitudinal constraints that match the current road environment.

[0204] By refining the longitudinal resistance term into wind resistance, rolling resistance, and slope resistance, and determining them based on the drag coefficient, frontal area, air density, vehicle speed, rolling resistance coefficient, vehicle mass, and road slope, the vehicle speed optimization process can obtain a longitudinal force expression that more closely resembles actual working conditions. This ensures consistency between subsequent longitudinal force calculations and tire force constraint construction. Consequently, the response accuracy of the speed optimization model on low-adhesion surfaces to changes in road conditions and vehicle state can be improved, making the solution results more consistent with the force boundaries in actual driving.

[0205] S303. Construct a resultant force based on longitudinal and lateral forces, and compare the resultant force with the adhesion limit corresponding to the road adhesion coefficient to determine the tire force circle constraint.

[0206] Among them, longitudinal force is a mechanical quantity used to form a resultant force with lateral force and compare it with the adhesion limit, specifically corresponding to the force component of the tire in the direction of travel; lateral force is a mechanical quantity used to form a resultant force with longitudinal force and compare it with the adhesion limit, specifically corresponding to the lateral force borne by the tire when the vehicle is turning laterally; the resultant force is used to characterize the combined result of longitudinal force and lateral force, and its magnitude reflects the current comprehensive stress state of the tire; the road adhesion coefficient is used to characterize the road grip capability and correspondingly determine the adhesion limit, which represents the maximum adhesion capability that the tire and the road surface can provide.

[0207] In actual implementation, the longitudinal force is first obtained based on the vehicle's current longitudinal driving or braking requirements, and the lateral force is obtained by combining parameters such as path curvature and vehicle speed. The two are then combined to obtain the resultant force, which can be represented by a vector synthesis method as the combined effect of the longitudinal force and the lateral force.

[0208] Subsequently, the adhesion limit under the given road surface conditions is determined based on the road surface adhesion coefficient in the environmental parameters, and the resultant force is compared with the adhesion limit. When the resultant force is less than or equal to the adhesion limit, the tire force circle constraint is deemed satisfied; when the resultant force exceeds the adhesion limit, it indicates that the tire stress has approached or exceeded the available adhesion capacity. This comparison allows the longitudinal and lateral coupled forces on the tire to be directly mapped to the constraint boundary in speed optimization and serve as the constraint input for subsequent cost optimization.

[0209] This scheme combines longitudinal and lateral forces into a unified resultant force and uses the adhesion limit corresponding to the road adhesion coefficient as the criterion. This clearly characterizes the force boundary of the tire on low-adhesion roads, allowing the speed optimization process to be constrained around the true grip limit and reducing constraint deviations caused by separate modeling of longitudinal and lateral forces. Since the resultant force comparison result directly reflects whether the tire force circle boundary has been broken, it improves the consistency of constraint expression and enhances the executability of the trajectory under conditions of curves, gradient changes, and adhesion fluctuations.

[0210] S304. Transform the tire force circle constraint into an inequality relationship between vehicle speed and the corresponding acceleration, and determine the margin parameter of the inequality relationship.

[0211] S305. Determine the margin parameter as a slack variable.

[0212] The tire force circle constraint characterizes the upper limit of the coupling between longitudinal and lateral forces of the vehicle under the current road surface adhesion conditions. In this scheme, this constraint is treated as a quadratic inequality relationship between vehicle speed and the corresponding acceleration. Vehicle speed characterizes the current motion state of the vehicle, and acceleration characterizes the rate of change of vehicle speed. Both participate in the inequality construction, mapping the tire adhesion boundary into a mathematical expression that can be optimized. The margin parameter characterizes the remaining space between the inequality relationship and the boundary conditions. Its value is determined by the difference between the expression on the left side of the inequality and the boundary terms. The closer the vehicle's operating state is to the adhesion limit, the smaller this margin parameter becomes.

[0213] In practical implementation, based on the vehicle's current speed, road curvature, road slope, and road surface adhesion coefficient, the lateral acceleration required at the vehicle speed is first calculated, and then combined with the longitudinal acceleration required to form a resultant force expression. This resultant force is then converted into a constraint expression regarding vehicle speed and acceleration based on the tire force circle boundary. Subsequently, this constraint expression is rearranged to obtain the margin metric that satisfies the constraints; this margin metric is the residual parameter. After determining the residual parameter as a relaxation variable, this relaxation variable serves as the direct input to the subsequent obstacle cost term, participating in the speed optimization solution process.

[0214] By explicitly transforming the tire force circle constraint into an inequality relationship between vehicle speed and acceleration, and using a margin parameter to accommodate the constraint margin, the adhesion boundary, which was originally difficult to directly participate in optimization, can be mapped into a calculable and penalized relaxation quantity. This allows the tire constraint to maintain a continuous expression in speed optimization and work synergistically with the cost function. The resulting relaxation variable can directly reflect the degree of proximity between the vehicle and the adhesion limit, thus providing a stable constraint expression and consistent convergence input for subsequent solutions.

[0215] Based on vehicle speed, vehicle mass, drag coefficient, frontal area, rolling resistance coefficient, path curvature, road slope, road surface adhesion coefficient, and air density, longitudinal drag models and lateral mechanical models are established respectively to calculate longitudinal resultant force and lateral centrifugal force. These two models are synthesized into a tire force vector and compared with the adhesion limit to establish a tire force circle constraint. This nonlinear constraint is then algebraically expanded and rearranged into a quadratic inequality concerning vehicle speed and acceleration. The residual parameters on the right-hand side of the inequality are extracted as relaxation variables. This processing step unifies the complex multi-source heterogeneous parameters into a standard quadratic inequality mathematical form, transforming the originally non-convex friction circle physical boundary into a convex optimization framework-friendly algebraic expression. The extraction of residual parameters (relaxation variables) provides direct numerical input for the subsequent construction of the obstacle cost function, ensuring a rigorous connection between constraint modeling and optimization solution in mathematical structure.

[0216] In one specific embodiment, the vehicle acquires the following parameters in real time via onboard sensors, high-precision maps, or V2X communication:

[0217] Vehicle specifications: weight gravitational acceleration drag coefficient windward area Rolling resistance coefficient ;

[0218] Road and environmental parameters: Based on high-precision maps or sensing results, obtain each discrete time step within the planning time domain. Corresponding path curvature Road slope and road surface adhesion coefficient For example, a 200m long road might include:

[0219] 0~50m: Straight track, Ice and snow;

[0220] 50~120m: Curves, curvature increases linearly from 0 to Reduce it to 0 again. Slippery;

[0221] 120~200m: Straight track , downhill, dry.

[0222] Planning time domain Discrete time step Total steps Based on the vehicle's current mileage And predict speed, mapping road parameters to each time step.

[0223] Furthermore, at each discrete time step k, based on the current vehicle speed... and the corresponding road slope Calculate the longitudinal drag term: ; air density Standard atmospheric pressure.

[0224] Define time-varying parameters: , , , The tire force circle constraint is transformed into a constraint on acceleration. and speed The quadratic inequality: This constraint ensures that the resultant force of the longitudinal force and the lateral force does not exceed the adhesion limit at any given time.

[0225] Then, determine the slack variables. The logarithmic barrier function is used to handle inequality constraints, and a safety threshold is introduced. To avoid numerical instability: when hour, ;when When using a quadratic approximation Among them, barrier factors The value can be adjusted according to the road surface adhesion: a smaller value (e.g., 0.005) is used for dry roads to balance efficiency, while a larger value (e.g., 0.02) is used for icy and snowy roads to strengthen the constraint.

[0226] Furthermore, Figure 4 A flowchart illustrating the vehicle speed optimization method provided in this application embodiment. Figure 4 .like Figure 4 As shown, step S104 involves analytically deriving the obstacle cost term based on vehicle parameters to obtain convergence information for the obstacle cost term, and step S105 involves constructing an optimization objective and iteratively solving it based on the convergence information and the total cost function to obtain the vehicle's speed optimization parameters, including:

[0227] S401. Based on the vehicle speed and the corresponding acceleration, calculate the first derivative of the obstacle cost term to obtain the gradient information, and calculate the second derivative of the first derivative to obtain the Hessian matrix information.

[0228] S402. Use gradient information and Hessian matrix information as convergence information.

[0229] In this scheme, vehicle speed is used to characterize the current longitudinal motion state of the vehicle, and acceleration is used to characterize the trend of vehicle speed change. Both serve as the derivative of the obstacle cost term to extract the local variation features required for optimization. The obstacle cost term is a cost expression constructed from tire force circle constraints through relaxation variables and a safety threshold. Its value exhibits a nonlinear change with vehicle speed and acceleration. Gradient information is used to describe the descent direction of the obstacle cost term at the current point, and Hessian matrix information is used to describe its local curvature characteristics. Together, they constitute a representation of the convergence of the cost function.

[0230] In its implementation, the processing module receives the current vehicle speed, corresponding acceleration, and the obstacle cost term expression generated by the obstacle factor. It then performs analytical differentiation on the vehicle speed and acceleration as independent variables. Taking the partial derivative of the obstacle cost term with respect to vehicle speed yields the rate of change in the vehicle speed direction; similarly, taking the partial derivative with respect to acceleration yields the rate of change in the acceleration direction. These partial derivatives are combined to form gradient information, reflecting the sensitivity of the obstacle cost term to vehicle speed and acceleration at the current iteration point. Subsequently, the processing module further differentiates the first derivative to obtain second-order partial derivatives with respect to vehicle speed and acceleration. These second-order partial derivatives are then combined to form the Hessian matrix information, characterizing the local curvature and coupling relationship of the obstacle cost term near that point.

[0231] In practical applications, analytical derivation can be performed using symbolic differentiation, or, when the obstacle cost term expression is complex, a combined analytical and numerical approach can be used to ensure that the gradient information and Hessian matrix information are consistent with the obstacle cost term. The Hessian matrix information is typically output as a two-dimensional matrix, where the diagonal terms correspond to the second-order changes of the single variable vehicle speed or acceleration, and the off-diagonal terms correspond to the cross-coupling terms between vehicle speed and acceleration. This convergence information is then input into the velocity optimization solver to determine whether the current iteration direction and step size satisfy the convergence condition.

[0232] By using gradient and Hessian matrix information as convergence information, the optimization process can simultaneously obtain directional and curvature information. This makes the solution of the obstacle cost term under low adhesion conditions more consistent with local nonlinear characteristics and makes the iterative update of the velocity optimization parameters more stable. Since the convergence information is directly derived from the analytical derivation of vehicle speed and acceleration from the obstacle cost term, it can provide an optimization metric consistent with the total cost function and provide an accurate convergence criterion for subsequent velocity trajectory solving.

[0233] Using vehicle speed and corresponding acceleration as independent variables, a rigorous sign-level chain rule is performed on the obstacle cost term. During the differentiation process, the indirect dependency path of the longitudinal resistance term propagating to the constraint boundary is fully identified and accounted for. First-order partial derivatives are calculated to construct the gradient vector, and second-order partial derivatives are calculated to synthesize the Hessian matrix. Both are defined as convergence information. This step, through analytical derivation, eliminates the approximation error of numerical differencing. The gradient information accurately indicates the fastest search direction for obstacle cost descent, and the Hessian matrix precisely characterizes the local curvature features of the cost surface. The combination of these two features enables the optimization algorithm to adaptively adjust the search direction and update step size, significantly reducing iterative oscillations near the constraint boundary and improving the overall convergence efficiency and trajectory smoothness of the optimization process.

[0234] S403. Based on vehicle speed, acceleration, and vehicle jerk, a decision vector is constructed by combining these factors.

[0235] S404. Based on the convergence information and the total cost function, construct the optimization objective and use the optimization objective to iteratively solve the decision vector to obtain the speed optimization parameters.

[0236] In this system, vehicle speed characterizes the vehicle's longitudinal motion at the current moment, and acceleration characterizes the trend of speed change; together, they constitute the state variables. Vehicle jerk characterizes the rate of change of acceleration and serves as a control variable in the optimization process. The decision vector is formed by concatenating the state variables and control variables, and internally contains the discrete-time sequences of vehicle speed, acceleration, and jerk, facilitating constraint expression and target search within a unified mathematical model. Convergence information consists of the gradient information of the obstacle cost term and the Hessian matrix information. The total cost function summarizes the obstacle cost corresponding to the tire force constraint, the reference speed cost, the dynamic constraint cost, and the ride comfort cost to form an iteratively solvable target model.

[0237] In practical implementation, the vehicle's current speed, acceleration, and jerk set by the controller can be initialized as the initial values ​​of the decision vector. Convergence information is then mapped to the local curvature and descent direction information in the optimization objective. The optimization objective can be established using discrete-time optimal control. The state update equation, control constraints, and total cost function are uniformly written into the objective function and constraint set. The decision vector is then iteratively updated to reduce the total cost function successively and satisfy the convergence criterion, ultimately outputting the speed optimization parameters. These speed optimization parameters correspond to the target vehicle speed, target acceleration, and related control quantities for the next control cycle and are sent to the underlying longitudinal control unit for tracking.

[0238] Since the convergence information reflects the changing trend of the obstacle cost term near the current state, the decision vector can be adjusted along the descent direction within the feasible region during the iteration process, thus ensuring that the solution simultaneously satisfies tire force constraints and vehicle dynamics constraints. The resulting speed optimization parameters can maintain continuous speed changes under low-adhesion road surfaces and match the vehicle's actual available gripping force, giving the output trajectory good executability and control stability.

[0239] Vehicle speed and acceleration within discrete time steps are defined as state variables, and vehicle jerk is defined as a control variable directly adjusted by the optimizer. The variables from each time step are sequentially concatenated to construct a high-dimensional decision vector. A nonlinear optimization problem is constructed based on convergence information (gradient and Hessian matrix) and the total cost function. Sequential quadratic programming or interior-point algorithms are used to iteratively update the decision vector. In each iteration, gradient information is used to determine the descent direction, and the Hessian matrix information is used to determine the step size, until the termination condition is met. This step, based on the reasonable partitioning of state and control variables, transforms continuous-time trajectory optimization into a finite-dimensional vector optimization problem, significantly reducing the solution dimensionality. The convergence-driven iterative mechanism allows the decision vector to quickly approach the optimal solution along the cost descent path within the feasible region, effectively balancing safety boundary constraints and driving efficiency objectives under low-adhesion road conditions. The output results can be directly used for command generation in the underlying controller.

[0240] Optionally, vehicle speed and acceleration can be used as state variables, and vehicle jerk can be used as control variables. The state variables and control variables can be combined into a decision vector.

[0241] In discrete-time optimal control problems, state variables describe the state of the system at each time step. The values ​​of state variables are determined by the state and control variables of the previous time step, following state transition relationships. In this application, the state variables are vehicle speed and acceleration, representing the vehicle's speed and rate of change of speed at a given time, respectively. Vehicle speed directly reflects the vehicle's speed, while acceleration directly reflects whether the vehicle is accelerating or decelerating and the degree of acceleration.

[0242] In optimal control problems, the control variable refers to the input quantity that the optimizer can directly adjust. The value of the control variable is determined by the optimizer in each iteration, and it drives the state variables to evolve gradually over time through state transition relationships. In this application, the control variable is jerk, which is the rate of change of acceleration, characterizing how quickly acceleration increases or decreases. A larger jerk means that the acceleration itself changes rapidly, and passengers will experience a noticeable jolt or pitching motion; a smaller jerk means that the acceleration changes more smoothly, resulting in a more comfortable ride.

[0243] A decision vector is a long vector formed by arranging the state and control variables of all time steps in the planning time domain in chronological order. The decision vector is the sole object of the optimizer's operation. By adjusting the values ​​of each component in the decision vector, the optimizer searches for the optimal combination that minimizes the total cost function within the constrained feasible region. The dimension of the decision vector is equal to the number of time steps multiplied by the number of variables at each time step.

[0244] By selecting jerk as the control variable, the planned output velocity trajectory naturally possesses third-order continuity, eliminating the need for additional smoothing post-processing steps and directly meeting ride comfort requirements. By combining state and control variables into a decision vector, the continuous-time trajectory optimization objective is transformed into a finite-dimensional vector optimization objective, enabling mature numerical optimization algorithms to solve it directly. Furthermore, the dimension of the decision vector is linearly related to the number of time steps, allowing for flexible adjustment based on the planning time domain length, balancing planning accuracy and computational efficiency.

[0245] Figure 5 A flowchart illustrating the vehicle speed optimization method provided in this application embodiment. Figure 5 .like Figure 5 As shown, step S404, iteratively solving the decision vector using the optimization objective, includes:

[0246] S501. In each iteration, the convergence direction and step size are determined based on gradient information and Hessian matrix information.

[0247] S502. If the change in the total cost function is less than the convergence tolerance, and / or the number of iterations reaches the preset upper limit, terminate the iteration and output the speed optimization parameters.

[0248] The decision vector represents the variable to be solved in the vehicle speed optimization process. It can be composed of a combination of vehicle speed, acceleration, and jerk, and is updated in each iteration based on the convergence direction and step size. Gradient information represents the first-order trend of the total cost function at the current decision vector, while Hessian matrix information represents the second-order curvature of the total cost function. Together, they determine the descent direction and update magnitude of the iterative search. Convergence tolerance limits the permissible deviation between two adjacent iterations of the total cost function, and a preset upper limit limits the maximum number of iterations to avoid continuous divergence in the solution process or excessive computation time.

[0249] In its implementation, the system receives a total cost function constructed based on tire force circle constraints, obstacle cost terms, reference speed cost terms, and ride comfort cost terms. The current decision vector is then substituted into this function to calculate the corresponding target value. Subsequently, the first derivative of the decision vector with respect to the target value is calculated to obtain gradient information, and the second derivative is calculated to obtain Hessian matrix information. A Newton-type update variable is constructed based on the gradient and Hessian matrix information to determine the convergence direction and step size. The step size can be limited to a preset range by a line search mechanism to ensure that the updated decision vector satisfies the vehicle's longitudinal motion constraints. After each update, the system recalculates the total cost function, compares the changes between two adjacent iterations, and determines that the optimization result meets the accuracy requirements when the change is less than the convergence tolerance; or, when the number of iterations reaches a preset upper limit, it determines that the solution boundary has been reached and stops updating, finally outputting the corresponding speed optimization parameters. If a specific model of numerical solution module is used, it has high matrix operation efficiency, which can shorten the real-time solution time. In practical applications, other models of this component can also be selected, and this application does not limit this selection.

[0250] This solution method jointly determines the update direction using gradient and Hessian matrix information, enabling the decision vector to converge stably along the descent path of the total cost function. The solution process is controlled by dual termination conditions: the change in magnitude and the upper limit of iteration. Consequently, the output speed optimization parameters are consistent with the constraints of low-adhesion road surfaces, allowing the vehicle to achieve executable speed control results while meeting safety boundaries.

[0251] In one specific embodiment, with speed and acceleration As a state variable, with accelerometer Assuming the control variables are used, a discrete-time optimal control problem is constructed. The state transition equation is as follows: , .

[0252] The overall cost function consists of three parts:

[0253] Reference speed cost item: The reference speed The weighting is determined based on a comprehensive consideration of road speed limits, curvature, and coefficient of friction. ;

[0254] Smoothness cost: ;

[0255] Obstacle cost item: .

[0256] The total cost function is Simultaneously satisfying state and control boundary constraints: , , Initial state , Given by the vehicle's current state.

[0257] To accelerate optimization convergence, the first and second derivatives of the barrier cost with respect to the state variables are analytically derived. Because and All depend on (pass These indirect terms need to be included when differentiating.

[0258] First, calculate the auxiliary factors:

[0259] ;

[0260] .

[0261] Secondly, calculation Partial derivative with respect to v_k: ;

[0262] Therefore, we get: , To obtain the first derivative as , .

[0263] The derivation of the second derivative (elements of the Hessian matrix) is as follows:

[0264] make ,but , , .

[0265] in, , .

[0266] It is important to note that in the calculation of the second derivative, the cross term... because right The partial derivatives only come from Therefore, the cross term in the above formula is... Part of .

[0267] Next, the Sequential Quadratic Programming (SQP) algorithm is used to solve the above nonlinear optimization objective. The state and control variables are combined into a decision vector. We construct the Lagrangian function and iteratively solve the quadratic programming subproblem. Utilizing the analytical gradient and Hessian matrix information described above can significantly improve the convergence speed. We then set a convergence tolerance. The maximum number of iterations is 100.

[0268] Optimization yields the optimal velocity sequence and acceleration sequence It can be sent to the underlying controller (such as a model predictive controller or a PID controller) for tracking control, so as to enable the vehicle to pass safely and stably on complex low-adhesion roads.

[0269] Optionally, the barrier factor in this embodiment and safety threshold It can be flexibly adjusted according to road conditions and computing resources: on dry, high-adhesion road surfaces Up, can reduce Up to 0.005 and increase Reduce the constraint weight to 0.01 to increase the solution speed; suitable for ice, snow, and low-adhesion road surfaces. Up, can increase Reduce to 0.02 and decrease The value is set to 0.0005 to strictly ensure that the constraint is met. By adjusting the above parameters, this method can adapt to the speed planning requirements of different vehicle models and different scenarios.

[0270] Figure 6 A flowchart illustrating the vehicle speed optimization method provided in this application embodiment. Figure 6 .like Figure 6 As shown, the vehicle speed optimization method provided in this application embodiment further includes:

[0271] S601. Update the vehicle's road parameters and environmental parameters at each discrete time step within the preset planning time domain.

[0272] S602. The updated road parameters and environmental parameters are used to update the time-varying parameters in the tire force circle constraint, the obstacle factor in the obstacle cost term, and the preset safety threshold.

[0273] The preset planning time domain is used to limit the future calculation range of the speed optimization model. The discrete time step is used to divide this time domain into multiple solution nodes so that road and environmental parameters can be reread or interpolated at each node. The vehicle's road parameters include information such as path curvature and road slope that change with location, while the environmental parameters include information such as road adhesion coefficient and air density that change with the scene. The time-varying parameters in the tire force circle constraint are used to characterize the constraint quantities that change with road and environment, such as adhesion limit, lateral force margin, or resultant force boundary. The obstacle factor is used to adjust the penalty intensity of the logarithmic obstacle function or its approximate form, and the preset safety threshold is used to limit the decision boundary for relaxation variables to enter the obstacle cost term.

[0274] In practical implementation, the controller can obtain the road curvature, slope, and road adhesion coefficient corresponding to the current predicted location at each discrete time step based on high-precision maps, inertial navigation positioning results, and environmental perception results. It also updates the air density by combining meteorological estimation results. These data are then mapped to time-varying parameters in the tire force circle constraint, ensuring that the constraint boundary remains consistent with the current adhesion conditions. Simultaneously, the obstacle factor can be recalibrated based on the updated adhesion coefficient, and the safety threshold can be reset based on the road surface slippage, slope variation, and vehicle speed, ensuring that the relaxation variables correspond to appropriate obstacle penalty intervals in different scenarios. This update process is typically executed periodically by the onboard processor. The updated parameters are directly written into the constraint matrix and cost term expression of the current optimization objective. In practical applications, other models of this processing unit can also be selected; this application does not limit this selection.

[0275] By continuously refreshing road and environmental parameters within the preset planning time domain, tire force circle constraints, obstacle cost terms, and safety thresholds can be synchronously adapted to changes in road adhesion and geometric conditions. This ensures that the speed optimization results maintain a consistent constraint expression with the current scenario and improves the stability and trajectory executability of the optimization process on low-adhesion surfaces.

[0276] S603. Based on the updated time-varying parameters, obstacle factors, and preset safety thresholds, redetermine the convergence information and total cost function.

[0277] Among them, the time-varying parameters are used to characterize the latest changes in road curvature, road slope, and pavement adhesion coefficient within the planning time domain, and are updated synchronously with the environmental perception results at each discrete time step; the obstacle factor is used to characterize the penalty strength of the logarithmic obstacle function, and its value is related to the pavement adhesion coefficient; the preset safety threshold is used to limit the boundary of the relaxation variable entering the quadratic approximation interval. The convergence information corresponds to the gradient information and Hessian matrix information obtained after analytical derivation of the obstacle cost term, and the total cost function is composed of the obstacle cost term, the reference speed cost term, and the ride comfort cost term weighted together.

[0278] In practical implementation, when the vehicle enters a new discrete time step, the controller first recalculates the time-varying parameters in the tire force circle constraint based on the updated road and environmental parameters, reconstructs the obstacle factor based on the new road adhesion coefficient, and updates the preset safety threshold according to the relationship between relaxation variables and boundaries. Then, the updated results are substituted back into the analytical expression of the obstacle cost term, and the cost form in the logarithmic obstacle interval or the quadratic approximation interval is switched synchronously. The obstacle cost term is then redifferentiated with respect to vehicle speed and corresponding acceleration to obtain new gradient information and Hessian matrix information. The updated convergence information and the current total cost function are fed into the optimizer. Based on this, the optimizer reconstructs the search direction of the decision vector and the expression of the objective function, and continues to iteratively solve for the speed optimization parameters.

[0279] Since the time-varying parameters, obstacle factors, and preset safety thresholds are all matched with the latest road and environmental conditions, the redefined convergence information can reflect the local changes in the current cost surface, and the total cost function can also maintain consistency with the tire force circle constraint. With this approach, the optimization process can continuously update the constraint expression under conditions of adhesion coefficient fluctuations, curve changes, and slope changes, thus keeping the solution results synchronized with the actual gripping limit.

[0280] During the pre-planned time-domain progression, the road geometry parameters and environmental attachment parameters in front of the vehicle are re-acquired or interpolated and updated at each discrete time step. The latest environmental mapping is updated to the time-varying coefficients of the tire force circle constraint, the penalty factor of the obstacle cost term, and the safety threshold boundary. Based on the updated parameters, the analytical differentiation of the obstacle cost term is re-executed to update the convergence information, and the total cost function is reconstructed synchronously. This step overcomes the environmental adaptability lag caused by the fixed parameters used in traditional speed planning, enabling the constraint boundary and cost penalty intensity to adapt to changes in road curvature, slope undulation, and road surface slippage in real time. Through dynamic parameter updates and synchronous iteration of convergence information in the time domain, the planned trajectory can respond to upcoming complex road conditions in a feedforward manner, maximizing traffic efficiency and driving smoothness without exceeding the tire grip limit.

[0281] This application provides a vehicle speed optimization method applicable to vehicles in autonomous driving mode. It addresses the core technical challenges of accurately modeling the longitudinal and lateral force coupling constraints of tires on roads with low adhesion coefficients, the instability of optimization solutions caused by direct hard constraints, and the ease with which planning results exceed limits when road parameters change dynamically. The application constructs a complete technical link from parameter acquisition to optimal speed output.

[0282] This method first obtains the vehicle's own parameters (including vehicle speed, body mass, drag coefficient, frontal area, and rolling resistance coefficient), road geometric parameters (including path curvature and road slope), and environmental parameters (including road surface adhesion coefficient and air density). These three types of parameters together form the input basis for subsequent constraint modeling and cost calculation.

[0283] Secondly, based on the above parameters, the longitudinal force and lateral force are determined respectively. The longitudinal force is determined by the vehicle mass, vehicle speed and longitudinal resistance term. The longitudinal resistance term is further refined into wind resistance determined by the drag coefficient, frontal area, air density and vehicle speed, rolling resistance determined by the rolling resistance coefficient and vehicle mass, and slope resistance determined by the road slope and vehicle mass. The three types of resistance cover all the main sources of force on the vehicle in the longitudinal direction. The lateral force is determined by the vehicle mass, vehicle speed and path curvature.

[0284] Based on this, the resultant force of longitudinal and lateral forces is constructed and compared with the adhesion limit corresponding to the road surface adhesion coefficient. Tire force circle constraint is established to accurately reflect the coupling relationship between longitudinal and lateral forces. The more intense the acceleration, the less grip force is available for turning, and vice versa. This corrects the deviation of existing technologies that treat longitudinal and lateral acceleration independently or simply superimpose them linearly.

[0285] Subsequently, the tire force circle constraint is expanded and rearranged into a quadratic inequality concerning vehicle speed and acceleration, and the residual parameter of the inequality is defined as a slack variable, realizing the transformation from physical constraint to mathematical variable. A preset safety threshold is introduced for the slack variable, and a piecewise obstacle function is used to calculate the obstacle cost term: when the slack variable is greater than the safety threshold, a logarithmic obstacle function is used, making the penalty weak when the vehicle is far from the boundary and sharply increasing the penalty when it approaches the boundary, achieving a smooth soft constraint effect; when the slack variable is less than or equal to the safety threshold, a quadratic approximation is switched to avoid gradient explosion caused by the derivative of the logarithmic function approaching infinity, ensuring numerical stability under near-boundary conditions. The obstacle factor is adaptively adjusted according to the road adhesion coefficient; for example, a smaller value is used on dry roads to balance traffic efficiency, and a larger value is used on icy and snowy roads to strengthen safety constraints. Based on this, dynamic constraints (including boundary constraints of vehicle speed, acceleration, and jerk) are determined according to vehicle parameters, a reference speed cost term (the reference speed is set comprehensively based on road speed limit, path curvature, and road surface adhesion coefficient) and a ride comfort cost term (the smoothness of speed change is measured by the square of jerk). The three types of costs are weighted and summed to form a total cost function, which unifies and balances the optimization of driving objectives.

[0286] Furthermore, the obstacle cost term is analytically derived with respect to vehicle speed and acceleration, fully taking into account the indirect dependence of wind resistance transmitted through the longitudinal resistance term, to obtain the first derivative, i.e. gradient information, and the second derivative, i.e. Hessian matrix information, which are collectively referred to as convergence information. The first and second coefficients are taken piecewise according to the relationship between the relaxation variables and the safety threshold to ensure the accuracy and boundedness of the derivative information under all operating conditions.

[0287] Finally, the vehicle speed and acceleration are combined as state variables and the jerk as control variables to form a decision vector. Based on the convergence information and the total cost function, the optimization objective is constructed and solved iteratively. In each iteration, the gradient information and Hessian matrix information are used to determine the search direction and step size. The iteration is terminated when the change in the total cost function is less than the convergence tolerance or the number of iterations reaches the preset upper limit. The optimal speed sequence and acceleration sequence are output as speed optimization parameters and sent to the underlying controller to perform tracking control.

[0288] In addition, the method also supports dynamic updating of road parameters and environmental parameters at each discrete time step within the preset planning time domain, and updates the time-varying parameters of constraints, obstacle factors and safety thresholds accordingly, and refreshes convergence information and total cost function simultaneously, so that speed planning can respond in real time to changes in road slope, curvature and road surface adhesion coefficient, and maximize the use of tire grip while ensuring safety, taking into account traffic efficiency and driving smoothness.

[0289] Figure 7 This is a schematic diagram of the vehicle speed optimization device provided in an embodiment of this application. Figure 7 As shown, the vehicle speed optimization device 700 is applied to a vehicle in an autonomous driving state. The device includes:

[0290] The acquisition module 701 is used to acquire vehicle parameters, road parameters, and environmental parameters.

[0291] The determination module 702 is used to determine the tire force circle constraint and relaxation variables based on vehicle parameters, road parameters and environmental parameters, and to introduce a preset safety threshold for the relaxation variables to obtain the obstacle cost term;

[0292] The determination module 702 is also used to determine the corresponding dynamic constraints, reference speed cost terms and ride comfort cost terms of the vehicle based on the vehicle parameters, and to obtain the total cost function based on the obstacle cost terms, reference speed cost terms and ride comfort cost terms.

[0293] The parsing module 703 is used to perform analytical derivation of the obstacle cost term based on vehicle parameters to obtain the convergence information of the obstacle cost term;

[0294] The determination module 702 is also used to construct an optimization objective and iteratively solve it based on convergence information and the total cost function to obtain the vehicle speed optimization parameters.

[0295] In one possible embodiment, the vehicle parameters include at least: vehicle speed, vehicle mass, drag coefficient, frontal area, and rolling resistance coefficient;

[0296] Road parameters should include at least: path curvature and road slope;

[0297] Environmental parameters include at least: road surface adhesion coefficient and air density.

[0298] In one possible embodiment, the determining module 702 is further configured to:

[0299] Based on vehicle parameters, road parameters, and environmental parameters, determine the longitudinal and lateral forces of the vehicle.

[0300] Based on longitudinal and lateral forces, tire force circle constraints and relaxation variables are determined.

[0301] In one possible embodiment, the determining module 702 is further configured to:

[0302] The longitudinal resistance term of the vehicle is determined based on vehicle speed, vehicle mass, drag coefficient, frontal area, rolling resistance coefficient, road gradient, and air density.

[0303] The longitudinal force is determined based on the vehicle body mass, vehicle speed, and longitudinal resistance term.

[0304] In one possible embodiment, the longitudinal resistance term includes: wind resistance, rolling resistance, and slope resistance;

[0305] Wind resistance is determined based on the drag coefficient, frontal area, air density, and vehicle speed; rolling resistance is determined based on the rolling resistance coefficient and vehicle mass; and gradient resistance is determined based on the road gradient and vehicle mass.

[0306] In one possible embodiment, the determining module 702 is further configured to:

[0307] The resultant force is constructed based on longitudinal and lateral forces, and the resultant force is compared with the adhesion limit corresponding to the road adhesion coefficient to determine the tire force circle constraint.

[0308] In one possible embodiment, the determining module 702 is further configured to:

[0309] The tire force circle constraint is transformed into an inequality relationship between vehicle speed and the corresponding acceleration, and the margin parameter of the inequality relationship is determined.

[0310] The margin parameter is defined as a slack variable.

[0311] In one possible embodiment, the determining module 702 is further configured to:

[0312] Determine the obstacle factor based on the road surface adhesion coefficient;

[0313] When the slack variable is greater than the preset safety threshold, the barrier cost term is calculated using the logarithmic barrier function based on the barrier factor and the slack variable.

[0314] In one possible embodiment, the determining module 702 is further configured to:

[0315] When the slack variable is less than or equal to the preset safety threshold, the obstacle cost term is obtained by a quadratic approximation based on the obstacle factor, the preset safety threshold, and the slack variable.

[0316] In one possible embodiment, the parsing module 703 is further configured to:

[0317] Based on the vehicle speed and the corresponding acceleration, the first derivative of the obstacle cost term is calculated to obtain the gradient information, and the second derivative is calculated based on the first derivative to obtain the Hessian matrix information;

[0318] Gradient information and Hessian matrix information are used as convergence information.

[0319] In one possible embodiment, the determining module 702 is further configured to:

[0320] A decision vector is constructed by combining vehicle speed, acceleration, and vehicle jerk.

[0321] Based on convergence information and the total cost function, an optimization objective is constructed, and the decision vector is iteratively solved using the optimization objective to obtain the speed optimization parameters.

[0322] In one possible embodiment, the determining module 702 is further configured to:

[0323] Vehicle speed and acceleration are used as state variables, and vehicle jerk is used as a control variable. The state variables and control variables are combined into a decision vector.

[0324] In one possible embodiment, the determining module 702 is further configured to:

[0325] In each iteration, the convergence direction and step size are determined based on gradient information and Hessian matrix information;

[0326] If the change in the total cost function is less than the convergence tolerance, and / or the number of iterations reaches the preset upper limit, the iteration is terminated and the speed optimization parameters are output.

[0327] In one possible embodiment, the vehicle speed optimization device 700 is further configured to:

[0328] Update the vehicle's road and environmental parameters at each discrete time step within the preset planning time domain;

[0329] The updated road and environmental parameters are used to update the time-varying parameters in the tire force circle constraint, the obstacle factor in the obstacle cost term, and the preset safety threshold.

[0330] In one possible embodiment, the vehicle speed optimization device 700 is further configured to:

[0331] Based on the updated time-varying parameters, barrier factors, and preset safety thresholds, the convergence information and total cost function are redefined.

[0332] The vehicle speed optimization device provided in this embodiment can execute the vehicle speed optimization method of the above embodiment. Its implementation principle and technical effect are similar, and will not be described again here.

[0333] In the specific implementation of the aforementioned vehicle speed optimization device, each module can be implemented as a processor. The processor can execute computer execution instructions stored in the memory, so that the processor executes the aforementioned vehicle speed optimization method.

[0334] Figure 8 This is a schematic diagram of the control unit provided in this application. Figure 8 As shown in the figure, this application embodiment provides a vehicle, which is equipped with a control unit. The control unit is used to optimize the vehicle speed using the method provided above.

[0335] The control unit 800 includes at least one processor 801 and a memory 802.

[0336] Optionally, the device 800 also includes a communication component 803. The processor 801, memory 802, and communication component 803 are connected via a bus 804.

[0337] In a specific implementation, at least one processor 801 executes computer execution instructions stored in memory 802, causing at least one processor 801 to perform the above-described method.

[0338] The specific implementation process of processor 801 can be found in the above method embodiments, and its implementation principle and technical effect are similar. It will not be repeated here.

[0339] In the above embodiments, it should be understood that the processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), etc. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the method disclosed in this invention can be directly implemented by a hardware processor, or implemented by a combination of hardware and software modules within the processor.

[0340] The memory may include random access memory (RAM) and may also include non-volatile memory (NVM), such as at least one disk storage device.

[0341] The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. Buses can be categorized as address buses, data buses, control buses, etc. For ease of illustration, the buses shown in the accompanying drawings are not limited to a single bus or a single type of bus.

[0342] The above description of the functions implemented by the vehicle speed optimization device and the main control device illustrates the solution provided by the embodiments of the present invention. It is understood that, in order to achieve the above functions, the vehicle speed optimization device or the main control device includes hardware structures and / or software modules corresponding to the execution of each function. By combining the units and algorithm steps of the various examples described in the embodiments of the present invention, the embodiments of the present invention can be implemented in hardware or a combination of hardware and computer software. Whether a function is executed by hardware or by computer software driving hardware depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of the technical solution of the embodiments of the present invention.

[0343] This application also provides a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, are used to implement the above-mentioned vehicle speed optimization method.

[0344] The aforementioned readable storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. The readable storage medium can be any available medium accessible to a general-purpose or special-purpose computer.

[0345] An exemplary readable storage medium is coupled to a processor, enabling the processor to read information from and write information to the readable storage medium. Alternatively, the readable storage medium can be an integral part of the processor. Both the processor and the readable storage medium can reside in an Application Specific Integrated Circuit (ASIC). Alternatively, the processor and the readable storage medium can exist as discrete components in a vehicle speed optimization device or a main control device.

[0346] The division of units is merely a logical functional division; in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be indirect coupling or communication connection through some interfaces, devices, or units, and may be electrical, mechanical, or other forms.

[0347] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0348] In addition, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0349] If a function is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0350] Those skilled in the art will understand that all or part of the steps of the above-described method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When executed, the program performs the steps of the above-described method embodiments; and the aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.

[0351] The technical solutions of this application have been described above with reference to the preferred embodiments shown in the accompanying drawings. However, it is readily understood by those skilled in the art that the scope of protection of this application is obviously not limited to these specific embodiments. The above embodiments are only used to illustrate the technical solutions of this application and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. These modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application.

Claims

1. A method of optimizing vehicle speed, characterized by, Applied to a vehicle in an autonomous driving state, the method includes: Obtain vehicle parameters, road parameters, and environmental parameters where the vehicle is located; Based on the vehicle parameters, road parameters, and environmental parameters, tire force circle constraints and relaxation variables are determined, and a preset safety threshold is introduced for the relaxation variables to obtain the obstacle cost term. Based on the vehicle parameters, the corresponding dynamic constraints, reference speed cost term, and ride comfort cost term are determined, and the total cost function is obtained by weighted summation of the obstacle cost term, the reference speed cost term, and the ride comfort cost term. Based on the vehicle parameters, the obstacle cost term is analyzed and derived to obtain the convergence information of the obstacle cost term; Based on the convergence information and the total cost function, an optimization objective is constructed and solved iteratively to obtain the vehicle speed optimization parameters.

2. The method of claim 1, wherein, The vehicle parameters include at least: vehicle speed, vehicle mass, drag coefficient, frontal area, and rolling resistance coefficient; The road parameters include at least: path curvature and road slope; The environmental parameters include at least: road surface adhesion coefficient and air density.

3. The method of claim 2, wherein, The determination of tire force circle constraints and relaxation variables based on the vehicle parameters, road parameters, and environmental parameters includes: Based on vehicle parameters, road parameters, and environmental parameters, determine the longitudinal and lateral forces of the vehicle. The tire force circle constraint and the relaxation variable are determined based on the longitudinal force and the lateral force.

4. The method according to claim 3, characterized in that, The determination of the longitudinal force of the vehicle based on vehicle parameters, road parameters, and environmental parameters includes: The longitudinal resistance term of the vehicle is determined based on vehicle speed, vehicle mass, drag coefficient, frontal area, rolling resistance coefficient, road gradient, and air density. The longitudinal force is determined based on the vehicle body mass, vehicle speed, and longitudinal resistance term.

5. The method according to claim 4, characterized in that, The longitudinal resistance terms include: wind resistance, rolling resistance, and slope resistance; Wind resistance is determined based on the drag coefficient, frontal area, air density, and vehicle speed; rolling resistance is determined based on the rolling resistance coefficient and vehicle mass; and gradient resistance is determined based on the road gradient and vehicle mass.

6. The method according to claim 3, characterized in that, The determination of the tire force circle constraint based on longitudinal and lateral forces includes: The resultant force is constructed based on longitudinal force and lateral force, and the resultant force is compared with the adhesion limit corresponding to the road surface adhesion coefficient to determine the tire force circle constraint.

7. The method according to claim 6, characterized in that, The step of determining the slack variables includes: The tire force circle constraint is transformed into an inequality relationship between vehicle speed and the corresponding acceleration, and the residual parameter of the inequality relationship is determined. The remaining parameter is determined as the slack variable.

8. The method according to claim 2, characterized in that, The step of introducing a preset safety threshold for the slack variable to obtain the barrier cost term includes: Determine the obstacle factor based on the road surface adhesion coefficient; When the slack variable is greater than the preset safety threshold, the barrier cost term is calculated using the logarithmic barrier function based on the barrier factor and the slack variable.

9. The method according to claim 8, characterized in that, The method further includes: When the slack variable is less than or equal to a preset safety threshold, the obstacle cost term is obtained by a quadratic approximation calculation based on the obstacle factor, the preset safety threshold, and the slack variable.

10. The method according to claim 1, characterized in that, The step of obtaining the convergence information of the obstacle cost term includes: Based on the vehicle speed and the corresponding acceleration, the first derivative of the obstacle cost term is calculated to obtain the gradient information, and the second derivative is calculated based on the first derivative to obtain the Hessian matrix information; Gradient information and Hessian matrix information are used as convergence information.

11. The method according to claim 10, characterized in that, The step of obtaining the vehicle speed optimization parameters includes: A decision vector is constructed by combining vehicle speed, acceleration, and vehicle jerk. Based on convergence information and the total cost function, an optimization objective is constructed, and the decision vector is iteratively solved using the optimization objective to obtain the speed optimization parameters.

12. The method according to claim 11, characterized in that, The decision vector is constructed by combining vehicle speed, acceleration, and vehicle jerk, including: Vehicle speed and acceleration are used as state variables, and vehicle jerk is used as a control variable. The state variables and control variables are combined into a decision vector.

13. The method according to claim 11, characterized in that, The decision vector is solved iteratively using an optimization objective, including: In each iteration, the convergence direction and step size are determined based on gradient information and Hessian matrix information; If the change in the total cost function is less than the convergence tolerance, and / or the number of iterations reaches the upper limit, terminate the iteration and output the speed optimization parameters.

14. The method according to claim 1, characterized in that, The method further includes: Update the vehicle's road and environmental parameters at each discrete time step within the preset planning time domain; The time-varying parameters in the tire force circle constraint, the obstacle factor in the obstacle cost term, and the preset safety threshold are updated using the updated road parameters and environmental parameters.

15. The method according to claim 14, characterized in that, After updating the time-varying parameters in the tire force circle constraint, the obstacle factor in the obstacle cost term, and the preset safety threshold, the method further includes: Based on the updated time-varying parameters, barrier factors, and preset safety thresholds, the convergence information and total cost function are redefined.

16. A vehicle speed optimization device, characterized in that, Applied to a vehicle in an autonomous driving state, the device includes: The acquisition module is used to acquire vehicle parameters, road parameters where the vehicle is located, and environmental parameters. The determination module is used to determine tire force circle constraints and relaxation variables based on the vehicle parameters, road parameters, and environmental parameters, and to introduce a preset safety threshold for the relaxation variables to obtain the obstacle cost term; The determining module is further configured to determine the power constraints, reference speed cost term and ride comfort cost term corresponding to the vehicle based on the vehicle parameters, and obtain the total cost function based on the obstacle cost term, the reference speed cost term and the ride comfort cost term; The parsing module is used to perform analytical derivation processing on the obstacle cost term based on the vehicle parameters to obtain the convergence information of the obstacle cost term; The determining module is further configured to construct an optimization objective and iteratively solve it based on the convergence information and the total cost function to obtain the vehicle speed optimization parameters.

17. A vehicle, characterized in that, The vehicle is equipped with a control unit, which is used to optimize vehicle speed using the method described in any one of claims 1-15.

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