4Wis vehicle constraint construction, trajectory generation, spatiotemporal corridor construction method and system

Abstract

This invention belongs to the field of motion planning and chassis control technology for autonomous vehicles, specifically a method and system for constructing 4WIS vehicle constraints, generating trajectories, and constructing spatiotemporal corridors. The invention constructs a state stability constraint method, quantifying the degree to which vehicle states occupy the boundary of the stability domain, thus addressing shortcomings in dynamic stability constraints. Through a global collaborative constraint construction method, it integrates three types of constraints: environmental geometric safety, vehicle state stability, and control stability, establishing a robust global collaborative constraint framework. Based on this global collaborative constraint, it generates an optimal predicted driving trajectory that balances safety, stability, and smoothness, ensuring accurate and reliable trajectories. Finally, it constructs a spatiotemporal safety corridor, transforming non-convex obstacle avoidance constraints into convex linear constraints, achieving seamless integration between the planning and control layers. This invention effectively solves problems such as vehicle collisions, attitude instability, control jitter, and inaccurate trajectory prediction, significantly improving the safety and stability of four-wheel independent steering vehicles in complex urban scenarios.

Description

Technical Field

[0001] This invention belongs to the field of motion planning and chassis control technology for autonomous vehicles, specifically the 4WIS vehicle constraint construction, trajectory generation, and spatiotemporal corridor construction method and system. Background Technology

[0002] Motion planning for autonomous vehicles requires a comprehensive and rigorous constraint system to simultaneously ensure driving safety, dynamic stability, and trajectory prediction accuracy. Optimization planning methods based on linear constraints have become the mainstream technical solution for autonomous driving trajectory planning due to their high solution efficiency and adaptability to onboard real-time requirements.

[0003] Existing motion planning constraint construction technologies (such as the scheme described in existing patent CN112193244B) typically only focus on designing around road boundary restrictions, static and dynamic obstacle collision avoidance geometric constraints, and basic driving parameter constraints such as vehicle position, speed, steering angle, and acceleration. By linearizing the environmental constraints and basic vehicle execution constraints, they are integrated into the optimization framework to achieve basic obstacle avoidance and trajectory tracking.

[0004] However, such existing technologies are not foolproof and have some technical shortcomings: they do not consider the extent to which the vehicle's motion state occupies the boundary of the stable domain, and they do not include this core indicator in the constraint system, resulting in a lack of constraints on the vehicle's motion state and an extremely incomplete overall constraint structure. On the one hand, this deficiency makes it impossible for the planning process to pre-constrain and avoid the risk of the vehicle's state approaching the boundary of the stable domain, which can easily lead to vehicle yaw and side slip instability, failing to meet the driving stability requirements in complex traffic scenarios. On the other hand, due to the lack of key constraints on the extent to which the stable domain boundary is occupied, the constraints and model inputs of motion planning are incomplete, which will directly lead to a significant decrease in the accuracy of subsequent vehicle trajectory prediction. The planned trajectory will deviate from the actual dynamic stable feasible domain of the vehicle, making it difficult to guarantee trajectory tracking accuracy and causing a chain of problems such as unreasonable control commands and exceeding driving posture limits.

[0005] In summary, existing constraint construction methods, due to the lack of constraints on the degree of vehicle state occupancy of the stable domain boundary, not only make it difficult to form a sound vehicle motion constraint system, but also reduce the accuracy of trajectory prediction. They cannot take into account the obstacle avoidance safety, driving stability and trajectory accuracy of autonomous vehicles, thus restricting the application of autonomous driving technology in complex scenarios. Summary of the Invention

[0006] To address the technical problem of difficulty in forming a sound vehicle motion constraint system due to the lack of constraints on the occupancy of the stability domain boundary caused by vehicle state, this invention provides a method for constructing state stability constraints for a four-wheel independent steering vehicle and a method for constructing global collaborative constraints for a four-wheel independent steering vehicle. Furthermore, to address the technical problem of reduced vehicle trajectory prediction accuracy due to the lack of consideration for constraints on the occupancy of the stability domain boundary caused by vehicle state, this invention provides a method for generating predicted driving trajectories for a four-wheel independent steering vehicle and a method for constructing a spatiotemporal safety corridor for a four-wheel independent steering vehicle. Finally, this invention also provides an intelligent planning and control system for a four-wheel independent steering vehicle that executes the spatiotemporal safety corridor construction method.

[0007] A method for constructing state stability constraints for a four-wheel independent steering vehicle includes the following construction steps: Based on the centroid sideslip angle β and heading angular velocity r, which characterize the vehicle state, the critical profile formed by the maximum allowable sideslip angle and the maximum heading angular velocity at different vehicle speeds is used as the stable boundary. The internal closed region enclosed by the stable boundary constitutes the stable domain. A vehicle state occupancy model S is constructed using the stability domain: ; Among them, I k β represents the degree to which the vehicle state occupies the boundary of the stability domain at the k-th discrete time; k Let r be the centroid sideslip angle at the k-th discrete time step; k v is the heading angular velocity at the k-th discrete time; x,k Let β be the longitudinal speed of the vehicle body at the k-th discrete time; max (v x,k (v is the current vehicle speed) x,k Lower limit safe sideslip angle threshold; r max (v x,k ) represents the maximum safe heading angular velocity threshold at the current vehicle speed; M k Let be the stability margin of the vehicle's movement at the k-th discrete time. Based on S and the vehicle's center of gravity operating state, construct vehicle state stability constraints: ; Among them, v x,min v x,max These are the minimum and maximum speeds, respectively; M min This represents the minimum stability margin.

[0008] A method for constructing global cooperative constraints for a four-wheel independent steering vehicle includes the following construction steps: Obtain the road boundary constraints, static obstacle constraints, and dynamic obstacle constraints of the vehicle within the planning time domain, and denote the intersection of the three as the predicted spatial geometric safety constraints; Based on the vehicle's center of mass position, heading angle, sideslip angle, and vehicle speed, an equivalent curvature kinematic model F of the vehicle is constructed; F is linearized and decoupled to separate the vehicle state variables and control variables. Based on the vehicle state variables, a method for constructing state stability constraints for four-wheel independent steering vehicles is executed to construct vehicle state stability constraints. Based on the vehicle state stability constraints, vehicle control stability constraints are added based on vehicle control variables, and threshold ranges are limited for directional curvature, lateral curvature, longitudinal acceleration, and the changes of these three variables. By combining the predictive spatial geometric safety constraints, vehicle state stability constraints, and vehicle control stability constraints, a global collaborative constraint adapted to four-wheel independent steering vehicles is constructed.

[0009] As a further improvement to the above scheme, the process for obtaining each sub-constraint in the predicted spatial geometrical safety constraints is as follows: Road boundary constraints: Model the original road boundary as a linear half-space constraint. ; This causes the original road boundary to shrink inward by a safe distance d. safe,road The road safety feasible region constraint is obtained. Based on the linearized relationship of vehicle corner points Transforming linear half-space constraints into road boundary constraints ; Among them, C r d is the matrix consisting of the normal vectors corresponding to all road boundaries of the vehicle travel segment within the planning time domain; p is the coordinate vector of any point in the global coordinate system; d r P is a vector consisting of the intercepts of all road boundaries corresponding to the vehicle travel segments within the planning time domain; 1 represents a vector of all 1s with the same number dimension as the road boundaries; gcs,i,k Let A be the global coordinates of the i-th vehicle corner point at the k-th discrete time. i,k Let z be the Jacobian matrix of the vehicle state at the i-th vehicle corner point at the k-th discrete time; k c is the vehicle state vector at the k-th discrete time step; i,k Let be the position vector of the i-th vehicle corner point relative to the centroid at the k-th discrete time. Static obstacle boundary constraints: The j-th static obstacle is modeled as a convex polygon, and Minkowski dilation is used to expand the static safety distance, resulting in the half-space constraint of the restricted area of ​​the expanded static obstacle. Combined with the linearization relationship of vehicle corner points, a binary variable is introduced. With Big-M coefficient M staConstruct static obstacle separation constraints Simultaneously apply constraints ; in, For the j-th static obstacle convex polygon, the l-th... sta The normal vector of the edge; For the j-th static obstacle convex polygon, the l-th... sta The intercept corresponding to the edge; For the Big-M logic control of the i-th vehicle corner point at the k-th discrete time, for the j-th static obstacle convex polygon, the l-th... sta A 0-1 binary variable representing whether the edge constraint is effective or not; For static obstacles, the safety margin; L j Let be the total number of sides of the j-th static obstacle convex polygon; Dynamic obstacle boundary constraints: Dynamic obstacles are pre-modeled as equivalent convex polygons with fixed contours, which only translate as a whole with the predicted position, forming instantaneous convex polygon boundaries at each discrete moment; a uniform linear motion model is used to predict the position of the m-th dynamic obstacle at the k-th discrete moment. ; Perform safety distance expansion on dynamic obstacles after the predicted position to obtain the half-space constraint of the dynamic obstacle no-entry zone. Combined with the linearization relationship of vehicle corner points, a binary variable is introduced. With Big-M coefficient M dyn Constructing dynamic obstacle prediction and obstacle avoidance constraints ; in, Let m be the initial global position of the m-th dynamic obstacle; Let t be the uniform velocity vector of the m-th dynamic obstacle; k To plan the k-th discrete time point in the time domain; The matrix is ​​formed by the normal vectors corresponding to all boundaries of the m-th dynamic obstacle convex polygon after it has been translated to the predicted position at the k-th discrete time. The vector is formed by the intercepts of all boundaries of the m-th dynamic obstacle convex polygon after it has been translated to the predicted position at the k-th discrete time. For the Big-M logic control of the i-th vehicle corner point at the k-th discrete time, for the m-th dynamic obstacle convex polygon, the l-th... dyn A 0-1 binary variable representing whether the edge constraint is effective or not; For the m-th dynamic obstacle convex polygon at the k-th discrete time, the l-th... dyn The normal vector of the edge; For the m-th dynamic obstacle convex polygon at the k-th discrete time, the l-th... dyn The intercept of the strip; This refers to the safety margin for dynamic obstacles.

[0010] As a further improvement to the above scheme: construct an equivalent curvature kinematic model of the vehicle and separate the vehicle state variables and control variables. The specific steps are as follows: Based on the vehicle's center of mass position (X,Y) and heading angle Side slip angle β and vehicle longitudinal speed v x Construct the vehicle's equivalent curvature kinematic model F: ; Where X and Y are the lateral and longitudinal coordinates of the vehicle's center of mass in the global coordinate system; This represents the lateral velocity component of the vehicle's center of mass in the global coordinate system. v represents the longitudinal velocity component of the vehicle's center of mass in the global coordinate system. x The longitudinal velocity of the vehicle's center of mass in the vehicle coordinate system; Let be the actual longitudinal acceleration of the vehicle's center of mass in the vehicle coordinate system; cos, sin, and tan are the cosine, sine, and tangent functions, respectively. For heading curvature control; This represents the rate of change of the vehicle's sideslip angle. This is the lateral curvature control value; a x The longitudinal command acceleration of the vehicle's center of mass in the vehicle coordinate system; First-order Taylor linearization and decoupling are performed on F to decompose the coupled nonlinear motion relationship, and the vehicle state variables and control variables that can be quantized and constrained independently are separated, forming a linear state transition equation: ; ; ; ; ; ; Among them, z k z k+1 Let A be the vehicle state vector at the k-th and k+1-th discrete times; k B is the state transition matrix at the k-th discrete time step; k Let u be the control input matrix at the k-th discrete time step; k c is the vehicle control vector at the k-th discrete time step; k Δt is the linearization bias compensation term at the k-th discrete time step; I is the identity matrix; Δt is the discrete time step. , For the linearized reference point at the kth and k+1th discrete times, denoted as the nominal state vector; The nominal control vector for the linearized reference point at the k-th discrete time step; Let the state be the Jacobian matrix; To control the Jacobian matrix; X k Y k Let x be the horizontal and vertical coordinates of the vehicle's centroid at the k-th discrete moment in the global coordinate system. Let β be the heading angle of the vehicle at the k-th discrete time; k v is the vehicle's sideslip angle at the k-th discrete time; x,k Let be the longitudinal velocity of the vehicle's centroid in the vehicle coordinate system at the k-th discrete time; the superscript T denotes vector transpose; a x,k Let be the longitudinal command acceleration of the vehicle's center of mass in the vehicle coordinate system at the k-th discrete moment; This represents the heading curvature control value at the k-th discrete time. Let be the lateral curvature control quantity at the k-th discrete time.

[0011] A method for generating a predicted driving trajectory for a four-wheel independent steering vehicle includes the following generation steps: The global collaborative constraint construction method based on four-wheel independent steering vehicles is used to construct vehicle state variables, control variables and linear state transition equations, and establish the time-series recursive relationship of vehicle state between discrete moments. Based on the recursive relationship of vehicle state time sequence, a vehicle trajectory planning optimization model is constructed regarding vehicle state variables and control variables; Under the premise of satisfying the global collaborative constraints, the vehicle trajectory planning optimization model is minimized numerically to obtain the global optimal state sequence consisting of the vehicle's centroid position, heading angle, sideslip angle, and longitudinal speed in the planning time domain, as well as the global optimal control sequence consisting of longitudinal command acceleration, heading curvature, and lateral curvature. The optimal predicted driving trajectory of the vehicle is then fitted and generated in the planning time domain.

[0012] As a further improvement to the above scheme, the vehicle trajectory planning optimization model J is as follows: ; Among them, J trk For trajectory tracking; J mag To control the amplitude cost term; J Δu To control the incremental cost term; J stab J represents the stability cost term; safe For safety costs; ; Where N is the total number of discrete moments in the trajectory planning time domain; ω trk These are the trajectory tracking weighting coefficients; , Let x be the reference lateral and longitudinal coordinates of the vehicle's centroid at the k-th discrete moment in the global coordinate system. Let be the reference heading angle of the vehicle at the k-th discrete time. Let be the reference sideslip angle of the vehicle at the k-th discrete time. Let be the longitudinal reference vehicle speed of the vehicle's centroid in the vehicle coordinate system at the k-th discrete moment; ; Among them, w u To control the amplitude weighting coefficient; ; Where, ω Δu To control the incremental weighting coefficient; a x,k-1 Let be the longitudinal command acceleration of the vehicle's centroid in the vehicle coordinate system at the (k-1)th discrete moment; This represents the heading curvature control value at the (k-1)th discrete time. This represents the lateral curvature control value at the (k-1)th discrete time. ; Among them, w stab This is the stability weighting coefficient; ; Where, ω α For the safety cost weighting coefficient; α min This represents the minimum safe distance margin for vehicles.

[0013] As a further improvement to the above scheme: taking the initial state of the vehicle as the starting point of the iteration, and relying on the temporal recursive relationship of the vehicle state, the vehicle trajectory planning optimization model is minimized within the scope of the global collaborative constraints. For each discrete moment in the planning time domain, the optimal discrete state quantity and the optimal discrete control quantity are solved one by one. Among them, the optimal discrete state quantity corresponding to the k-th discrete moment includes the vehicle's centroid coordinates, heading angle, centroid sideslip angle, and longitudinal vehicle speed at that discrete moment. The optimal discrete state quantities of all discrete moments are arranged in temporal order to form the global optimal state sequence. The optimal discrete control quantity corresponding to the k-th discrete moment includes the longitudinal command acceleration, heading curvature control quantity, and lateral curvature control quantity at that moment. The optimal discrete control quantities of all discrete moments are arranged in temporal order to form the global optimal control sequence. Interpolation and smoothing fitting are performed on the optimal state sequence of the entire domain. The vehicle centroid coordinates, heading angle, centroid sideslip angle and longitudinal vehicle speed at each discrete time are continuously spliced ​​together to generate the optimal predicted driving trajectory of the vehicle with a continuous time sequence. At the same time, the optimal control sequence of the entire domain is subjected to time-series fitting processing to obtain a continuous control command sequence that is time-series continuous and adapted to the execution logic of the vehicle chassis actuator.

[0014] A method for constructing a spatiotemporal safety corridor for a four-wheel independent steering vehicle includes the following construction steps: Using the vehicle's center of mass as a reference, the position vectors of the four corner points of the vehicle relative to the center of mass are enlarged proportionally to obtain the enlarged global coordinates of the four corner points. The predicted spatial geometric safety constraints are constructed by substituting the global coordinates of the four corner points into the global collaborative constraint construction method for four-wheel independent steering vehicles. Based on the positional relationship between the vehicle's center of mass and the four corner points, the predicted spatial geometric safety constraints are transformed into center of mass linear inequality constraints with the global coordinates of the vehicle's center of mass as the core variable. Based on the centroid linear inequality constraint, the feasible region of the planar convex polygon enclosing the centroid of the vehicle is obtained from the optimal predicted driving trajectory generated by the four-wheel independent steering vehicle prediction driving trajectory generation method. The feasible regions of planar convex polygons corresponding to all discrete moments in the planning time domain are sequentially spliced ​​along the time axis to form a continuous safe region that combines spatial boundaries and temporal correlation. This continuous safe region is the spatiotemporal safety corridor.

[0015] As a further improvement to the above scheme: the centroid linear inequality constraint is: ; in, P is the constraint transformation coefficient matrix for the i-th vehicle corner point at the k-th discrete time, used to map the global coordinate constraints of the vehicle corner point to linear constraints of the vehicle centroid coordinates; gcs,k Let be the global coordinate vector of the vehicle's centroid at the k-th discrete time. α is the constraint boundary margin threshold for the i-th vehicle corner point at the k-th discrete time, used to limit the boundary limit range of the vehicle's passable area; safe c is the global fixed safety redundancy coefficient; i,k Let be the position vector of the i-th vehicle corner point relative to the centroid at the k-th discrete time.

[0016] A four-wheel independent steering vehicle intelligent planning and control system is used to execute a method for constructing a spatiotemporal safety corridor for a four-wheel independent steering vehicle, including a vehicle body, an environmental perception module, a vehicle constraint modeling module, a trajectory optimization planning module, a spatiotemporal safety corridor construction module, and a vehicle control execution module; The environmental perception module is used to collect environmental information such as road boundaries, moving and static obstacles, and the vehicle's own driving status parameters; The vehicle constraint modeling module is used to construct vehicle state stability constraints, control stability constraints, and predictive space geometric safety constraints, and simultaneously obtain global collaborative constraints. It also constructs and linearly decouples the vehicle's equivalent curvature kinematics model and establishes the vehicle's linear state transition equations. The trajectory optimization and planning module is used to construct a multi-objective trajectory planning and optimization model based on global collaborative constraints and linear state transition equations, solve for the optimal state sequence and control sequence, and fit to generate the optimal predicted driving trajectory. The spatiotemporal safety corridor construction module is used to solve the feasible region of convex polygons at each time step based on the optimal predicted driving trajectory, through vehicle corner point safety amplification and constraint dimensionality reduction transformation, and to construct a spatiotemporal safety corridor adapted to the trajectory by splicing the time sequence. The vehicle control execution module is used to receive trajectory commands and safety constraint commands, and drive the four-wheel independent steering vehicle to complete driving actions.

[0017] Compared with the prior art, the beneficial effects of the present invention are: 1. The method for constructing state stability constraints for four-wheel independent steering vehicles of the present invention first uses the sideslip angle β and yaw angular velocity r, which characterize the core state of the vehicle, as a benchmark. Based on the maximum allowable sideslip angle and maximum yaw angular velocity of the vehicle at different vehicle speeds, a stability boundary is delineated and enclosed to form a stability domain, thus clarifying the core spatial range of vehicle dynamic stability. Then, a vehicle state occupancy model S is specifically constructed to calculate the occupancy degree I of the vehicle state on the stability domain boundary at the k-th discrete time. k and the corresponding driving stability margin M k This method intuitively quantifies the proximity of the vehicle's actual motion state to the stability domain boundary, directly filling the key constraint gap in existing technologies regarding the degree of vehicle state occupancy of the stability domain boundary. Finally, by combining this state occupancy model with the vehicle's center of mass operating state, a complete vehicle state stability constraint is constructed, including the center of mass sideslip angle limit, heading angular velocity limit, vehicle speed range, and minimum stability margin requirement. This transforms the previously missing stability domain occupancy constraint into a quantifiable and executable rigid constraint condition, fundamentally solving the technical problem of not being able to form a sound vehicle motion constraint system due to the lack of this constraint. It upgrades the vehicle motion constraint system to a complete system that takes into account the control of dynamic stability boundary occupancy, and also provides key stability constraint support for improving the accuracy of driving trajectory prediction in the future.

[0018] 2. The four-wheel independent steering vehicle global collaborative constraint construction method of this invention integrates road boundary, static and dynamic obstacle constraints into a unified predictive spatial geometric safety constraint, realizing a complete closed loop of collision-free safety constraints at the environmental level. Simultaneously, relying on the vehicle's equivalent curvature kinematics model and completing linear decoupling processing, it accurately adapts to the multi-mode maneuvering characteristics of four-wheel independent steering vehicles, including yaw, side shift, and conventional steering, significantly reducing the complexity of optimization solutions. Its core advantage lies in directly introducing and executing a state stability constraint construction method, fundamentally supplementing the key constraint on the degree of vehicle state occupancy of the stability domain boundary that is missing in existing technologies, making the vehicle motion constraint system inherently sound. Furthermore, vehicle control stability constraints are added on this basis. By imposing strict threshold limits on directional curvature, lateral curvature, longitudinal acceleration, and their variations, problems such as abrupt changes in control commands and actuator overload are effectively avoided. Ultimately, by combining environmental geometric safety constraints, vehicle state stability constraints, and vehicle control stability constraints, a comprehensive, deeply coupled, all-domain collaborative constraint is constructed, which not only completely solves the core defects of traditional constraint systems such as fragmentation, incompleteness, and lack of stable domain occupancy control, but also provides a complete feasible domain for trajectory planning of four-wheel independent steering vehicles that combines safety, stability, and executability. This significantly improves the accuracy of subsequent trajectory prediction and the smoothness of control execution, perfectly adapting to the safe, stable, and efficient driving requirements of four-wheel independent steering vehicles in complex urban scenarios.

[0019] 3. The method for generating predicted driving trajectories for four-wheel independent steering vehicles of the present invention establishes a recursive relationship of vehicle state time sequence based on the integration of environmental safety, state stability, and control smoothness global cooperative constraints. This ensures from the root that the trajectory recursion conforms to the vehicle's dynamic characteristics and safety boundary requirements. The trajectory planning optimization model constructed based on this recursive relationship can comprehensively take into account the requirements of position tracking, stability control, and control smoothness. Under the strict constraints of global cooperative constraints, the minimization numerical solution ensures that the obtained global optimal state sequence and optimal control sequence meet the rigid requirements of collision-free passage, dynamic stability, and executable control commands throughout the entire process. The final fitted optimal predicted driving trajectory accurately matches the motion law of four-wheel independent steering vehicles, completely solving the problems of low trajectory prediction accuracy, driving posture exceeding limits, and large control fluctuations caused by the lack of constraints. At the same time, it provides a high-quality benchmark trajectory with safety, stability, and smoothness for subsequent spatiotemporal safety corridor construction and lateral and longitudinal cooperative control, greatly improving the overall effect of trajectory planning and tracking control.

[0020] 4. The spatiotemporal safety corridor construction method for four-wheel independent steering vehicles of the present invention uses the optimal predicted driving trajectory of the vehicle as a benchmark. First, the vehicle corner points are proportionally enlarged to reserve sufficient geometric safety redundancy in advance, effectively offsetting trajectory tracking errors during actual driving and fundamentally avoiding collision risks caused by minor deviations. Then, the complex predicted spatial geometric safety constraints are transformed into linear inequality constraints with the global coordinates of the vehicle's center of mass as the core variable. This simplifies the traditional non-convex, difficult-to-solve obstacle avoidance logic into linear constraints that can be directly handled by convex optimization, significantly reducing the solution difficulty and computation time of the subsequent control layer. The feasible region of the convex polygon in the time plane is spliced ​​along the time axis to form a continuous spatiotemporal safety corridor that combines spatial boundaries and temporal correlation. This solidifies the global safety decisions of the planning layer into hard constraints that can be directly reused by the control layer. It completely solves the problem of discontinuous control and poor real-time performance caused by the need to repeatedly introduce integer variables to solve non-convex problems in the control layer. It also defines a strict collision-free safe movement range for the vehicle's center of mass at every moment in the planning time domain, perfectly realizing a safe and seamless connection between the planning layer and the control layer. It fully adapts to the real-time, safe and stable driving control requirements of four-wheel independent steering vehicles in complex dynamic traffic scenarios. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of the structure of the present invention.

[0022] Figure 2 This is a comparison diagram of stability boundaries at different vehicle speeds.

[0023] Figure 3 The β-r stability margin heatmap is shown at a vehicle speed of 50 km / h.

[0024] Figure 4 A spatiotemporal safety corridor diagram for a four-wheel independent steering vehicle. Detailed Implementation

[0025] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0026] like Figure 1As shown, this specific implementation method is applied to the autonomous driving trajectory planning and safety management scenario of four-wheel independent steering intelligent vehicles. It addresses the technical problems of traditional vehicle trajectory planning, such as not taking into account the characteristics of four-wheel independent steering, geometric collision risk, driving posture instability, control command jitter, and insufficient dynamic safety redundancy. It follows a complete technical link of state stability constraint construction → global collaborative constraint construction → optimal prediction trajectory solution → spatiotemporal safety corridor extraction → intelligent control execution, to achieve collision-free, stable, smooth, and highly safe intelligent driving of four-wheel independent steering vehicles in complex road environments.

[0027] In addition, all discrete moments are uniformly discretized based on a fixed time step Δt, with a planned time domain length of T and a total number of discrete moments N = T / Δt. All calculations are performed in real time in the vehicle domain controller to meet the real-time driving control requirements of the vehicle.

[0028] I. Method for Constructing Global Cooperative Constraints for Four-Wheel Independent Steering Vehicles

[0029] This global collaborative constraint construction method takes complex urban traffic scenarios as its application background and addresses the trajectory planning requirements of four-wheel independent steering (4WIS) vehicles. It unifies and integrates environmental geometric safety constraints, vehicle state stability constraints, and vehicle control stability constraints to form a global collaborative constraint covering all dimensions of "environment-vehicle-control", providing a strict feasible domain boundary for subsequent trajectory optimization solutions.

[0030] (i) Obtaining and constructing predictive spatial geometrical safety constraints

[0031] Predictive spatial geometric safety constraints form the environmental foundation of global collaborative constraints, ensuring that 4WIS vehicles do not exceed road boundaries or collide with static / dynamic obstacles within the planning time domain. This section, based on the vehicle's outer corner point model, transforms road boundaries, static obstacles, and dynamic obstacles into linear constraints solvable by MILP; the intersection of these three is the predicted spatial geometric safety constraint.

[0032] 1. Preprocessing of vehicle outline corner point model

[0033] Before constructing the predictive spatial geometric safety constraints, a 4WIS vehicle outer corner point model is first established, expanding the vehicle from a center-of-mass point to a real geometric rigid body, thus avoiding collision misses caused by relying solely on center-of-mass obstacle avoidance: (1) Define the global coordinates P of the vehicle's center of mass. gcs =[X,Y] T The heading angle is .

[0034] (2) Set geometric parameters: The distance from the center of mass to the foremost point of the vehicle is l f,body The distance from the center of mass to the rearmost point of the vehicle is l. r,bodyThe distance from the center of mass to the leftmost side of the vehicle is w. l The distance w from the center of gravity to the rightmost side of the vehicle r .

[0035] (3) Define the coordinates r of the four corner points of the vehicle (front left FL, front right FR, rear left RL, rear right RR) in the vehicle coordinate system. loc,i In order: , , , .

[0036] (4) By rotation matrix Transform the corner coordinates to the global coordinate system: , where P gcs,i,k Let be the global coordinates of the i-th vehicle corner point at the k-th discrete time.

[0037] (5) Make a first-order linear approximation of the global corner coordinates to obtain the linear relationship between the corners and the vehicle state variables: A i,k Let z be the Jacobian matrix of the vehicle state at the i-th vehicle corner point at the k-th discrete time; k c is the vehicle state vector at the k-th discrete time step; i,k Let be the position vector of the i-th vehicle corner point relative to the centroid at the k-th discrete time.

[0038] 2. Construct road boundary constraints

[0039] Road boundary constraints are used to restrict vehicles to stay within the feasible road area throughout their journey and to maintain a safe distance. (1) Model the original road boundary as a linear half-space constraint. C r d is the matrix consisting of the normal vectors corresponding to all road boundaries of the vehicle travel segment within the planning time domain; p is the coordinate vector of any point in the global coordinate system; d r It is a vector consisting of the intercepts corresponding to all road boundaries of the vehicle travel segment within the planning time domain.

[0040] (2) To ensure the safe distance d between the vehicle and the road boundary safe,road By shrinking the original boundary inward, we obtain the road safety feasible region constraint. , where 1 is an all-1 vector consistent with the number dimension of the road boundary.

[0041] (3) Substitute the linearized vehicle corner coordinates into the vehicle corner-level road boundary constraints. This constraint ensures that the four corners of the vehicle are always within the safe road area, with no risk of crossing the boundary.

[0042] 3. Construct static obstacle constraints

[0043] Static obstacles (guardrails, buildings, fixed facilities) have fixed positions, and obstacle avoidance is achieved through Minkowski expansion and Big-M logic constraints: (1) Model the j-th static obstacle as a convex polygon, and use Minkowski dilatation to extend the static safety distance d of the obstacle. safe The restricted area semi-space constraint is obtained. ,in For the j-th static obstacle convex polygon, the l-th... sta The normal vector of the edge; For the j-th static obstacle convex polygon, the l-th... sta The intercept corresponding to the edge.

[0044] (2) Introduce 0-1 binary variables With Big-M coefficient M sta Transforming non-convex obstacle avoidance logic into linear constraints ,in For the Big-M logic control of the i-th vehicle corner point at the k-th discrete time, for the j-th static obstacle convex polygon, the l-th... sta A 0-1 binary variable representing whether the edge constraint is effective or not; For static obstacles, the safety margin; L j Let be the total number of sides of the j-th static obstacle convex polygon.

[0045] (3) Apply logical completeness constraints to ensure that each corner point selects at least one separation boundary for each static obstacle. L j Let be the total number of sides of the j-th static obstacle convex polygon.

[0046] 4. Construct dynamic obstacle constraints

[0047] The positions of dynamic obstacles (pedestrians, vehicles) change over time. Time-varying obstacle avoidance is achieved using uniform velocity prediction combined with Big-M constraints. (1) The dynamic obstacle is pre-modeled as a convex polygon with a fixed contour, which only translates as a whole with the predicted position, forming an instantaneous convex polygon boundary at each discrete moment; the position of the m-th dynamic obstacle at the k-th discrete moment is predicted using a uniform linear motion model. ,in Let m be the initial global position of the m-th dynamic obstacle; Let t be the uniform velocity vector of the m-th dynamic obstacle; k Let k be the k-th discrete time in the planning time domain.

[0048] (2) Perform safety distance dilation on the dynamic obstacles at the predicted location to obtain time-varying half-space constraints. ,in The matrix is ​​formed by the normal vectors corresponding to all boundaries of the m-th dynamic obstacle convex polygon after it has been translated to the predicted position at the k-th discrete time. It is a vector composed of the intercepts of all boundaries of the m-th dynamic obstacle convex polygon after it has been translated to the predicted position at the k-th discrete time.

[0049] (3) Introduce binary variables With Big-M coefficient M dyn Construct dynamic obstacle avoidance linear constraints: ,in For the Big-M logic control of the i-th vehicle corner point at the k-th discrete time, for the m-th dynamic obstacle convex polygon, the l-th... dyn A 0-1 binary variable representing whether the edge constraint is effective or not; For the m-th dynamic obstacle convex polygon at the k-th discrete time, the l-th... dyn The normal vector of the edge; For the m-th dynamic obstacle convex polygon at the k-th discrete time, the l-th... dyn The intercept of the strip; This refers to the safety margin for dynamic obstacles.

[0050] (4) Apply logical completeness constraints L m Let m be the number of sides of the convex polygon of the m-th dynamic obstacle.

[0051] 5. Integrating predictive spatial geometrical safety constraints

[0052] constrain the road boundary F road Static obstacle constraint F sta Dynamic obstacle constraint F dyn By combining the equations, we obtain the geometrical safety constraint F in the predicted space. geo =F road ∩F sta ∩F dyn This constraint ensures that the vehicle's outline remains free from collisions and does not cross boundaries throughout the planning time domain.

[0053] (ii) Constructing the equivalent curvature kinematic model of the 4WIS vehicle and completing linear decoupling.

[0054] To adapt to the mixed-integer linear programming (MILP) linear optimization framework, a low-dimensional equivalent curvature kinematic model needs to be established to replace the high-dimensional complex model that directly optimizes the four-wheel steering angle. At the same time, independent state and control variables are separated to provide a model foundation for subsequent constraint construction.

[0055] 1. Construct a 4WIS equivalent curvature kinematic model

[0056] The 4WIS vehicle possesses three typical motion modes: conventional steering, crabbing lateral movement, and pure yaw. It achieves a wide range of maneuverability through independent coordinated steering of the front and rear wheels. These three motion modes validate that the 4WIS vehicle can overcome the motion limitations of traditional two-wheel steering, achieving efficient lateral maneuverability and attitude adjustment through coordinated front and rear wheel steering. To reduce the dimensionality of the upper-level optimization problem and avoid the coupling complexity and solution difficulties caused by directly using the four wheel-level steering angles as decision variables, this model introduces yaw curvature and lateral movement curvature to characterize the vehicle's core motion capabilities.

[0057] Let the vehicle's center of mass be located at (X,Y) in the global coordinate system, and its heading angle be... (representing the orientation of the vehicle's longitudinal axis), sideslip angle β (representing the angle between the direction of the center of gravity velocity and the vehicle's longitudinal axis), and vehicle longitudinal speed v x .

[0058] Because the actual speed direction of the vehicle is And the arc length s of the centroid trajectory satisfies Based on this, the original expression for the rate of change of the vehicle's center of gravity position in the global coordinate system is derived as follows: ; Expanding and simplifying the above expression, we get: ; To accurately describe the yaw and lateral maneuverability of the 4WIS vehicle, the yaw curvature is defined. With lateral curvature : ; ; in, It characterizes the rate of change of heading angle with path arc length, reflecting the rate of change of vehicle orientation; It characterizes the rate of change of the center of gravity sideslip angle with the path arc length, reflecting the rate of change of the center of gravity velocity direction relative to the vehicle body attitude.

[0059] The total path curvature ρ is defined as: ; Using the chain rule, the relationship between curvature and angular velocity is established: ; ; Further introduce longitudinal command acceleration a x By integrating the relationship between longitudinal and lateral motion, the equivalent curvature kinematic model F of the 4WIS vehicle used in this embodiment is finally obtained: ; Where X and Y are the lateral and longitudinal coordinates of the vehicle's center of mass in the global coordinate system; This represents the lateral velocity component of the vehicle's center of mass in the global coordinate system. v represents the longitudinal velocity component of the vehicle's center of mass in the global coordinate system. x The longitudinal velocity of the vehicle's center of mass in the vehicle coordinate system; Let r be the actual longitudinal acceleration of the vehicle's center of mass in the vehicle coordinate system; cos, sin, and tan are the cosine, sine, and tangent functions, respectively; r, All are vehicle heading angular velocities; For heading curvature control; This represents the rate of change of the vehicle's sideslip angle. This is the lateral curvature control value; a x This is the longitudinal command acceleration of the vehicle's center of mass in the vehicle coordinate system.

[0060] Based on the above equivalent curvature kinematic model F, the standardized definitions of the vehicle state vector and the vehicle control vector are clarified: , used to fully characterize the real-time motion state of the vehicle; , where a x Used to adjust the longitudinal speed of the vehicle. Used to adjust the vehicle's heading angle. Used to adjust the offset of the center of gravity velocity direction relative to the vehicle body attitude.

[0061] Compared to the traditional modeling method that directly optimizes the four wheel-level steering angles, the equivalent curvature kinematics model F modeling method significantly reduces the optimization dimension of the upper-level planning and control, while fully preserving the coordinated maneuverability of the 4WIS vehicle's yaw and side-shift motions, and can flexibly adapt to the motion requirements of multiple modes such as conventional steering, crabbing, and pure yaw.

[0062] 2. First-order linearization of the model and state transition equations

[0063] The MILP solver only supports handling linear equality and inequality constraints, while the 4WIS equivalent curvature kinematic model, even after discretization, remains nonlinear and cannot be directly embedded into the MILP optimization framework. Therefore, this embodiment performs first-order Taylor linearization on the nonlinear model at the nominal points of the planned reference trajectory to eliminate nonlinear terms, obtaining linear state transition equations that can be directly used for MILP solving. The specific implementation steps are as follows: (1) Compact expression of kinematic model matrix The 4WIS equivalent curvature kinematic model derived above is organized into a matrix form, and combined with the defined state vector. With upper-level control vector The continuous-time model is simplified into a unified nonlinear form: In the formula, f(z,u) is the nonlinear right-hand side function corresponding to the equivalent curvature kinematic model.

[0064] (2) Continuous model explicit Euler discretization

[0065] To adapt to the time domain of discrete programming, an explicit Euler method is used to model the continuous-time model at discrete time t. k Discretize the discrete state with a step size of Δt to obtain the discrete state update equation: In the formula, z k z k+1 Let u be the vehicle state vector at the k-th and k+1-th discrete times; k Let be the vehicle control vector at the k-th discrete time.

[0066] The discrete update equation still retains nonlinear characteristics and does not meet the linear solution requirements of MILP, so it needs to be further linearized.

[0067] (3) Define the linearization deviation variable

[0068] Select the nominal state vector on the planning reference trajectory With nominal control vector As a linearization reference point, define the state deviation and control deviation: , .

[0069] (4) Linearization of first-order Taylor expansion

[0070] At the reference point By performing a first-order Taylor expansion on the nonlinear function f(z,u), and neglecting second-order and higher-order small quantities, we obtain the linearized state update relation in the form of deviation: ; ; ; ; ; in, , Let be the state deviation at the k-th and k+1-th discrete times; This represents the control deviation at the k-th discrete time. Let the state be the Jacobian matrix; To control the Jacobian matrix.

[0071] (5) Restore the original variables and construct the linear state transition equation.

[0072] By restoring the deviation to the original state and control variables, a linear state transition equation that can be directly incorporated into the MILP optimization framework is derived: ; The parameters in the formula are defined as follows: ; ; ; ; ; Among them, z k z k+1 Let A be the vehicle state vector at the k-th and k+1-th discrete times; k B is the state transition matrix at the k-th discrete time step; k Let u be the control input matrix at the k-th discrete time step; k c is the vehicle control vector at the k-th discrete time step; k Δt is the linearization bias compensation term at the k-th discrete time step; I is the identity matrix; Δt is the discrete time step. , For the linearized reference point at the kth and k+1th discrete times, denoted as the nominal state vector; The nominal control vector for the linearized reference point at the k-th discrete time step; Let the state be the Jacobian matrix; To control the Jacobian matrix; X k Y k Let x be the horizontal and vertical coordinates of the vehicle's centroid at the k-th discrete moment in the global coordinate system. Let β be the heading angle of the vehicle at the k-th discrete time; k v is the vehicle's sideslip angle at the k-th discrete time; x,k Let be the longitudinal velocity of the vehicle's centroid in the vehicle coordinate system at the k-th discrete time; the superscript T denotes vector transpose; a x,k Let be the longitudinal command acceleration of the vehicle's center of mass in the vehicle coordinate system at the k-th discrete moment; This represents the heading curvature control value at the k-th discrete time. Let be the lateral curvature control quantity at the k-th discrete time.

[0073] After the first-order linearization process described above, the original nonlinear 4WIS kinematic model is transformed into a purely linear state transition relationship, which is fully compatible with the linear constraints and optimization solution rules of MILP, providing a compliant model foundation for subsequent safe trajectory generation.

[0074] (III) Constructing vehicle state stability constraints

[0075] By combining the 4WIS vehicle dynamics characteristics, speed-related state stability constraints are constructed to avoid instability caused by excessive yaw or side deviation during obstacle avoidance.

[0076] 1. Speed-dependent stability boundary and stability region

[0077] The sideslip angle β and the angular velocity r of the center of mass are the core steady state variables.

[0078] Based on vehicle mass, tire lateral stiffness, and road adhesion coefficient, determine the limiting stability boundary β at different vehicle speeds. max (v x,k ), r max (v x,k ), where β max (v x,k (v is the current vehicle speed) x,k Lower limit safe sideslip angle threshold; r max (v x,k ) represents the minimum safe heading angular velocity threshold at the current vehicle speed.

[0079] Maximum permissible sideslip angle β at different longitudinal vehicle speeds max (v x,k Maximum angular velocity r max (v x,k The critical profile formed by the boundary is used as the stability boundary. The closed area enclosed by the stability boundary is the vehicle stability domain, and the area outside the stability boundary is the region where the vehicle is prone to instability. Figure 2 and Figure 3 As shown, the stability characteristics of the vehicle under different conditions and speeds are intuitively presented: Figure 2 To compare the stability boundaries at different vehicle speeds, the β-r stability domain profiles for three speeds—50 km / h (blue dashed line), 80 km / h (red dashed line), and 110 km / h (green dashed line)—are shown. As the vehicle speed increases, the stability domain ellipse shrinks significantly, indicating that the allowable range of sideslip angle and yaw rate decreases under high-speed conditions, reducing the stability margin and making the vehicle more prone to instability.

[0080] Figure 3 This is a heatmap of the β-r stability margin at a vehicle speed of 50 km / h. The horizontal axis represents the sideslip angle β (in rad), and the vertical axis represents the yaw rate r (in rad / s). The central black dot represents the vehicle's equilibrium point. The stability level is represented by a color gradient: the central region is dark blue (high stability margin), transitioning outwards to reddish-yellow (low stability margin), with the outermost black dashed line representing the stability boundary. It can be seen that the vehicle has the highest stability margin near the equilibrium point, and the stability gradually decreases as the state point moves away from the equilibrium point and closer to the boundary, with the overall stability region being elliptical.

[0081] Overall, Figure 2 and Figure 3 It clearly reveals the distribution law of vehicle stability with sideslip angle and yaw rate, as well as the contraction effect of vehicle speed on the stability domain, providing an intuitive quantitative basis for vehicle active safety control (such as stability constraint design).

[0082] 2. State occupancy and stability margin

[0083] For the k-th discrete time, the longitudinal speed of the vehicle is known to be v. x,k By combining key conditions such as the vehicle's inherent parameters and the road surface adhesion coefficient, the limit boundary of the center of gravity sideslip angle that is permissible for vehicle dynamics at the current vehicle speed can be determined. With the yaw rate limit boundary .

[0084] Since the sideslip angle β and the yaw rate r have different dimensions, and their allowable boundaries change dynamically with vehicle speed, they cannot be directly compared or superimposed with constraints. Therefore, the state variables need to be dimensionlessly normalized to uniformly map the vehicle state at different speeds to the standard stability domain.

[0085] Define the normalized centroid side slip angle β norm With normalized yaw rate r norm : ; ; After normalization, it satisfies: |β norm |≤1,|r norm |≤1.

[0086] This operation can map the vehicle state at any speed to a unified dimensionless plane, completely eliminating dimensional differences and boundary changes caused by vehicle speed.

[0087] If only independent constraints |β norm |≤β max ,|r norm |≤r max This is equivalent to constructing a rectangular stable boundary, but the actual dynamic characteristics of the vehicle show that the sideslip angle and yaw rate are not completely independent. When one state variable approaches its limit, the safety margin of the other state variable will decrease synchronously. The rectangular boundary cannot reflect the coupling and occupancy relationship between the two.

[0088] To accurately characterize the stability occupancy under the combined effect of β and r, the stability domain at the current vehicle speed is approximated as an elliptic domain, and the standard equation in the normalized plane is: ; Substituting the normalized variables back, we obtain the elliptic stability region constraints in the physical plane: ; The ellipse , Using the long and short half-axis, it not only preserves the independent limit boundaries of the two state variables, but also quantifies the overall occupancy of the stability domain under the coupling effect of the two, perfectly matching the actual dynamic stability characteristics of the vehicle.

[0089] Based on the above analysis, a vehicle state occupancy model S is constructed using the stability domain: ; Among them: I k β represents the degree to which the vehicle state occupies the boundary of the stability region at the k-th discrete time; k Let be the centroid sideslip angle at the k-th discrete time. v is the heading angular velocity at the k-th discrete time; x,k Let β be the longitudinal speed of the vehicle body at the k-th discrete time; max (v x,k (v is the current vehicle speed) x,k Lower limit safe sideslip angle threshold; r max (v x,k ) represents the maximum safe heading angular velocity threshold at the current vehicle speed; M k Let be the stability margin of the vehicle's movement at the k-th discrete time.

[0090] When M k When M > 0, the vehicle state is within the stable region; k The larger the value of M, the farther the vehicle state is from the stability boundary, and the more sufficient the stability margin. k When M approaches 0, it indicates that the vehicle state is at the stability boundary; when M... k When <0, it indicates that the vehicle state has exceeded the stability domain corresponding to the current speed.

[0091] 3. State stability constraint formula

[0092] Integrating stability boundaries, vehicle speed constraints, and stability margin constraints, a complete state stability constraint F is formed. stab,state : ; Among them, v x,min v x,max These are the minimum and maximum speeds, respectively; M min This represents the minimum stability margin.

[0093] The vehicle state stability constraints constructed in this section use the centroid sideslip angle β and yaw rate r as the core state characterization quantities. Based on the vehicle dynamic stability boundary (β-r planar elliptical stability domain, the stability domain shrinks more significantly at higher vehicle speeds), a stability domain that dynamically changes with vehicle speed is established. By defining the stability domain occupancy degree and stability margin index, the stability redundancy of the vehicle state is quantified. Then, by integrating the amplitude limits of β and r, the vehicle speed operating range, and the minimum stability margin requirement, a closed-loop state stability constraint is formed to ensure that the vehicle is always within the dynamic stability domain during driving, avoiding sideslip or yaw instability, and providing rigid stability boundary constraints for trajectory planning.

[0094] (iv) Constructing vehicle control stability constraints

[0095] To avoid abrupt changes in control variables and actuator overload, amplitude and rate of change constraints are applied to the upper-level control variables based on state stability constraints, forming control stability constraints to ensure smooth trajectory and executable control.

[0096] 1. Curvature control quantity constraint (F) ρ )

[0097] Amplitude constraint: Limits the maximum curvature to avoid steering overload. ; ; in, , These are the maximum and minimum values ​​of the heading curvature control quantity; , These represent the maximum and minimum values ​​of the lateral curvature control quantity.

[0098] Rate of change constraint: Limits abrupt changes in curvature between adjacent time steps to ensure smooth turning. ; ; in, This is the heading curvature control quantity at the (k+1)th discrete time. The lateral curvature control quantity at the (k+1)th discrete time; This represents the maximum value of the change in heading curvature control. This represents the maximum value of the change in lateral curvature control.

[0099] 2. Longitudinal acceleration constraint (F) a )

[0100] Amplitude constraint: Limits acceleration and deceleration intensity to conform to vehicle dynamic performance. ; Among them, a x,min ax,max Let a be the minimum and maximum values ​​of the longitudinal command acceleration of the vehicle's center of gravity in the vehicle coordinate system. x,k Let be the longitudinal command acceleration of the vehicle's center of mass in the vehicle coordinate system at the k-th discrete moment.

[0101] Acceleration variation constraint: Suppressing sudden acceleration changes and improving ride comfort. ; Among them, a x,k+1 Let be the longitudinal command acceleration of the vehicle's centroid in the vehicle coordinate system at the (k+1)th discrete moment; The maximum value of the longitudinal command acceleration change of the vehicle's center of gravity in the vehicle coordinate system.

[0102] 3. Integration of stability control constraints

[0103] By combining the constraints on the magnitude and change of curvature and acceleration, we obtain the control stability constraint F. stab,ctrl =F ρ ∩F a .

[0104] All of the above inequalities are linear equations or inequalities, which can be directly embedded into MILP. By restricting the magnitude and variation of curvature control and longitudinal acceleration, the reference trajectory generated by the planning layer has better smoothness while satisfying environmental constraints, and also provides a more reasonable reference input for subsequent nonlinear model predictive control (NMPC) lateral and longitudinal coordinated tracking.

[0105] (v) The establishment and integration of global collaborative constraints

[0106] By combining the predictive spatial geometric safety constraints, vehicle state stability constraints, and vehicle control stability constraints across the entire domain, a global collaborative constraint adapted to 4WIS vehicle trajectory planning is formed: F all =F geo ∩F stab,state ∩F stab,ctrl .

[0107] (vi) Summary

[0108] This method for constructing a full-domain collaborative constraint for four-wheel independent steering vehicles builds a "environment-vehicle-control" multi-dimensional constraint system to meet trajectory planning needs. First, based on the vehicle's outer corner point model, road boundaries, static obstacles linearized by Minkowski expansion and Big-M logic constraints, and dynamic obstacles processed by uniform speed prediction and time-varying half-space constraints are uniformly transformed into predictive space geometric safety constraints. Then, a low-dimensional equivalent curvature kinematic model is constructed, and a linear state transition equation adapted to MILP solution is obtained through first-order Taylor linearization. Next, state stability constraints are constructed based on the β-r vehicle speed-related stability domain, and amplitude and rate of change constraints are applied to curvature and acceleration control quantities to form control stability constraints. Finally, the three types of constraints are combined to form a unified full-domain collaborative constraint, ensuring that the trajectory is collision-free, the state is stable, and the control is executable, providing a compliant and feasible domain boundary for subsequent trajectory optimization solutions.

[0109] II. Methods for Generating Predicted Driving Trajectory for Four-Wheel Independent Steering Vehicles

[0110] This method for generating predicted driving trajectories for four-wheel independent steering vehicles uses the global collaborative constraints of four-wheel independent steering vehicles as the boundary of the feasible domain. Based on the linear state transition relationship of the 4WIS equivalent curvature kinematics model, a trajectory planning optimization model is constructed and solved by mixed integer linear programming. Finally, the optimal predicted driving trajectory that satisfies environmental safety, vehicle stability, and smooth control is generated, providing a benchmark input for subsequent spatiotemporal safety corridor extraction and chassis control.

[0111] (a) Establishing a time-series recursive relationship for vehicle status

[0112] Based on the linear state transition equation constructed in this invention, and combined with the constraint conditions at each discrete moment in the global collaborative constraint, a temporal recursive logic for the vehicle state in the planning time domain is established: 1. The linear state transition equation is the core formula for trajectory recursion: The definitions of each parameter in the formula are completely consistent with those in the method for constructing global collaborative constraints for four-wheel independent steering vehicles, ensuring model coherence.

[0113] 2. Starting from the vehicle's initial state (The subscript init indicates the initial state) is used as the starting point for recursion. The process proceeds step-by-step according to a fixed discrete time step Δt, and the vehicle state vector z at the k-th discrete time step is... k With control vector u k Substituting into the linear state transition equation, we can obtain the vehicle state vector z at time k+1. k+1 .

[0114] 3. Each step of the recursive process is subject to the full-domain coordination constraint of a four-wheel independent steering vehicle. allStrict constraints are imposed to ensure that the recursive state sequence and control sequence are always within the feasible domain of environmental safety, vehicle stability, and control execution.

[0115] (II) Constructing a vehicle trajectory planning optimization model

[0116] To achieve the optimal balance between trajectory tracking accuracy, ride smoothness, operational stability, and geometric safety, a trajectory planning optimization model is constructed, incorporating five optimization objectives: trajectory tracking, control amplitude, control increment, stability, and safety margin. The total cost function J of the optimization model is a weighted sum of all sub-items. .

[0117] 1. Trajectory tracking item J trk

[0118] Used to constrain the deviation of the predicted state from the reference trajectory sequence in the time domain, ensuring that the planned trajectory conforms to the preset driving path: ; Where N is the total number of discrete moments in the trajectory planning time domain; ω trk These are the trajectory tracking weighting coefficients; , Let x be the reference lateral and longitudinal coordinates of the vehicle's centroid at the k-th discrete moment in the global coordinate system. Let be the reference heading angle of the vehicle at the k-th discrete time. Let be the reference sideslip angle of the vehicle at the k-th discrete time. Let be the longitudinal reference vehicle speed of the vehicle's centroid in the vehicle coordinate system at the k-th discrete moment.

[0119] 2. Control Amplitude Cost Item J mag

[0120] Used to suppress excessive longitudinal or lateral maneuvering forces and prevent chassis actuator overload: ; Among them, w u To control the amplitude weighting coefficient.

[0121] 3. Control the incremental cost term J Δu

[0122] Used to limit the amount of control change between adjacent time steps, thereby improving the smoothness of the trajectory and control: ; Where, ω Δu To control the incremental weighting coefficient; a x,k-1 Let be the longitudinal command acceleration of the vehicle's centroid in the vehicle coordinate system at the (k-1)th discrete moment; This represents the heading curvature control value at the (k-1)th discrete time. It represents the lateral curvature control quantity at the (k-1)th discrete time.

[0123] 4. Stability cost term J stab

[0124] Used to suppress unstable tendencies such as lateral slip and yaw, keeping the solution away from the unstable region: ; Among them, w stab This is the stability weighting coefficient.

[0125] 5. Safety Cost Item J safe

[0126] This is used to reward trajectories with high safety margins, thereby improving the safety redundancy of the planning results. ; Where, ω α For the safety cost weighting coefficient; α min This represents the minimum safe distance margin for vehicles.

[0127] (III) Minimizing the solution of the optimization model

[0128] Starting from the initial state of the vehicle, within the constraints of the global cooperative constraint of a four-wheel independent steering vehicle, a mixed integer linear programming solver is used to minimize the vehicle trajectory planning optimization model J, and the optimal solution is obtained time-by-time.

[0129] 1. Solve the input

[0130] Vehicle initial state vector z init Planning time-domain parameters, reference trajectory sequence, global collaborative constraints, and vehicle inherent parameters.

[0131] 2. Solving constraints

[0132] The entire process satisfies the global collaborative constraints.

[0133] 3. Solve and output

[0134] Global optimal state sequence: composed of the optimal state vectors at each discrete time step. Arranged sequentially, it contains the optimal values ​​of centroid coordinates, heading angle, centroid sideslip angle, and longitudinal speed; the optimal state vector combination at each discrete moment constitutes the global optimal state sequence. .

[0135] Global optimal control sequence: composed of the optimal control vectors at each discrete time step. Arranged sequentially, it contains the optimal values ​​of longitudinal command acceleration, directional curvature control, and lateral curvature control; the optimal control vector combination at each discrete moment constitutes the global optimal control sequence. .

[0136] (iv) Fitting and generating the optimal predicted driving trajectory

[0137] A smooth fit is performed on the discrete optimal sequence obtained from solving mixed-integer linear programming to generate a time-continuous optimal predicted driving trajectory and control commands: Interpolation and smoothing fitting are performed on the optimal state sequence of the entire domain. The centroid coordinates, heading angle, centroid sideslip angle and longitudinal vehicle speed at discrete time points are continuously spliced ​​together to obtain the optimal predicted driving trajectory of the vehicle covering the planning time domain. The trajectory contains continuous change information of position, attitude and vehicle speed.

[0138] The optimal control sequence across the entire domain is subjected to time-series fitting to generate a continuous control command sequence that adapts to the execution logic of the chassis actuators of a four-wheel independent steering vehicle, ensuring that the control commands are free from abrupt changes and can be directly issued and executed.

[0139] Methods for constructing spatiotemporal safety corridors for three- and four-wheel independent steering vehicles

[0140] This method for constructing a spatiotemporal safety corridor for four-wheel independent steering vehicles, based on the optimal predicted driving trajectory and the vehicle's external geometric features, transforms the non-convex obstacle avoidance logic obtained by solving mixed integer linear programming into a convex spatiotemporal safety region. This provides a collision-free, directly solvable convex constraint feasible region for subsequent nonlinear model predictive control, avoiding the repeated introduction of integer variables for solution in the control layer.

[0141] (a) The corner points of the vehicle outline are enlarged proportionally.

[0142] Using the vehicle's center of gravity as a reference, a globally fixed safety redundancy coefficient is used to proportionally enlarge the vehicle's outer corner points, reserving sufficient safety margin: 1. Extract the position vectors c of the four outer corner points of the vehicle relative to the centroid at time k. i,k =P gcs,i,k -P gcs,k (i=1,2,3,4, corresponding to the left front, right front, left back, and right back corner points).

[0143] 2. Set a global fixed safety redundancy factor α safe ≥1, the position vector is scaled up proportionally to obtain the magnified global coordinates of the corner point: .

[0144] The magnified corner coordinates ensure that no collision will occur during actual vehicle operation, even if there are tracking errors.

[0145] (ii) Transform into centroid linear inequality constraints

[0146] Substituting the amplified corner constraints into the predicted spatial geometric safety constraints, and utilizing the fixed geometric relationship between the centroid and the corners, the corner-level constraints are transformed into centroid linear inequality constraints with the global coordinates of the vehicle's centroid as the core variable: ; in, P is the constraint transformation coefficient matrix for the i-th vehicle corner point at the k-th discrete time, used to map the global coordinate constraints of the vehicle corner point to linear constraints of the vehicle centroid coordinates; gcs,k Let be the global coordinate vector of the vehicle's centroid at the k-th discrete time. α is the constraint boundary margin threshold for the i-th vehicle corner point at the k-th discrete time, used to limit the boundary limit range of the vehicle's passable area; safe c is the global fixed safety redundancy coefficient; i,k Let be the position vector of the i-th vehicle corner point relative to the centroid at the k-th discrete time.

[0147] The centroid linear inequality constraint is in a purely linear form and can be directly embedded into the optimization framework of subsequent nonlinear model predictive control without having to deal with non-convex logic and integer variables.

[0148] (III) Solving for the feasible region of a planar convex polygon at a single time step

[0149] Based on the centroid linear inequality constraint, the solution is obtained on the optimal predicted trajectory obtained by the four-wheel independent steering vehicle prediction trajectory generation method, resulting in a single discrete-time planar convex polygon feasible region S enclosing the vehicle's centroid. k : 1. Feasible region S of a planar convex polygon k It is the intersection of linear constraints, belongs to a convex set, and satisfies the convex optimization solution requirements of nonlinear model predictive control.

[0150] 2. Feasible region S of a planar convex polygon k The safe positions for the vehicle's center of mass to move at the k-th discrete time are defined. If the center of mass is located within this region, the vehicle's outline will not collide or cross the boundary.

[0151] (iv) The temporal splicing forms a spatiotemporal safety corridor

[0152] The feasible regions of single-time planar convex polygons corresponding to all discrete moments in the planning time domain are sequentially spliced ​​along the time axis to form a continuous safe region that combines spatial boundaries and temporal correlation. This region is the spatiotemporal safety corridor for four-wheel independent steering vehicles. 1. The mathematical expression of the spatiotemporal safety corridor is: It covers all discrete moments within the planned time domain.

[0153] 2. The spatiotemporal safety corridor transforms the original complex non-convex obstacle avoidance problem into a convex region constraint that only requires constraining the position of the centroid in the subsequent nonlinear model predictive control. The control layer only needs to ensure that the vehicle's centroid is within the corridor section at the corresponding moment to achieve collision-free safe driving throughout the entire process.

[0154] 3. The spatiotemporal safety corridor perfectly matches the optimal predicted driving trajectory while retaining sufficient geometric safety margin, balancing trajectory tracking accuracy and driving safety.

[0155] like Figure 4 The spatiotemporal safety corridor for a four-wheel independent steering vehicle is presented in a three-dimensional coordinate system: the x and y axes represent the planar road position, and the t axis represents the time dimension; the transparent green cuboids are the single-time planar convex polygon safe feasible regions at different times (t0, t1, t2, t3, t4) within the planning time domain, which are sequentially spliced ​​along the time axis to form a continuous spatiotemporal safety corridor, defining the collision-free spatial boundary of the vehicle's center of mass at each time; the red straight line is the optimal predicted trajectory (center of mass reference path) obtained by solving the mixed integer linear programming (MILP) of the planning layer, and the colored gradient curve is the two-dimensional planar projection of the trajectory, intuitively showing its position change on the road plane; the black lines are the road boundaries, which limit the spatial range of the corridor. Figure 4 The spatiotemporal safety corridor clearly demonstrates how it transforms the original non-convex obstacle avoidance problem into a convex region constraint that can be directly handled by the control layer. This ensures that the vehicle's center of gravity is within the corresponding feasible region at each moment, achieving collision-free safe driving throughout the entire process. At the same time, it takes into account both trajectory tracking accuracy and safety redundancy, providing a unified safety boundary guarantee for the planning and control layers.

[0156] IV. A Coordinated Lateral and Longitudinal Control Method Based on Nonlinear Model Predictive Control for Four-Wheel Independent Steering Vehicles

[0157] This four-wheel independent steering vehicle employs a nonlinear model predictive control-based lateral and longitudinal coordinated control method. Based on the optimal discrete trajectory and control sequence obtained by the aforementioned four-wheel independent steering vehicle predictive trajectory generation method, and the spatiotemporal safety corridor obtained by the four-wheel independent steering vehicle spatiotemporal safety corridor construction method, a nonlinear model predictive controller without integer variables is constructed to undertake closed-loop trajectory tracking and local error correction tasks. Under the constraints of the spatiotemporal safety corridor and the stability boundary constraints that vary with vehicle speed, the longitudinal acceleration, yaw curvature, and side-shift curvature are optimized by rolling to achieve coordinated control of longitudinal speed adjustment and lateral and yaw maneuvers. This approach balances trajectory tracking accuracy, vehicle driving stability, and control smoothness. Furthermore, the upper-level curvature control quantity is mapped to wheel-level steering angle commands, directly driving the four-wheel independent steering chassis actuators, thus completing the full-link control closed loop from the planning layer to the chassis execution layer.

[0158] (I) Constructing a nonlinear model for predictive control problems

[0159] This section constructs a nonlinear model predictive control optimization problem adapted to four-wheel independent steering vehicles, using the same model and state and control variable definitions as the planning layer, and achieving closed-loop tracking under spatiotemporal safety corridor and stability boundary constraints.

[0160] 1. Definitions of State Variables and Control Variables

[0161] To ensure model consistency between the trajectory planning layer and the control layer, the nonlinear model predictive control uses the state and control variables defined in the aforementioned method for constructing global cooperative constraints for four-wheel independent steering vehicles: The vehicle state vector at the k-th discrete moment: ; The vehicle control vector at the k-th discrete time step: .

[0162] This cooperative control method uses the optimal state sequence obtained by the aforementioned predicted driving trajectory generation method. With optimal control sequence Using the reference input, rolling optimization is performed within the prediction time domain to achieve closed-loop tracking and error correction of the optimal trajectory.

[0163] 2. Nonlinear prediction model

[0164] This cooperative control method uses the multi-mode kinematic model based on curvature representation derived in the aforementioned method for constructing full-domain cooperative constraints for four-wheel independent steering vehicles as the nonlinear prediction model. Its continuous form is as follows: ; Where f(z, u) is the nonlinear right-hand side function of the 4WIS equivalent curvature kinematic model, specifically in the form of: ; With a discrete step size of Δt for nonlinear model predictive control, the continuous model is discretized using the explicit Euler method to obtain a discrete form of the predictive model: The prediction model is completely consistent with the nonlinear discrete state update equation before linearization of the planning layer, ensuring the model homogeneity between the planning layer and the control layer and avoiding tracking errors introduced due to model differences.

[0165] 3. Stability Boundary Constraints

[0166] To avoid instability risks caused by sudden changes in the centroid sideslip angle β and yaw rate r in pursuit of trajectory tracking accuracy, this cooperative control method explicitly incorporates speed-dependent stability boundary constraints into the nonlinear predictive model predictive control: ; in, , The vehicle state stability constraint defined in the aforementioned method for constructing vehicle state stability constraints, which varies with vehicle speed v x,k Dynamically changing limit stability boundary; under low-speed parking or reversing conditions, v can be set... x,k < 0 and allow Increase it appropriately, and the stability boundary function according to |v x,k The evaluation showed that the boundary constraints are more relaxed under low-speed conditions, which is suitable for low-speed maneuvering requirements.

[0167] 4. Spatiotemporal safety corridor constraints

[0168] In this cooperative control method, instead of repeatedly introducing integer variables for obstacle avoidance in nonlinear model predictive control, the vehicle's centroid is directly constrained to lie within the corridor section at the corresponding time in the prediction time domain. This constraint transforms the original non-convex obstacle avoidance problem into a convex region constraint in the prediction time domain, achieving collision-free control without the introduction of integer variables, and significantly improving the continuity and efficiency of closed-loop tracking solution.

[0169] 5. Nonlinear Model Predictive Control Optimization Objective Function

[0170] Using the optimal state sequence and optimal control sequence obtained by the aforementioned predicted driving trajectory generation method as the tracking target, a weighted cost function H in the prediction time domain is constructed. By minimizing H, a trade-off is achieved between tracking accuracy, control smoothness, and stability. ; Where, N c To control the number of discrete time points in the prediction time domain; n is the step size index in the prediction time domain.

[0171] z k+n The predicted state vector at the (k+n)th discrete time in the time domain is defined as follows: This includes vehicle position, heading angle, center of gravity sideslip angle, and longitudinal speed. is the reference state vector at step k+n, which is the globally optimal state sequence generated by MILP and serves as the reference target for the state variables. Q is the weight matrix for state tracking, used to penalize the deviation between the predicted state and the reference state; the larger the diagonal elements in Q, the higher the required tracking accuracy for the corresponding state variables (such as position and vehicle speed). It is a weighted L2 norm used to quantify the deviation between the predicted trajectory and the reference trajectory.

[0172] u k+n The predictive control vector for the (k+n)th discrete time in the time domain is defined as follows: It includes longitudinal acceleration, directional curvature, and lateral curvature. is the reference control vector at step k+n, which is the globally optimal control sequence generated by MILP and serves as the reference target for the control input. R is the weight matrix for the control amplitude, used to penalize the degree to which the control input deviates from the reference control sequence; the larger R is, the closer the control action is to the setting of the planning layer, avoiding large-amplitude control. It is a weighted L2 norm used to quantify the deviation between predictive control and reference control.

[0173] Δu k+n To predict the control increment at the (k+n)th discrete time in the time domain, reflecting the drastic change in the control quantity, S is the weight matrix of the control increment, used to penalize abrupt changes in the control quantity; the larger S is, the smoother the control action, but the response speed will decrease accordingly. It is a weighted L2 norm used to quantify the rate of change of control actions.

[0174] r k+n Yaw rate is a core indicator for predicting the yaw rate at the (k+n)th discrete moment in the time domain. An excessively large yaw rate can lead to vehicle instability. The centroid sideslip angle is a core indicator of vehicle stability, used to predict the (k+n)th discrete time step in the time domain. An excessively large angle can lead to sideslip or loss of control. ω r As the stability penalty weight for yaw rate, ω r The larger the value, the stronger the controller's suppression of yaw rate exceeding the limit. ω β ω is the stability penalty weight for the centroid sideslip angle. β The larger the value, the stronger the controller's suppression of excessive centroid sideslip angle.

[0175] The first term tracks the reference state sequence generated by the mixed-integer linear programming to ensure trajectory tracking accuracy. The second term constrains the degree to which the control input deviates from the reference control sequence, preventing the control quantity from deviating significantly from the planning layer settings. The third term suppresses abrupt changes in control quantity between adjacent time steps, improving control smoothness. The latter two terms further penalize excessive yaw rate and sideslip angle, enhancing driving stability. When trajectory tracking error conflicts with stability constraints, the controller can appropriately sacrifice some tracking accuracy, prioritizing the suppression of excessive yaw and sideslip responses to ensure vehicle driving safety.

[0176] In summary, nonlinear model predictive control reads the current vehicle state, reference trajectory sequence, and corresponding spatiotemporal safety corridor in each control cycle, solves for the optimal control sequence in the prediction time domain, and applies only the first control variable; then it enters the next control cycle, and performs rolling optimization again with the new vehicle state as the initial value, so as to achieve closed-loop tracking and error correction of the reference trajectory.

[0177] (II) Realization of Horizontal and Vertical Coordinated Control

[0178] This collaborative control method uses a unified optimization framework of nonlinear model predictive control to simultaneously determine the control quantities of longitudinal acceleration, yaw curvature, and lateral displacement curvature, thereby achieving collaborative control of longitudinal speed regulation and lateral and yaw maneuvers. This solves the stability problem caused by the decoupling of longitudinal and lateral directions in traditional hierarchical control.

[0179] 1. Cooperative control logic

[0180] When the reference trajectory requires large curvature maneuvers in a local area, but the current vehicle speed is high and the stability boundary is tightened, the controller uses a coordinated strategy of "longitudinal speed reduction + lateral curvature redistribution" to reduce the vehicle speed to expand the stability domain boundary while adjusting the distribution ratio of yaw curvature and side slip curvature. This avoids the center of gravity sideslip angle or yaw rate exceeding the stability boundary by simply increasing the steering curvature, thus achieving safe maneuvering under high-speed conditions.

[0181] 2. Scrolling optimization control process

[0182] The rolling optimization process within each control cycle is as follows: Status Reading: Obtain the current actual status z of the vehicle. k And read the reference state sequence in the prediction time domain. Reference control sequence And the corresponding spatiotemporal safety corridor section constraint parameters at that time.

[0183] Optimization solution: Based on the current vehicle state z k Using the initial values, a sequential quadratic programming approach is used to iteratively solve the above nonlinear constrained optimization problem, yielding the optimal control sequence in the prediction time domain. ; Control execution: Apply only the first control variable in the optimal control sequence. To the chassis execution layer; Cyclic loop: In the next control cycle, the above steps are repeated to achieve rolling optimization and closed-loop control.

[0184] Since the spatiotemporal safety corridor has solidified the obstacle avoidance "OR logic" decision of the planning layer into a convex region constraint, the nonlinear model predictive control inner layer no longer has the control discontinuity problem caused by "side-switching or path-switching"; at the same time, the corridor constraint is composed of the intersection of half space, and the four outer corner points of the vehicle can be directly used for constraint verification during online collision detection, so as to achieve fast and efficient collision detection verification.

[0185] (III) Wheel-level rotation angle allocation and execution instruction generation

[0186] The output of nonlinear model predictive control is the curvature layer control quantity (heading curvature, lateral curvature) and longitudinal acceleration command. This method uses a multimodal unified mapping relationship to map the upper curvature control quantity into wheel-level steering angle commands that can be directly executed by the four-wheel independent steering chassis, thus completing the control closed loop.

[0187] 1. Calculation of equivalent rotation angles of front and rear axles

[0188] Based on the mapping relationship of the aforementioned 4WIS multi-mode kinematic model, the equivalent front and rear axle rotation angles are calculated from the heading curvature and lateral curvature: ; ; Where, δ f δ r These are the equivalent front axle rotation angle and rear axle rotation angle, respectively, and L is the wheelbase between the front and rear axles.

[0189] 2. Four-wheel steering angle geometry distribution

[0190] Based on the geometric relationship O between the equivalent axle rotation angle and the four wheel rotation angles, the equivalent rotation angles of the front and rear axles are allocated to the four wheels: left front, right front, left rear, and right rear. To avoid steering conflicts between the left and right wheels and reduce the wheel-level allocation dimension, this cooperative control method adopts symmetrical allocation (parallel steering) as the default strategy, that is, the rotation angles of the left and right wheels on the same axle are equal.

[0191] ; Where, δ fl δ fr δ rl δ rr These are the steering angle commands for the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively.

[0192] 3. Actuator limiting and command issuance

[0193] The calculated four-wheel steering angle commands are subject to amplitude and rate-of-change constraints imposed by the steering actuators to prevent exceeding the physical limits of the steering mechanism. Simultaneously, execution constraints from the power system are applied to the longitudinal acceleration commands, ultimately generating four-wheel steering angle and longitudinal acceleration commands that can be directly sent to the chassis actuators. In scenarios requiring further improvement in tire side-slip characteristics and geometric consistency, a small left-right differential correction can be superimposed on the symmetrical allocation. This correction is merely a fine-tuning of the wheel-level execution layer and does not alter the unified curvature decision structure of the upper-level nonlinear model predictive control.

[0194] V. Simulation Experiments and Performance Verification

[0195] To verify the effectiveness of the four-wheel independent steering vehicle global collaborative constraint construction, predicted driving trajectory generation, spatiotemporal safety corridor construction, and lateral and longitudinal collaborative control method described in this invention, simulation experiments were conducted based on typical urban complex traffic conditions to complete the full verification from five dimensions: vehicle parameters, experimental scenarios, comparison methods, evaluation indicators, and experimental results.

[0196] (I) Experimental Platform and Vehicle Core Parameters

[0197] This simulation experiment uses uniform vehicle parameters and actuator constraints to ensure the fairness of the comparative experiment. The core parameters are shown in Table 1.

[0198] Table 1 Vehicle Parameter Settings

[0199] (II) Simulation Experiment Scenario Setting

[0200] This invention sets up a typical obstacle avoidance scenario in urban mixed traffic, covering the core operating conditions of urban roads. The scenario is described as follows: Starting from the initial lane, the vehicle needs to complete a series of actions within a limited road space, including static obstacle avoidance, dynamic obstacle avoidance, lane return, and reaching the target point. The scenario includes road boundary constraints, static fixed obstacles, and dynamic moving obstacles, fully reproducing the complex unstructured traffic environment of the city.

[0201] (III) Comparative Experiment Method Setup

[0202] To highlight the advantages of the method of this invention, a classic method in the field of autonomous driving is selected as a comparison, and the comparison methods are shown in Table 2.

[0203] Table 2 Comparison Methods

[0204] (iv) Experimental Results and Analysis

[0205] The experimental results of the three methods in urban mixed traffic obstacle avoidance scenarios are shown in Table 3.

[0206] Table 3 Experimental Results of Obstacle Avoidance Scenario in Urban Mixed Traffic

[0207] Table 3 shows the comprehensive performance comparison results of the method described in this invention with two mainstream 4WIS vehicle trajectory planning and control methods across all dimensions, covering four core evaluation dimensions: traffic efficiency, geometric safety, vehicle stability, and control smoothness. This comprehensively verifies the overall technical advantages of the method described in this invention. From the data comparison, the method described in this invention achieves superior performance across all four dimensions compared to the comparison methods: In terms of traffic efficiency, the method described in this invention has a travel time of only 16 seconds, 20% shorter than the comparison methods, while maintaining a path length roughly the same, significantly improving traffic efficiency in complex scenarios without increasing path redundancy; in terms of geometric safety, the method described in this invention has a minimum obstacle distance of 0.254m, avoiding both the extreme close-range collision risk of 0.0215m in the Frenet+4WIS-MPC method and the risk of collisions like those in the HybridA method. The +4WIS-LMPC method, which is overly conservative and leaves redundancy, achieves an optimal balance of "safety without being conservative." The minimum road boundary distance of 0.365m fully meets road constraints, eliminating the risk of exceeding limits. Regarding vehicle stability, the method of this invention has the lowest maximum yaw rate (0.170 rad / s) and maximum center-of-gravity sideslip angle (0.021 rad) among the three methods. It also has the lowest average stability index and the highest minimum stability margin (0.977), indicating that the vehicle remains in the center of the β-r stability domain throughout the entire journey, with sufficient stability margin, significantly reducing the risk of yaw and sideslip instability. In terms of control smoothness and actuator load, the method of this invention has a maximum wheel rotation angle of only 0.0698 rad, which is 32%~48.8% of the comparative methods, significantly reducing the workload of the steering actuator. At the same time, the maximum acceleration (3.0 m / s²) and maximum jerk (4.0 m / s³) are far lower than the comparative methods, with the jerk only 28.8%~29.5% of the comparative methods, effectively suppressing acceleration abrupt changes, significantly improving ride comfort, and avoiding frequent large movements of the power and steering systems. Overall, the method of this invention, through the full-link solution of MILP safe trajectory generation, spatiotemporal safe corridor constraints, and NMPC lateral and longitudinal collaborative control, perfectly adapts to the multi-mode maneuvering characteristics of 4WIS vehicles, and solves the core pain points of traditional methods in complex urban scenarios, such as conservative obstacle avoidance, insufficient stability, and large control fluctuations.

[0208] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for constructing state stability constraints for a four-wheel independent steering vehicle, characterized in that, The following are the construction steps: Based on the centroid sideslip angle β and heading angular velocity r, which characterize the vehicle state, the critical profile formed by the maximum allowable sideslip angle and the maximum heading angular velocity at different vehicle speeds is used as the stable boundary. The internal closed region enclosed by the stable boundary constitutes the stable domain. A vehicle state occupancy model S is constructed using the stability domain: ； Among them, I k β represents the degree to which the vehicle state occupies the boundary of the stability domain at the k-th discrete time; k Let r be the centroid sideslip angle at the k-th discrete time step; k v is the heading angular velocity at the k-th discrete time; x,k Let β be the longitudinal speed of the vehicle body at the k-th discrete time; max (v x,k (v is the current vehicle speed) x,k Lower limit safe sideslip angle threshold; r max (v x,k ) represents the maximum safe heading angular velocity threshold at the current vehicle speed; M k Let be the stability margin of the vehicle's movement at the k-th discrete time. Based on S and the vehicle's center of gravity operating state, construct vehicle state stability constraints: ； Among them, v x,min v x,max These are the minimum and maximum speeds, respectively; M min This represents the minimum stability margin.

2. A method for constructing global cooperative constraints for a four-wheel independent steering vehicle, characterized in that, The following are the construction steps: Obtain the road boundary constraints, static obstacle constraints, and dynamic obstacle constraints of the vehicle within the planning time domain, and denote the intersection of the three as the predicted spatial geometric safety constraints; Based on the vehicle's center of mass position, heading angle, sideslip angle, and vehicle speed, an equivalent curvature kinematic model F of the vehicle is constructed; F is linearized and decoupled to separate the vehicle state variables and control variables. Based on the vehicle state variables, the method for constructing the state stability constraints of a four-wheel independent steering vehicle as described in claim 1 is executed to construct the vehicle state stability constraints. Based on the vehicle state stability constraints, vehicle control stability constraints are added based on vehicle control variables, and threshold ranges are limited for directional curvature, lateral curvature, longitudinal acceleration, and the changes of these three variables. By combining the predictive spatial geometric safety constraints, vehicle state stability constraints, and vehicle control stability constraints, a global collaborative constraint adapted to four-wheel independent steering vehicles is constructed.

3. The method for constructing global cooperative constraints for a four-wheel independent steering vehicle according to claim 2, characterized in that, The process for obtaining the sub-constraints in the predicted spatial geometrical security constraints is as follows: Road boundary constraints: Model the original road boundary as a linear half-space constraint. ; This causes the original road boundary to shrink inward by a safe distance d. safe,road The road safety feasible region constraint is obtained. ; Based on the linearized relationship of vehicle corner points Transforming linear half-space constraints into road boundary constraints ; Among them, C r d is the matrix consisting of the normal vectors corresponding to all road boundaries of the vehicle travel segment within the planning time domain; p is the coordinate vector of any point in the global coordinate system; d r P is a vector consisting of the intercepts of all road boundaries corresponding to the vehicle travel segments within the planning time domain; 1 represents a vector of all 1s with the same number dimension as the road boundaries; gcs,i,k Let A be the global coordinates of the i-th vehicle corner point at the k-th discrete time. i,k Let z be the Jacobian matrix of the vehicle state at the i-th vehicle corner point at the k-th discrete time; k c is the vehicle state vector at the k-th discrete time step; i,k Let be the position vector of the i-th vehicle corner point relative to the centroid at the k-th discrete time. Static obstacle boundary constraints: The j-th static obstacle is modeled as a convex polygon, and Minkowski dilation is used to expand the static safety distance, resulting in the half-space constraint of the restricted area of ​​the expanded static obstacle. Combined with the linearization relationship of vehicle corner points, a binary variable is introduced. With Big-M coefficient M sta Construct static obstacle separation constraints Simultaneously apply constraints ; in, For the j-th static obstacle convex polygon, the l-th... sta The normal vector of the edge; For the j-th static obstacle convex polygon, the l-th... sta The intercept corresponding to the edge; For the Big-M logic control of the i-th vehicle corner point at the k-th discrete time, for the j-th static obstacle convex polygon, the l-th... sta A 0-1 binary variable representing whether the edge constraint is effective or not; For static obstacles, the safety margin; L j Let be the total number of sides of the j-th static obstacle convex polygon; Dynamic obstacle boundary constraints: Dynamic obstacles are pre-modeled as equivalent convex polygons with fixed contours, which only translate as a whole with the predicted position, forming instantaneous convex polygon boundaries at each discrete moment; a uniform linear motion model is used to predict the position of the m-th dynamic obstacle at the k-th discrete moment. ; Perform safety distance expansion on dynamic obstacles after the predicted position to obtain the half-space constraint of the dynamic obstacle no-entry zone. Combined with the linearization relationship of vehicle corner points, a binary variable is introduced. With Big-M coefficient M dyn Constructing dynamic obstacle prediction and obstacle avoidance constraints ; in, Let m be the initial global position of the m-th dynamic obstacle; Let t be the uniform velocity vector of the m-th dynamic obstacle; k To plan the k-th discrete time point in the time domain; The matrix is ​​formed by the normal vectors corresponding to all boundaries of the m-th dynamic obstacle convex polygon after it has been translated to the predicted position at the k-th discrete time. The vector is formed by the intercepts of all boundaries of the m-th dynamic obstacle convex polygon after it has been translated to the predicted position at the k-th discrete time. For the Big-M logic control of the i-th vehicle corner point at the k-th discrete time, for the m-th dynamic obstacle convex polygon, the l-th... dyn A 0-1 binary variable representing whether the edge constraint is effective or not; For the m-th dynamic obstacle convex polygon at the k-th discrete time, the l-th... dyn The normal vector of the edge; For the m-th dynamic obstacle convex polygon at the k-th discrete time, the l-th... dyn The intercept of the strip; This refers to the safety margin for dynamic obstacles.

4. The method for constructing global cooperative constraints for a four-wheel independent steering vehicle according to claim 2, characterized in that, The specific steps for constructing an equivalent curvature kinematic model of the vehicle and separating the vehicle state variables and control variables are as follows: Based on the vehicle's center of mass position (X,Y) and heading angle Side slip angle β and vehicle longitudinal speed v x Construct the vehicle's equivalent curvature kinematic model F: ； Where X and Y are the lateral and longitudinal coordinates of the vehicle's center of mass in the global coordinate system; This represents the lateral velocity component of the vehicle's center of mass in the global coordinate system. v represents the longitudinal velocity component of the vehicle's center of mass in the global coordinate system. x The longitudinal velocity of the vehicle's center of mass in the vehicle coordinate system; Let be the actual longitudinal acceleration of the vehicle's center of mass in the vehicle coordinate system; cos, sin, and tan are the cosine, sine, and tangent functions, respectively. For heading curvature control; This represents the rate of change of the vehicle's sideslip angle. This is the lateral curvature control value; a x The longitudinal command acceleration of the vehicle's center of mass in the vehicle coordinate system; First-order Taylor linearization and decoupling are performed on F to decompose the coupled nonlinear motion relationship, and the vehicle state variables and control variables that can be quantized and constrained independently are separated, forming a linear state transition equation: ； ； ； ； ； ； Among them, z k z k+1 Let A be the vehicle state vector at the k-th and k+1-th discrete times; k B is the state transition matrix at the k-th discrete time step; k Let u be the control input matrix at the k-th discrete time step; k c is the vehicle control vector at the k-th discrete time step; k Δt is the linearization bias compensation term at the k-th discrete time step; I is the identity matrix; Δt is the discrete time step. , For the linearized reference point at the kth and k+1th discrete times, denoted as the nominal state vector; The nominal control vector for the linearized reference point at the k-th discrete time step; Let the state be the Jacobian matrix; To control the Jacobian matrix; X k Y k Let x be the horizontal and vertical coordinates of the vehicle's centroid at the k-th discrete moment in the global coordinate system. Let β be the heading angle of the vehicle at the k-th discrete time; k v is the vehicle's sideslip angle at the k-th discrete time; x,k Let be the longitudinal velocity of the vehicle's centroid in the vehicle coordinate system at the k-th discrete time; the superscript T denotes vector transpose; a x,k Let be the longitudinal command acceleration of the vehicle's center of mass in the vehicle coordinate system at the k-th discrete moment; This represents the heading curvature control value at the k-th discrete time. Let be the lateral curvature control quantity at the k-th discrete time.

5. A method for generating a predicted driving trajectory for a four-wheel independent steering vehicle, characterized in that, The following generation steps are included: Based on the global cooperative constraint construction method for four-wheel independent steering vehicles as described in claim 4, vehicle state variables, control variables, and linear state transition equations are constructed, and a time-series recursive relationship of vehicle state between discrete moments is established. Based on the recursive relationship of vehicle state time sequence, a vehicle trajectory planning optimization model is constructed regarding vehicle state variables and control variables; Under the premise of satisfying the global collaborative constraints, the vehicle trajectory planning optimization model is minimized numerically to obtain the global optimal state sequence consisting of the vehicle's centroid position, heading angle, sideslip angle, and longitudinal speed in the planning time domain, as well as the global optimal control sequence consisting of longitudinal command acceleration, heading curvature, and lateral curvature. The optimal predicted driving trajectory of the vehicle is then fitted and generated in the planning time domain.

6. The method for generating a predicted driving trajectory for a four-wheel independent steering vehicle according to claim 5, characterized in that, The specific vehicle trajectory planning optimization model J is as follows: ； Among them, J trk For trajectory tracking; J mag To control the amplitude cost term; J Δu To control the incremental cost term; J stab J represents the stability cost term; safe For safety costs; ； Where N is the total number of discrete moments in the trajectory planning time domain; ω trk These are the trajectory tracking weighting coefficients; , Let x be the reference lateral and longitudinal coordinates of the vehicle's centroid at the k-th discrete moment in the global coordinate system. Let be the reference heading angle of the vehicle at the k-th discrete time. Let be the reference sideslip angle of the vehicle at the k-th discrete time. Let be the longitudinal reference vehicle speed of the vehicle's centroid in the vehicle coordinate system at the k-th discrete moment; ； Among them, w u To control the amplitude weighting coefficient; ； Where, ω Δu To control the incremental weighting coefficient; a x,k-1 Let be the longitudinal command acceleration of the vehicle's centroid in the vehicle coordinate system at the (k-1)th discrete moment; This represents the heading curvature control value at the (k-1)th discrete time. This represents the lateral curvature control value at the (k-1)th discrete time. ； Among them, w stab This is the stability weighting coefficient; ； Where, ω α For the safety cost weighting coefficient; α min This represents the minimum safe distance margin for vehicles.

7. The method for generating a predicted driving trajectory for a four-wheel independent steering vehicle according to claim 5, characterized in that, Starting with the initial state of the vehicle, and relying on the temporal recursive relationship of the vehicle state, the vehicle trajectory planning optimization model is minimized within the constraints of global collaborative constraints. For each discrete moment in the planning time domain, the optimal discrete state quantity and optimal discrete control quantity are solved one-to-one. The optimal discrete state quantity corresponding to the k-th discrete moment includes the vehicle's centroid coordinates, heading angle, centroid sideslip angle, and longitudinal vehicle speed at that moment. The optimal discrete state quantities at all discrete moments are arranged in temporal order to form the global optimal state sequence. The optimal discrete control quantity corresponding to the k-th discrete moment includes the longitudinal command acceleration, heading curvature control quantity, and lateral curvature control quantity at that moment. The optimal discrete control quantity at all discrete moments is arranged in temporal order to form the global optimal control sequence. Interpolation and smoothing fitting are performed on the optimal state sequence of the entire domain. The vehicle centroid coordinates, heading angle, centroid sideslip angle and longitudinal vehicle speed at each discrete time are continuously spliced ​​together to generate the optimal predicted driving trajectory of the vehicle with a continuous time sequence. At the same time, the optimal control sequence of the entire domain is subjected to time-series fitting processing to obtain a continuous control command sequence that is time-series continuous and adapted to the execution logic of the vehicle chassis actuator.

8. A method for constructing a spatiotemporal safety corridor for a four-wheel independent steering vehicle, characterized in that, The following are the construction steps: Using the vehicle's center of mass as a reference, the position vectors of the four corner points of the vehicle relative to the center of mass are enlarged proportionally to obtain the enlarged global coordinates of the four corner points. The predicted spatial geometric safety constraint is constructed by substituting the global coordinates of the four corner points into the global collaborative constraint construction method for four-wheel independent steering vehicles as described in any one of claims 2-4. Based on the positional relationship between the vehicle's center of mass and the four corner points, the predicted spatial geometric safety constraint is transformed into a center of mass linear inequality constraint with the global coordinates of the vehicle's center of mass as the core variable. Based on the centroid linear inequality constraint, the feasible region of the planar convex polygon enclosing the centroid of the vehicle is obtained from the optimal predicted driving trajectory generated by the four-wheel independent steering vehicle prediction driving trajectory generation method in any one of claims 5-7. The feasible regions of planar convex polygons corresponding to all discrete moments in the planning time domain are sequentially spliced ​​along the time axis to form a continuous safe region that combines spatial boundaries and temporal correlation. This continuous safe region is the spatiotemporal safety corridor.

9. A method for constructing a spatiotemporal safety corridor for a four-wheel independent steering vehicle according to claim 8, characterized in that, The centroid linear inequality constraint is: ； in, P is the constraint transformation coefficient matrix for the i-th vehicle corner point at the k-th discrete time, used to map the global coordinate constraints of the vehicle corner point to linear constraints of the vehicle centroid coordinates; gcs,k Let be the global coordinate vector of the vehicle's centroid at the k-th discrete time. α is the constraint boundary margin threshold for the i-th vehicle corner point at the k-th discrete time, used to limit the boundary limit range of the vehicle's passable area; safe c is the global fixed safety redundancy coefficient; i,k Let be the position vector of the i-th vehicle corner point relative to the centroid at the k-th discrete time.

10. A four-wheel independent steering vehicle intelligent planning and control system, characterized in that, The method for constructing a spatiotemporal safety corridor for a four-wheel independent steering vehicle as described in claim 8 or 9 includes a vehicle body, an environmental perception module, a vehicle constraint modeling module, a trajectory optimization planning module, a spatiotemporal safety corridor construction module, and a vehicle control execution module. The environmental perception module is used to collect environmental information such as road boundaries, moving and static obstacles, and the vehicle's own driving status parameters; The vehicle constraint modeling module is used to construct vehicle state stability constraints, control stability constraints, and predictive space geometric safety constraints, and simultaneously obtain global collaborative constraints. It also constructs and linearly decouples the vehicle's equivalent curvature kinematics model and establishes the vehicle's linear state transition equations. The trajectory optimization and planning module is used to construct a multi-objective trajectory planning and optimization model based on global collaborative constraints and linear state transition equations, solve for the optimal state sequence and control sequence, and fit to generate the optimal predicted driving trajectory. The spatiotemporal safety corridor construction module is used to solve the feasible region of convex polygons at each time step based on the optimal predicted driving trajectory, through vehicle corner point safety amplification and constraint dimensionality reduction transformation, and to construct a spatiotemporal safety corridor adapted to the trajectory by splicing the time sequence. The vehicle control execution module is used to receive trajectory commands and safety constraint commands, and drive the four-wheel independent steering vehicle to complete driving actions.

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