An automatic driving semi-trailer truck platoon control optimization method and system under complex road alignment

Abstract

The application discloses a kind of complex road line under automatic driving semi-trailer truck platoon control optimization method and system.S1, the discrete coordinate point of real-time acquisition front road and slope, overheight, collect own state information, other truck state information in platoon, establish vehicle coupling dynamics equation;S2, by chain rule conversion to spatial domain, curvature, slope line parameter is mapped as dynamic constraint in rolling space prediction domain optimization;S3, to the linearization of spatial domain nonlinear model and constraint, construct multi-objective optimization function and translation quadratic form solution, obtain optimal trajectory and control sequence;S4, using hierarchical collaborative control, upper layer distributed MPC completes path, speed and platoon spacing collaborative control;Lower based on articulated phase plane determines instability trend, early warning zone is fed back to upper layer and tightens safety boundary, dangerous zone triggers brake intervention.The method effectively improves the control stability and driving safety of semi-trailer truck platoon under complex road.

Description

Technical Field

[0001] This invention relates to the field of intelligent connected commercial vehicle platooning control technology, and in particular to an optimization method and system for platooning control of autonomous semi-trailer trucks under complex road alignments. Background Technology

[0002] With the development of automation in long-haul logistics, semi-trailer truck platooning has become a research hotspot due to its advantages in fuel saving and improved traffic efficiency caused by air resistance. Current semi-trailer truck platooning control schemes are mostly based on time-domain dynamic models. However, in complex alignment scenarios such as continuous curves and undulating slopes on mountain roads, the coupling error between road curvature, slope, and vehicle dynamics is amplified, significantly reducing trajectory tracking accuracy and platooning stability. The relative rotational degrees of freedom between the tractor and trailer introduced by the articulated structure of the semi-trailer further complicate the kinematic coupling relationship under curve conditions, making it difficult for time-domain models to accurately describe the continuous impact of curvature and slope varying with road arc length on the articulated dynamics.

[0003] In terms of articulated stability control, existing solutions mainly rely on hard constraints on the articulation angle or post-event braking intervention, focusing only on feedback correction for a single articulation dimension. They lack a systematic feedforward prediction mechanism that links formation coordination, vehicle tracking, and articulated stability at three levels, making them prone to intervention lag and unsolvable optimization problems under extreme curve conditions. Existing dual-layer curvature adaptive MPC for passenger vehicles is only applicable to single-vehicle path tracking and adjusts the prediction time domain only through a single input (heading deviation), failing to simultaneously adjust stability weights and constraint margins. This makes it unsuitable for multiple instability conditions such as semi-trailer folding and trailer swaying. Most solutions only update curvature constraints at a single point in real time, without constructing dynamic constraint boundaries for the entire look-ahead sequence, resulting in poor constraint matching throughout the curve and unsolvable optimization problems.

[0004] In distributed formation architecture, traditional single-vehicle MPC only distinguishes between predicted and optimal trajectories, lacking hypothetical trajectory definitions and rolling update rules for V2V interaction, and formation collaborative computing lacks a standardized interaction carrier; traditional hierarchical control only sends instructions from the upper layer to the lower layer, and the lower layer's stable state cannot correct the upper layer's optimization boundary in reverse, and the impact of V2V communication latency and packet loss on formation stability under distributed architecture also lacks systematic treatment; existing wind resistance models have fixed coefficients and are not dynamically adjusted with formation arc length and spacing, resulting in significant mismatch in high-speed curve models.

[0005] In summary, existing technologies suffer from poor alignment adaptability, delayed instability intervention, limited adaptive dimensions, and incomplete formation interaction logic, failing to meet the high-precision and stable driving requirements of semi-trailer truck formations on mountainous trunk roads. Therefore, a novel optimization method for semi-trailer truck formation control under complex road alignments is needed to address the problems of poor alignment adaptability, delayed turn suppression, insufficient hierarchical coordination, and lack of consideration for wind resistance coupling in existing solutions. Summary of the Invention

[0006] In view of this, the purpose of this invention is to provide an optimization method and system for autonomous semi-trailer truck platooning control under complex road alignments. This method adapts to curved and sloping roads through spatial domain arc length modeling and designs a multi-dimensional road curvature pre-compensation mechanism to counteract curvature disturbances. It employs dual-input fuzzy multi-dimensional adaptive control of curvature amplitude and curvature change rate, simultaneously adjusting prediction parameters, stability weights, and constraint margins. A complete flow system of prediction, hypothesis, and optimal trajectories is constructed, standardizing the distributed platooning interaction logic. Combining a two-way collaborative architecture between upper and lower layers with differential braking of the tractor and trailer axles as a safety net, this method balances multiple optimization objectives, including driving safety, path tracking accuracy, and platooning consistency.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: an optimization method for autonomous driving semi-trailer truck platooning control under complex road alignments, characterized by the following specific implementation steps:

[0008] Step S1: Real-time acquisition of discrete coordinates, slope, and superelevation of the road ahead; collection of self-state information and state information of other trucks in the platoon; and establishment of vehicle coupled dynamics equations.

[0009] Step S2: The curvature and slope linear parameters are transformed into the spatial domain through the chain rule, and the dynamic constraints in the rolling spatial prediction domain optimization are mapped to achieve feedforward suppression of instability risk.

[0010] Step S3: Linearize the spatial domain nonlinear model and constraints, construct a multi-objective optimization function and transform it into a quadratic form for solution to obtain the optimal trajectory and control sequence;

[0011] Step S4: A hierarchical collaborative control is adopted. The upper layer distributed MPC completes the collaborative control of path, speed and formation spacing; the lower layer determines the instability trend based on the articulated phase plane, the early warning zone feeds back to the upper layer to tighten the safety boundary, and the danger zone triggers braking intervention.

[0012] In a preferred embodiment, step S1 is implemented as follows:

[0013] Step S11: Obtain the discrete coordinate point sequence (X,Y) of the road reference path and the longitudinal slope using the vehicle-mounted high-precision map. Horizontal superelevation ;

[0014] The vehicle acquires its own vehicle status information, including the longitudinal speed v of the tractor, through onboard sensors and an articulation angle acquisition unit. 1x Lateral velocity v 1y yaw rate Hinge angle γ, hinge angular velocity Trailer yaw rate Depend on The following components were synthesized: Tractor mass m1, trailer mass m2, and tractor yaw moment of inertia I. z1 Trailer yaw moment of inertia I z2 Tractor wheelbase l f Trailer wheelbase l r Distance from center of mass to traction pin l c1 l c2 Wheelbase B, center of gravity height h g The vehicle's physical parameters are provided by the preset vehicle parameter table in the vehicle controller; the tire side stiffness coefficient f is obtained by fitting tire test data.

[0015] Obtain the status information of neighboring vehicles within the platoon through V2V communication, including the positions of the leading and convoy vehicles. j The speeds u of the leading and trailing vehicles j The yaw angle between the leading vehicle and the lead vehicle The articulation angle γ between the leading vehicle and the lead vehicle j Used for subsequent cooperative error term e i,coop The interaction between the calculation and the assumed trajectory;

[0016] The current road adhesion coefficient μ is obtained in real time through an on-board road condition estimation algorithm, which serves as the basis for calculating the tire force boundary and the semi-trailer stability constraint (TSSC) stability boundary; a conservative safety value μ is adopted. safe :

[0017]

[0018] In the formula, μ min This is the minimum adhesion limit for the road surface; To estimate the adhesion coefficient in real time; k μ σ is the safety margin factor; μ To estimate the variance of the attachment;

[0019] Fifth-order polynomial smoothing is applied to the discrete reference path points to obtain a continuously differentiable path function y=f(s). The curvature is then calculated using the arc length s as the independent variable. With rate of change of curvature :

[0020]

[0021] Curvature values ​​are extracted from the corresponding arc length intervals according to the prediction time domain range to form a look-ahead curvature sequence, which serves as the known external input parameter for model predictive control.

[0022] Step S12: Construct a complete set of rigid body dynamic equations for the tractor and trailer, each with longitudinal, lateral, and yaw motions, using a Newton-Euler multibody framework; construct a zero-space projection matrix based on the hinge velocity constraint of the traction pin, eliminate the non-independent longitudinal and lateral motion components of the trailer, and reduce the dimensionality to obtain a fourth-order rigid body motion model containing only four independent physical degrees of freedom: longitudinal, lateral, and yaw motion of the tractor and yaw motion of the trailer; based on this, the hinge angle... Introduced as independent state variables, the state vector is combined to form a five-state coupled prediction model containing five state variables: the longitudinal velocity, lateral velocity, yaw rate of the tractor, the yaw rate of the trailer, and the articulation angle. The yaw angle of the tractor unit. The trailer yaw angle is used; the five-state coupled prediction model incorporates the gravity components corresponding to road slope and superelevation to adapt to the stress characteristics of complex curved and sloping roads.

[0023] The slope decomposition method is used to decouple the comprehensive slope angle into longitudinal climbing angle and lateral tilt angle, and the longitudinal and lateral decoupling calculation of the gravity component is completed. Based on the look-ahead curvature sequence, the steady-state sideslip angle, steady-state yaw rate and steady-state hinge angle of the curve are pre-calculated as the linearization reference working point.

[0024] Tire lateral stiffness varies linearly with axle vertical load C i :

[0025] C i =f·F Zi

[0026] In the formula, f is the normalized lateral stiffness, F Zi The vertical load corresponds to the axle; the vertical load of each axle is calculated based on the total vehicle mass, axle load distribution, and lateral load transfer during curves.

[0027] Step S13: Based on graph theory, complete the standardized modeling of the formation communication topology, define the adjacency matrix and in-degree matrix, and introduce the traction matrix to give the lead vehicle-navigator following topology PLF and the double lead vehicle following topology TPF; the matrix representation of the two communication topologies provides a unified mathematical framework for dynamic topology switching and stability analysis.

[0028] Step S14: Establish a semi-trailer truck air resistance model that considers the correction of the platoon spacing, calculate the wind resistance force of the tractor and trailer respectively, embed the wind resistance into the longitudinal dynamic equation, and dynamically correct the wind resistance coefficient with the arc length distance between the vehicle and the vehicle in front.

[0029] Construct a dynamic drag model related to the following distance, and calculate the resultant air resistance F of the whole vehicle. W :

[0030]

[0031] Dynamic drag reduction with exponential decay of drag coefficient :

[0032]

[0033] In the formula: ρ is the air density; A is the windward area; C d d is the drag coefficient of a single vehicle; s η is the arc length spacing of the workshop. d This represents the maximum drag reduction ratio; d is the attenuation characteristic length; min Minimum safe following distance; C d0 V is the standard drag coefficient for a single vehicle. x This represents the vehicle's longitudinal speed.

[0034] In a preferred embodiment, step S2 is implemented as follows:

[0035] Step S21: Perform the transformation from the time domain to the spatial domain based on the chain rule, using the complete Frenet relation:

[0036]

[0037] In the formula, s is the arc length of the road centerline. Let V be the arc length velocity. x V is the longitudinal velocity of the vehicle. y Let be the lateral velocity at the vehicle's center of gravity. e is the angle between the vehicle's heading and the road tangent. y This is a lateral positional deviation. Let f(x,u) represent the road curvature, be the time-domain form of the vehicle's nonlinear state-space equation, where x is the state vector and u is the control vector; set To avoid spatial domain singularity issues under low-speed conditions; after the transformation, all vehicle states, tracking errors, and constraints are mapped to the arc length coordinate system, and the expected vehicle spacing in the formation is defined as the arc length spacing along the road.

[0038] After the conversion, the vehicle's dynamic state, tracking error, and constraints all use arc length s as the independent variable; the expected vehicle distance within the formation is defined as the arc length distance along the road, and the states of neighboring vehicles are directly aligned using arc length coordinates after being obtained via V2V communication, without the need for additional conversion; to ensure There is a positive lower bound under low-speed operating conditions.

[0039] make ,in ; Indicates the curvature of the road. The minimum permissible value for arc-length velocity;

[0040] Using a spatial sampling step size Δs to perform forward Euler discretization on the above spatial domain differential equations, a nonlinear discrete state-space model is obtained:

[0041] Where x(s) is the state vector of the current arc length step, and u(s) is the control input of the current arc length step. Let the state variable be the rate of change with respect to time. The arc-length velocity is determined by the complete Frenet relation;

[0042] This discrete state-space model serves as the basic controlled object for linearization and rolling optimization in step S3.

[0043] Step S22: The hard constraints are ordered from high to low priority as follows: TSSC includes yaw stability envelope and rollover LTR constraint, followed by tire attachment ellipse constraint, drive / brake torque constraint, and lateral position boundary constraint; among them, TSSC, with articulation angle and yaw rate difference between tractor and trailer as core variables, is the core safety boundary to prevent tipping and trailer swaying, and cannot be relaxed throughout the entire process.

[0044] A look-ahead sequential dynamic constraint system is adopted. The constraint boundary of each arc length step in the prediction time domain is updated according to the following rules: the curvature and slope are linked to update the upper limit of lateral acceleration and the torque limit, the road adhesion coefficient is linked to update the tire force boundary and TSSC envelope range, and the lane width is linked to update the lateral position boundary.

[0045] TSSC uses a normalized ellipsoid constraint form:

[0046]

[0047] In the formula, z s Let γ be the stable state vector, and γ be the hinge angle. For hinge angular velocity, P represents the difference in yaw rate between the tractor and trailer, LTR represents the lateral load transfer rate; s Let T be an ellipsoidal matrix that dynamically varies with velocity v, road surface adhesion coefficient μ, and vehicle mass m, where T represents the transpose.

[0048] The safe speed for a vehicle in a curve is determined jointly by the lateral acceleration limit and the articulated stability boundary, with the lower bound of both being used:

[0049]

[0050] In the formula, a y,max The upper limit of lateral acceleration is determined jointly by road surface adhesion and rollover threshold; The speed limit is derived from the upper limit of lateral acceleration. Valid for a period of time. The upper limit of vehicle speed is derived from the hinge angle stability boundary and is negatively correlated with the curvature amplitude;

[0051] Step S23: Design multi-dimensional steady-state feedforward compensation terms based on the entire look-ahead curvature sequence. These terms compensate for motion deviations caused by road curvature in advance from three dimensions: platooning speed, tractor steering, and semi-trailer articulation steady state. All feedforward quantities together constitute the steady-state feedforward benchmark, which is input to S3 as the initial reference for rolling optimization and the initial value for hot start.

[0052] ① Combining forward curvature planning with the synchronous smooth speed curve of the entire fleet, upper and lower limits are set for acceleration and jerk to ensure synchronous speed of the formation driving under curves and reduce the impact of articulation in the workshop;

[0053] ② Introduce an underspeed steering correction term to construct the steady-state steering feedforward, calculated using the following formula:

[0054] In the formula δ ff (s) represents the steady-state steering feedforward; L represents the tractor wheelbase; K v V represents the understeer gradient, characterizing the correction of steering gain by vehicle speed; 1x (s) represents the longitudinal speed of the tractor; k γ γ is the hinge angle compensation coefficient, used to map the hinge angle to the front wheel steering angle compensation amount; ref (s) represents the steady-state desired hinge angle;

[0055] ③ Abandoning the pure geometric hinge angle calculation method, a vehicle speed dynamics compensation coefficient is introduced to derive the steady-state expected hinge angle suitable for high-speed operating conditions:

[0056] In the formula, The longitudinal distance from the center of gravity of the tractor unit to the traction pin. The longitudinal distance from the trailer's center of gravity to the draw pin;

[0057] k on low adhesion coefficient road surfaces vγ Automatic adjustment to ensure that the feedforward compensation of the articulation angle does not exceed the tire force adhesion limit; at the same time, soft penalty constraints on the articulation angle and articulation angular velocity are added to the rolling optimization objective function, and the dynamic fluctuation of the articulation angle is further weakened by feedback control, and the two types of instability conditions, namely tractor folding and trailer swaying, are suppressed simultaneously.

[0058] The aforementioned speed feedforward, steering feedforward, and articulation angle feedforward together constitute a feedforward compensation mechanism for curvature disturbances. This mechanism pre-corrects the reference trajectory and steady-state benchmark before predictive control roll optimization, thereby achieving proactive suppression of instability risks.

[0059] Step S24: Construct a hierarchical constraint domain coordination mechanism, using the normalized hinged stability margin as the constraint index, and embedding feasible domain restrictions of the upper-level optimization problem. The constraint form is as follows:

[0060]

[0061] In the formula, To predict the normalized stability margin at step j in the time domain, M s,min,i (s) represents the minimum stability margin requirement for the current arc length. β is the actual value of the stability margin of the previous arc length step; β is the stability margin adjustment coefficient, which is a dual dynamic function of curvature and longitudinal slope. Increasing β on straight sections expands the economic optimization space, while automatically narrowing β on curved sections tightens the stability boundary.

[0062] In a preferred embodiment, step S3 is implemented as follows:

[0063] Step S31: For each control cycle, the optimal trajectory of the previous cycle after the rolling shift is used as the predicted trajectory, and the differential braking state correction of the previous cycle fed back in S42 is superimposed to update the initial state; the first-order Taylor expansion linearization is performed synchronously on the spatial domain nonlinear dynamic model and all nonlinear TSSC stability constraints; the linearization error is checked in real time, and the steady-state operating point is updated if the error exceeds the limit.

[0064] A fuzzy controller is constructed using curvature amplitude and curvature change rate as dual inputs, and the penalty weight matrix Q for prediction steps and hinge angle deviation is dynamically adjusted synchronously. γ Simultaneously update the stability margin coefficient β and wind resistance weight w based on the current curvature and slope. w Balancing control precision, computational efficiency, and driving stability;

[0065] Step S32: Construct a multi-objective optimization function, integrating hard constraint boundary conditions and soft constraint penalty terms:

[0066]

[0067] In the formula, J i Indicates the first The total optimization cost function for the vehicle, N p N represents the prediction time-domain steps, j represents the vehicle, and N represents the number of prediction time-domain steps. i e represents the total number of neighboring vehicles. i,track For individual trajectory tracking error, e i,coop,l To account for the state coordination error with neighboring vehicle l, Δγ i The hinge angle deviation, Δμ i For the control increment, Q is the trajectory tracking error weight matrix, and F is the formation coordination error weight matrix. γ R is the hinge angle deviation penalty weight matrix, R is the control increment penalty weight matrix, and P is the terminal cost weight matrix; P w,i P is the power of vehicle air resistance. w,base As the reference power, The penalty weight for yaw oscillation, The yaw rate of the tractor unit. The yaw rate of the trailer. For the difference in yaw rate, This is the terminal state error vector. To predict the final time in the time domain, s represents the current arc length position. This indicates predicting the future t at time s. The position of the arc length;

[0068] For yaw oscillation penalty term, weight The greater the curvature of the curve, the higher the stability penalty weight, and priority is given to suppressing the risk of trailer yaw. This is a relaxation factor penalty term; As the baseline weight for yaw penalty; The curvature sensitivity coefficient;

[0069] Step S33: Organize all linearization constraints into inequality constraints, and use the optimal solution from the previous cycle to start QP solution; when there is no feasible region, the relaxation factor will automatically adjust the soft constraints first; if there is still no feasible solution, the relatively hard constraints will be relaxed step by step according to the constraint priority from low to high; the TSSC absolute safety hard constraints will not be relaxed under any circumstances.

[0070] The solution space of the optimization problem within each control cycle is divided into three types of trajectory sequences with different lifecycles and interaction attributes: predicted trajectory, hypothetical trajectory, and optimal trajectory.

[0071] In a preferred embodiment, the predicted trajectory is defined as an open-loop state sequence formed by the rolling shift of the optimal trajectory of the previous cycle, which is stored in the local controller as the working base point for the linearization of the current cycle model and the initial value for the hot start of the optimization solution.

[0072] The hypothetical trajectory is defined as a complete predicted time-domain sequence obtained by truncating, shifting, and supplementing the current period's optimal trajectory with terminal state update rules. This trajectory is broadcast to neighboring vehicles in the formation via a V2V communication link, serving as an external consistency benchmark for neighboring vehicles to construct cooperative error terms, thereby ensuring the compatibility of optimization propositions for each vehicle in distributed optimization.

[0073] The optimal trajectory is defined as the sequence of feasible optimal solutions to the quadratic programming problem in the current cycle. The first segment of the control input is output to the actuator, and the remaining segments are used to update the predicted trajectory and the assumed trajectory for the next cycle after rolling shift.

[0074] Assuming the terminal state update rule consists of a rolling shift operation, arc length coordinate alignment constraints, and terminal feasible set projection, its update form is as follows:

[0075]

[0076] In the formula, K is the terminal feedback gain, derived from the discrete algebraic Riccati equation.

[0077] Solving for the controller weights, we find that they satisfy the positive definite closed-loop stability criterion, providing a quantitative theoretical basis for parameter tuning. For vehicles In the assumed terminal state of the next cycle, A s The discrete state matrix, For vehicles In the assumed terminal state of the current cycle, B s Let K be the discrete input matrix, and K be the terminal feedback gain matrix. In order to settle the score with the neighbor's vehicle, Let j be the assumed terminal state of the neighboring vehicle in the current period. Let i be the assumed terminal state of vehicle i in the current period; For vehicles The set of neighbors; Let represent the expected arc length spacing vector between vehicles j and i.

[0078] In a preferred embodiment, step S4 is implemented as follows:

[0079] Step S41: Adopt a synchronous distributed predictive control framework to support dynamic switching of PLF and TPL communication topologies; introduce a communication delay compensation mechanism; and adopt an incremental augmented state model at the upper layer.

[0080]

[0081] Let be the augmented state vector for the next arc-length step. Let Δs be the augmented state vector for the current arc-length step, and Δs be the spatial sampling step size. For the augmented state matrix, The augmented input matrix is ​​denoted by Δu(s), which is the control increment vector, ξ(s), which is the original state vector, and u(s-Δs), which is the control input of the previous cycle.

[0082] The optimal trajectory is obtained for each vehicle. Then, discard the first segment and proceed with the remaining segments. Assuming the trajectory at time s+Δs in the next period The first N p Segment, j=0,1,...,N p-1, the final stage is completed by the terminal state update rule; the hypothetical trajectory is transmitted to neighboring vehicles via V2V broadcast, and the terminal state of each vehicle's hypothetical trajectory is updated and completed according to the rule described in step S3. The terminal feedback gain ensures that the predicted time domain terminal state asymptotically converges to the desired queue. Under the premise of communication topology connectivity and latency meeting the upper limit, it supports the compatibility and formation consistency of distributed optimization; the received neighbor hypothetical trajectories are substituted into the cooperative error term to complete the optimization. The weighting coefficient of the cooperative error is determined by the communication topology adjacency matrix:

[0083] The formation closed-loop stability is satisfied by the terminal feedback gain K. Guarantee D p =D+P,λ i (*) represents the matrix eigenvalues, driving global formation consistency through local optima; A il Let A be the (i,l)th element of the communication topology adjacency matrix. il =1 indicates that vehicle i can receive the hypothetical trajectory information of vehicle l; , Let be the hypothetical trajectory state vectors of vehicle i and its neighboring vehicle l at arc length s, respectively; N is the desired arc length spacing vector between vehicles i and l; i Let i be the set of neighbors of vehicle i; This is the adjacency matrix of the communication topology. Let λ be the augmented in-degree matrix, where D is the in-degree matrix and P is the traction matrix; i (*) represents the eigenvalues ​​of the matrix, and δ is a positive number that guarantees stability margin, 0 < δ < 1;

[0084] Step S42: Lower-level construction of tractor-trailer cooperative differential The articulated controller uses the articulated angle reference value in the optimal trajectory output by the upper-level MPC as the controlled variable reference input; the controller uses the slip ratio difference U=ΔS between the left and right wheels as the control input and the articulated angle tracking error as the control input. Hinged angular velocity Difference in yaw rate between tractor and trailer The controlled quantity; among which The feedforward steady-state desired hinge angle defined in step S23 is used as the hinge angle tracking benchmark in the cost function of step S3, and the optimization result of this benchmark is used as the reference input in S42.

[0085] The state space form of the hinge regulator is as follows: subscript Represents the correlation matrix of the hinge regulator:

[0086]

[0087] in, , The time derivative of the state vector. It is the hinge angle. For hinge angular velocity, The difference in yaw rate between the tractor and trailer is represented by denoted as W; the yaw coupling disturbance between the tractor and trailer is represented by denoted as W. Solving using the Linear Matrix Inequality (LMI) The output feedback controller ensures that the closed-loop system is protected from disturbances. To the controlled output of The gain is less than the given value; For the control input of the slip ratio difference between the left and right wheels; A h For the state matrix of the hinged regulator, B h1 Let B be the perturbation input matrix. h2 To control the input matrix, C h D is the output matrix of the hinged regulator. h11 For the direct transfer matrix of the perturbation, D h12 To control the direct transfer matrix, the subscript h denotes the correlation matrix of the articulated regulator; the output feedback controller is solved using LMI to ensure the closed-loop system changes from disturbance W to the controlled output Z. The gain is less than the given value;

[0088] Equal and opposite braking forces F are applied to the left and right wheels on the same axle. b,L F b,R This generates a corrective yaw moment M. z At the same time, it does not produce longitudinal deceleration of the entire vehicle:

[0089]

[0090] In the formula, B is the wheelbase, and F is the track width. b,L F b,R The braking forces of the left and right wheels on the same axle are M and M respectively. z To generate the corrective yaw moment, F x,brake This refers to the longitudinal braking force of the entire vehicle; when the braking forces of the left and right wheels are equal in magnitude and opposite in direction, F b,R =-F b,L F x,brake =0;

[0091] Therefore, the equivalent control correction for differential braking is derived as follows:

[0092]

[0093] Where k δ k a This corresponds to the conversion gain; the additional longitudinal deceleration generated by differential braking is compensated in real time by the upper-level speed controller; Δδ brk , Δa x,brkThese are the equivalent steering correction and the equivalent longitudinal acceleration correction, respectively.

[0094] The differential braking effect is fed back to the upper-level MPC in the next cycle through three dimensions: First, the changes in longitudinal speed, hinge angle, and yaw rate caused by braking are used as state correction quantities to update the initial state of optimization in step S31; Second, the increase in longitudinal tire force occupied by differential braking is substituted into the tire adhesion ellipse constraint to correct the upper limit of available lateral force; Third, the total longitudinal braking force is embedded as a known disturbance quantity into the longitudinal dynamics feedforward and compensated in advance by the upper-level speed controller.

[0095] Step S43: The stability region is divided using the hinge angle-hinge angular velocity phase plane method. Three levels of instability thresholds are set: stable region, early warning region, and danger region. The stability margin adjustment coefficient is quantized and mapped to the stability margin adjustment coefficient in S24 through a dual-channel feedback mechanism of constraint margin and penalty weight. The hinge penalty weight Q of S32 γ Horizontal oscillation penalty weight K ω ;

[0096] Stable region: and The lower layer does not interfere, while the upper layer performs full performance optimization; β is taken as the nominal value β. nom Q γ K ω Take the nominal weight;

[0097] Warning zone: and The lower layer feeds back to the upper layer to tighten the constraint boundary and amplify the stabilizing weights. Q narrows linearly with the hinge angle deviation. γ K ω As the hinge angle deviation increases linearly, the specific mapping relationship is as follows:

[0098]

[0099] Where k β k Q To adjust the gain, the value range is (0,1); β nom γ is the nominal value of the stability margin. safe γ is the safety threshold for the hinge angle. warn Q is the hinge angle warning threshold. γ,nom The nominal value of the hinge penalty weight;

[0100] Danger Zone The lower layer directly initiates differential braking intervention, reconstructs the following feedback gain, and simultaneously forces the upper layer to decelerate; β is narrowed to its minimum value. min Q γ K ωMagnify the value to 3 to 5 times the nominal value to prioritize driving stability;

[0101] Step S44, Control Output Synthesis and Execution: The final control output is synthesized as follows:

[0102] The reference layer is the upper-layer MPC feedback control quantity. ; For the optimal front wheel steering angle of the upper-level MPC, The optimal longitudinal acceleration for the upper-layer MPC;

[0103] The feedforward compensation layer is the multi-dimensional road alignment feedforward compensation amount in step S23. It is added to the base layer in an additive manner; δ ff For feedforward compensation steering amount, a x,ff For feedforward compensation of longitudinal acceleration;

[0104] The safety correction layer is the differential braking correction amount of the lower layer. The warning zone and the danger zone are superimposed in a weighted manner, and the weight is determined by the third-level instability threshold in step S43; This is the differential braking steering correction amount. This is the longitudinal acceleration correction amount for differential braking;

[0105] Synthetic steering command δ cmd And the synthetic longitudinal acceleration command a x,cmd for:

[0106] Where λ brk For the braking intervention weight determined in step S43, the stable region is 0, the warning region increases linearly, and the danger region is 1.

[0107] Physically limited by the actuator After being limited by the rate of change, the output is sent to the steering system, drive system, and braking system to complete the final control execution; the ABS anti-lock braking system has the highest priority, and the next layer... When the brake command from the regulator causes the slip ratio of any wheel to exceed the ABS trigger threshold, the brake command for that axle is taken over by the ABS. The regulator retains braking authority for axles that have not triggered ABS to ensure braking safety; where δ is the front wheel steering angle control value, δ max The maximum permissible front wheel steering angle; a x For longitudinal acceleration control, a x,min and a x,max These are the lower limit of longitudinal acceleration, i.e., the maximum braking deceleration, and the upper limit, i.e., the maximum acceleration capability.

[0108] In a preferred embodiment, the formation adopts a PLF / TPL switchable communication topology, and the neighbor coordination error term in the objective function selects the corresponding neighbor vehicle according to the current communication topology, thereby driving global formation consistency through local optimization.

[0109] This invention also provides an automated semi-trailer truck platooning control optimization system for complex road alignments, comprising a processor, a memory, and a bus. The memory stores machine-readable instructions executed by the processor. When the system is running, the processor communicates with the memory via the bus, and when the machine-readable instructions are executed by the processor, the automated semi-trailer truck platooning control optimization method for complex road alignments is described above.

[0110] Compared with the prior art, the present invention has the following beneficial effects:

[0111] (1) This invention proposes a spatial domain arc length modeling method, which transforms the time domain model into the arc length coordinate system based on the chain rule. The road alignment parameters are explicitly embedded into the entire look-ahead constraint sequence, eliminating the time domain coupling deviation in the curve and slope scenario and greatly improving the consistency of formation trajectory tracking.

[0112] (2) The present invention constructs a multi-dimensional road curvature pre-compensation mechanism to offset curvature disturbances in advance from three dimensions: platoon speed, tractor steering, and articulated steady state. This reduces the risk of articulated folding and trailer swaying from the source, significantly reduces the burden on the feedback controller, and achieves pre-control of instability risk.

[0113] (3) The present invention adopts a dual-input multi-output fuzzy adaptive mechanism of curvature amplitude and curvature change rate, which simultaneously adjusts the prediction length, stable weight and constraint margin, taking into account both the computing power efficiency of straight road and the safety performance of curved road, which is superior to the traditional single-dimensional adaptive scheme.

[0114] (4) This invention defines three types of trajectories: prediction, hypothesis, and optimal, and provides complete generation, interaction, and rolling iteration logic. The hypothesis trajectory serves as a standardized interaction carrier for distributed formation, which solves the defects of non-standardized information interaction and inconsistent benchmarks in multi-vehicle collaborative communication.

[0115] (5) The present invention realizes the synchronous Taylor linearization of the dynamic model and all nonlinear stability constraints, and the dimensionality reduction of the hinged projection matrix effectively reduces the time consumption of on-board solution; the constraint hierarchical relaxation mechanism ensures that the absolute safety boundary is not relaxed throughout the process, and the control does not fail under extreme working conditions.

[0116] (6) The present invention designs a two-way collaborative architecture and a traction-trailer axle differential braking mechanism to provide differentiated bottom-line protection for two types of semi-trailer-specific instability conditions. The lower stable state can reversely regulate the upper optimized feasible domain to form a dual safety closed loop.

[0117] (7) This invention solves the terminal weights based on the discrete Riccati equation and completes the closed-loop stability proof under all working conditions with the piecewise Lyapunov function. The controller parameters have a quantitative tuning basis and are highly feasible for engineering implementation. The dynamic wind resistance model realizes the dynamic balance of curve and slope stability. Attached Figure Description

[0118] Figure 1 This is a flowchart illustrating a preferred embodiment of the present invention.

[0119] Figure 2 This is a detailed flowchart of the S1 multi-source information acquisition and coupling dynamics modeling of a preferred embodiment of the present invention;

[0120] Figure 3 This is a detailed flowchart of the S2 spatial domain transformation and constraint system construction according to a preferred embodiment of the present invention;

[0121] Figure 4 A detailed flowchart of the S3 linearization solution and reference trajectory generation in a preferred embodiment of the present invention;

[0122] Figure 5 The following is a detailed flowchart of the S4 hierarchical collaborative control execution according to a preferred embodiment of the present invention. Detailed Implementation

[0123] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0124] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0125] It should be noted that the terminology used herein is for the purpose of describing particular implementations only and is not intended to limit the exemplary implementations according to this application; as used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise; furthermore, it should be understood that when the terms “comprising” and / or “including” are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or combinations thereof.

[0126] like Figure 1-5 The figure shows the optimization method for autonomous semi-trailer truck platooning control under complex road alignments proposed in this invention, which includes the following steps.

[0127] 1. Obtain the discrete coordinate sequence of the road reference path within a 1 km range ahead, as well as the longitudinal slope i and lateral superelevation e, through the vehicle-mounted high-precision map module; collect the vehicle's own status, including the longitudinal speed v of the tractor, through the vehicle-mounted IMU, wheel speed sensors, and articulation angle encoder. x Lateral velocity vy yaw rate Hinge angle, hinge angular velocity The position, speed, yaw angle, and articulation angle of neighboring vehicles in the formation are obtained through C-V2X vehicle-to-vehicle communication.

[0128] ① Multi-source information collection

[0129] (1) Obtain the discrete coordinate point sequence (X,Y) of the road reference path within a 1 km range ahead, as well as the longitudinal slope, through the vehicle-mounted high-precision map. Horizontal superelevation The longitudinal slope and the lateral superelevation are both arc lengths. Functions:

[0130] i = i(s)

[0131] e = e(s)

[0132] In the formula, i and e are road geometry parameters directly provided by the map.

[0133] (2) Based on the discrete coordinate points provided by the map, perform fifth-order polynomial fitting and smoothing on the discrete reference path points to obtain a continuous, second-differentiable path function y=f(s). Solve for the first and second derivatives respectively, and calculate the curvature and the rate of change of curvature:

[0134]

[0135] After sliding filtering, the curvature and rate of change of curvature sequences of the corresponding arc length interval are extracted according to the prediction time domain and used as the external input reference for model predictive control.

[0136] (3) The vehicle's own state is collected through the onboard IMU, wheel speed sensor, and articulation angle encoder. The self-state vector is:

[0137]

[0138] In the formula, u1 is the longitudinal velocity of the tractor (m / s), v1 is the lateral velocity of the tractor (m / s), ω1 is the yaw rate of the tractor (rad / s), and γ is the articulation angle (rad). ω is the articulated angular velocity (rad / s), and Y is the lateral offset of the vehicle's center of gravity relative to the road reference line (m). Tractor yaw angle (rad).

[0139] (4) Obtain the interaction state vector of the j-th neighboring vehicle in the platoon through C-V2X vehicle-to-vehicle communication:

[0140]

[0141] In the formula, The coordinates (m) of the road arc length of the neighboring vehicle. The longitudinal speed (m / s) of the neighboring vehicle. γ is the yaw angle (rad) of the neighboring vehicle. j The articulation angle (rad) of the neighboring vehicle.

[0142] (5) The current road surface adhesion coefficient μ is obtained in real time through an on-board road surface state estimation algorithm, which serves as the basis for calculating the tire force boundary and TSSC. To ensure safety, a conservative safety value is adopted:

[0143]

[0144] In the formula, μ min This is the minimum adhesion limit for the road surface; To estimate the adhesion coefficient in real time; k μ σ is the safety margin factor; μ The variance is estimated for attachment.

[0145] (6) The masses m1 and m2 of the tractor and trailer, and the yaw moment of inertia I z1 I z2 wheelbase l f l r Distance from center of mass to traction pin l c1 l c2 Wheelbase B, center of gravity height h g The vehicle's physical parameters are provided by the preset vehicle parameter table in the vehicle controller; the tire lateral stiffness coefficient f is obtained by fitting tire test data.

[0146] The aforementioned real-time collected dynamic state variables, road surface adhesion coefficient, and preset vehicle physical parameters together constitute the complete data foundation for S12 coupled dynamics modeling.

[0147] ② Decoupling of road alignment and slope

[0148] The slope decomposition method is used to determine the comprehensive slope angle θ of the spatial road. v Decomposed into longitudinal climbing angle By using the lateral tilt angle β, the longitudinal and lateral components of gravity are decoupled.

[0149]

[0150] In the formula, This refers to the yaw angle of the vehicle relative to the road direction. The yaw angle of the tractor unit. This refers to the azimuth angle of the road reference line. Due to the difference in articulation angles, the tractor and trailer have their own longitudinal climbing angles θ1 and θ2 and lateral tilt angles.

[0151] ③ Newton-Euler multibody complete dynamic equations and hinged constraint projection dimensionality reduction

[0152] The tractor and semi-trailer are considered as independent rigid bodies in planar motion, each possessing three degrees of freedom: longitudinal translation, lateral translation, and yaw rotation. The complete system has a total of six degrees of freedom. Based on the Newton-Euler multibody dynamics framework, a complete set of constrained equations is constructed. Then, non-independent degrees of freedom are eliminated through hinged constraint zero-space projection, resulting in a fourth-order independent dynamic model. The form is as follows:

[0153] (1) Define the complete generalized velocity vector in the body coordinate system:

[0154]

[0155] In the formula, The longitudinal velocity, lateral velocity, and yaw rate of the tractor's center of gravity;

[0156] The longitudinal velocity, lateral velocity, and yaw rate of the semi-trailer's center of gravity.

[0157] The system mass-inertia matrix is ​​in block diagonal form, representing the translational and rotational inertia of the rigid body:

[0158]

[0159] In the formula, (m1, m2) represent the total mass of the tractor and the semi-trailer, respectively; (I z1 ,I z2 ) are the yaw moment of inertia of the tractor and the semi-trailer, respectively.

[0160] The Coriolis-centrifugal force matrix for planar motion characterizes the inertial force coupling caused by the entrainment motion:

[0161]

[0162] By introducing Lagrange multipliers to describe the constraint reaction force at the traction pin hinge, and combining this with the gravity component after slope decoupling, a complete constrained dynamic equation is constructed:

[0163]

[0164] In the formula:

[0165] It is a generalized external force vector, which includes the longitudinal and lateral forces of the tires and the gravity component of the slope.

[0166] The Jacobian matrix for hinged constraint velocity;

[0167] The Lagrange multipliers are the longitudinal and lateral constraint reaction forces of the traction pin.

[0168] The hinge angle is the difference between the yaw angle of the semi-trailer and the tractor.

[0169] The specific form of the generalized external force vector is:

[0170]

[0171] In the formula, θ1 and θ2 are the longitudinal climbing angles of the tractor and semi-trailer, and (β1 and β2) are the lateral tilt angles of the tractor and semi-trailer, calculated by the slope decoupling method in step S12; (F xf F xr F xt ) represents the longitudinal tire force on each axle, (F) yf F yr F yt ) represents the lateral tire force on each axle; see ④ for the tire force model for the specific calculation formula.

[0172] (2) Hinged kinematic constraints and Jacobian matrix

[0173] At the hinge point of the traction pin, the positions and velocities of the two rigid bodies are continuous, constituting two kinematic constraints. The traction velocity of the hinge point in the tractor vehicle's coordinate system is as follows:

[0174]

[0175] The entrainment velocity of the articulation point in the semi-trailer's body coordinate system:

[0176]

[0177] By performing a coordinate rotation transformation through the hinge angle γ, the absolute velocities of the two rigid bodies at the hinge point are equal, which can be simplified into a standard velocity constraint form. The constrained Jacobian matrix is ​​obtained as follows:

[0178]

[0179] The system has 6-2=4 independent degrees of freedom, and the constraint reaction forces are only along the row vector direction of the Jacobian matrix.

[0180] (3) Null-space projection dimensionality reduction and 4th-order independent model

[0181] Four independent generalized velocities with clearly defined physical meanings were selected:

[0182]

[0183] Non-independent velocity (v) 2x v 2y The null space projection matrix can be uniquely determined by the constraint equations. Satisfying the orthogonality condition To achieve the mapping from complete speed to independent speed.

[0184]

[0185] Multiply both sides of the complete dynamic equation by the left side. ,use Eliminating the hinge constraint term; differentiating the velocity mapping yields... Substituting these values ​​into the equations, we finally obtain a fourth-order independent dynamic model:

[0186] Definitions of each reduced-order matrix:

[0187] Reduced quality matrix: Symmetric positive definite;

[0188] Reduced-order Coriolis-centrifugal force matrix: ;

[0189] Reduced-order generalized force: .

[0190] Under normal driving conditions, the articulation angle amplitude is relatively small, which meets the requirements. The reduced-order quality matrix simplifies to a constant coefficient matrix, which can be directly used for the design of predictive controllers for linear models.

[0191]

[0192] ④ Tire force and kinematic coupling

[0193] A linear tire model is used to describe the tire mechanical properties at small slip angles:

[0194]

[0195] In the formula, C ai For the lateral stiffness of the tires on each axle, α i C represents the tire slip angle for each axle; li For the longitudinal stiffness of the tire, s i This represents the tire slip ratio for each axle.

[0196] The tractor and trailer are connected by a drawbar, forming a kinematic constraint. At the articulation point, the absolute velocities of the two rigid bodies are continuous. Based on coordinate rotation transformation, a mapping equation is established between the trailer's center-of-mass velocity and the tractor's motion state and articulation parameters:

[0197]

[0198] In the formula, l c1 l is the longitudinal distance from the center of gravity of the tractor to the traction pin. c2 This is the longitudinal distance from the trailer's center of gravity to the draw pin. It is the hinge angle.

[0199] Combined with the definition of hinged angular velocity Convert the trailer yaw rate to an equivalent value.

[0200] Substitute into the kinematic equation to eliminate Then, substituting the complete kinematic relationships and tire force model into the six-degree-of-freedom multibody dynamics equations, eliminating the traction pin articulation constraint force and the trailer's longitudinal and lateral non-independent velocity variables, the final result is obtained as follows: The system of fifth-order nonlinear differential equations, consisting of independent state variables, serves as the dynamic basis for subsequent spatial domain transformation and model predictive controller design.

[0201] ⑤ Based on graph theory, complete the standardized modeling of formation communication topology, using a directed graph G. N ={V,E,A} describes the formation communication topology, where V is the set of vehicle vertices, E is the set of communication edges, and A is the adjacency matrix, with elements defined as follows:

[0202]

[0203] Define the in-degree matrix ,in Let the communication in-degree of the i-th vehicle be denoted; define the restraint matrix. If vehicle i can receive information from the navigator vehicle, then P ii =1, otherwise 0.

[0204] For PLF and TPL topologies, corresponding matrix forms are given respectively, providing a unified mathematical framework for dynamic topology switching and stability analysis.

[0205] ⑥ Air drag coupling modeling

[0206] A semi-trailer truck air resistance model considering platoon spacing correction is established. The overall vehicle air resistance consists of the tractor's air resistance and the trailer's air resistance. The expression for the resultant longitudinal air resistance force is as follows:

[0207]

[0208] Dynamic drag reduction: exponential decay of drag coefficient

[0209] In the formula: ρ is the air density, A is the vehicle's frontal area, and V... x This refers to the longitudinal speed of the vehicle. The dynamic drag coefficient varies with the arc length distance d between the vehicle and the vehicle in front. s Dynamic correction – the smaller the following distance, the stronger the wake drag reduction effect and the lower the drag coefficient.

[0210] The resultant force of wind resistance F WAs a longitudinal external force, it is superimposed on the longitudinal dynamic equations of the fifth-order nonlinear differential equation system obtained in ④, and used for subsequent spatial domain transformation and predictive control.

[0211] II. Spatial Domain Transformation and Constraint System Construction

[0212] ① Spatial domain transformation based on the chain rule, using complete Frenet relations:

[0213]

[0214] In the formula, s is the arc length of the road centerline, and V x For the longitudinal speed of the vehicle, e is the angle between the vehicle's heading and the road tangent. y For lateral positional deviation; set To avoid spatial domain singularity issues under low-speed conditions; after the transformation, all vehicle states, tracking errors, and constraints are mapped to the arc length coordinate system, and the expected platoon distance is defined as the arc length spacing along the road.

[0215] Based on the chain rule, the nonlinear state-space equations of the system are... Mapping from the time domain to the spatial domain:

[0216] In the formula, the state vector Control vector Among them, v 1x v 1y These are the longitudinal and lateral speeds of the tractor unit, respectively. γ is the yaw rate of the tractor, and γ is the articulation angle. ω is the hinge angular velocity, and Y is the lateral position deviation.

[0217] After conversion, the vehicle's dynamic state, tracking error, and constraints are all expressed in arc length. The independent variable is ; the expected vehicle spacing in the formation is defined as the arc length distance along the road. After the status of neighboring vehicles is obtained through V2V communication, they are directly aligned with the arc length coordinates without any additional conversion.

[0218] By using a fixed arc length step size Δs to perform forward Euler discretization on the above spatial domain differential equations, a nonlinear discrete state-space model is obtained:

[0219] In the formula The complete calculation is based on the aforementioned Frenet relation. This discrete model serves as the controlled object for linearization and rolling optimization in step S3.

[0220] ② Hard constraints on road alignment parameter mapping

[0221] Road alignment features are transformed into control and state hard constraints, divided into two levels: absolute safety hard constraints and relative performance hard constraints. The priorities, from highest to lowest, are: TSSC (Total Safety Constraints), tire adhesion ellipse constraint, rollover threshold constraint, drive / braking torque constraint, and lateral position boundary constraint. All constraints are updated arc-wise along the prediction time domain, forming a look-ahead sequential dynamic constraint system.

[0222] Lateral acceleration constraints are derived jointly from road curvature and rollover threshold:

[0223] In the formula, μ is the road surface adhesion coefficient, B is the wheel track, and h is the wheel track width. g The height of the center of mass.

[0224] The safe speed for a vehicle in a curve is determined jointly by the lateral acceleration limit and the articulation angle stability boundary, with the lower bound of both being used:

[0225] In the formula, The speed limit is derived from the upper limit of lateral acceleration. The upper limit of vehicle speed is derived from the hinge angle stability boundary and is negatively correlated with the curvature amplitude.

[0226] Drive / braking torque constraints are derived from longitudinal slope:

[0227] In the formula, T max T min For the rated maximum drive / brake torque, r eff This is the effective radius of the wheel.

[0228] Lateral position boundary constraints are derived from lane width:

[0229] In the formula, Lane width, This refers to the width of the vehicle.

[0230] The tire attachment ellipse constraint is:

[0231] In the formula, F z For vertical loads, slope and load transfer corrections are taken into account.

[0232] ③ Double-layered suppression mechanism for head-down risk

[0233] The phase plane method is used to divide the hinged stability region, and the product of the hinge angle and the hinge angular velocity is used as the criterion for instability tendency:

[0234]

[0235] Based on this criterion, a two-layer feedforward + feedback suppression mechanism is constructed:

[0236] Feedforward layer: Based on the entire look-ahead curvature sequence, a multi-dimensional steady-state feedforward compensation term is designed to compensate for motion deviations caused by road curvature in advance from three dimensions: platooning speed, tractor steering, and semi-trailer articulated steady state.

[0237] Firstly, by combining forward curvature planning with a synchronized and smooth speed curve for the entire fleet, upper and lower limits are set for acceleration and jerk to ensure synchronized speeds during convoy driving in curves and reduce the impact of articulations in the workshop.

[0238] Secondly, an underspeed steering correction term is introduced to construct the steady-state steering feedforward, calculated using the following formula:

[0239]

[0240] Third, abandoning the pure geometric hinge angle calculation method, we introduce a vehicle speed dynamics compensation coefficient to derive the steady-state expected hinge angle suitable for high-speed operating conditions:

[0241]

[0242] k on low adhesion coefficient road surfaces vγ Automatic adjustment to ensure that the articulation angle feedforward compensation does not exceed the tire force adhesion limit.

[0243] Feedback layer: Add hinge angle deviation to the rolling optimization objective function. Difference with yaw rate The soft constraint penalty term actively suppresses the dynamic fluctuation of the articulation angle through rolling optimization, and simultaneously suppresses two types of instability conditions: tractor folding and trailer shimmy. By actively suppressing dynamic fluctuations in the articulation angle through rolling optimization, it simultaneously suppresses two types of instability conditions: tractor folding and trailer swaying.

[0244] A hierarchical constraint domain coordination mechanism is constructed, using the normalized hinged stability margin as the constraint index, and embedding feasible domain restrictions of the upper-level optimization problem. The constraint form is as follows:

[0245]

[0246] In the formula, To predict the normalized stability margin at step j in the time domain, M s,min,i (s) represents the minimum stability margin requirement for the current arc length. β is the actual value of the stability margin of the previous arc length step; β is the stability margin adjustment coefficient, which is a dual dynamic function of curvature and longitudinal slope. Increasing β on straight sections expands the economic optimization space, while automatically narrowing β on curved sections tightens the stability boundary.

[0247] III. Linearization Solution and Reference Trajectory Generation

[0248] ①Predicted trajectory generation and synchronous linearization

[0249] At the start of each control cycle, the optimal trajectory from the previous cycle is rolled forward by one step along the arc length to generate the predicted trajectory for the current cycle, which is stored as an open-loop state sequence in the local controller. This predicted trajectory serves two functions: first, as a unified reference operating point for the current cycle's dynamic model and all nonlinear stability constraint Taylor expansions; second, as the initial value for the QP solver's hot start.

[0250] Based on the state points (x0, u0) on the predicted trajectory, the spatial domain nonlinear model is... First-order Taylor expansion is performed synchronously with nonlinear stability constraints:

[0251] The state matrix Control Matrix A linear time-varying spatial domain prediction model is obtained.

[0252] ② Dual-input fuzzy adaptive parameter update

[0253] With curvature amplitude rate of change of curvature For the input, a dual-input multi-output fuzzy controller is constructed, and the following optimization parameters are dynamically adjusted synchronously: prediction steps N p Control steps N c (or press N) c =[N p / 3] Fixed ratio correlation), spatial sampling step size Δs, hinge penalty weight Q γ Horizontal oscillation penalty weight K ω Wind resistance efficiency weight w w The stability margin adjustment coefficient is not adjusted by the fuzzy controller, but is jointly determined by the road alignment analytical function in step S24 and the three-level instability threshold mapping in step S43.

[0254] The input and output universes of discourse of the fuzzy controller are both normalized to [0,1], and a triangular membership function is used. The core rules include:

[0255] When the curvature is small and the rate of change of curvature is low (straight road conditions), increase the number of prediction steps to improve the economic optimization perspective, reduce the stability penalty weight, and increase the wind resistance efficiency weight, prioritizing computational efficiency and fuel-saving effects.

[0256] When the curvature is large and the rate of change of curvature is high (curved slope condition), the sampling step size is increased to improve the prediction resolution, amplify the stability penalty weight, and reduce the wind resistance efficiency weight, so as to prioritize the safety of driving on curves.

[0257] By using fuzzy adaptive control, dynamic parameter matching is achieved for straight road and curved / slope scenarios, balancing control accuracy, real-time performance, and safety.

[0258] ③ Construction of multi-objective optimization function

[0259] For the i-th semi-trailer truck, construct a prediction time domain N. p Control time domain N c The optimization objective function is as follows:

[0260]

[0261] Meaning of each item:

[0262] Tracking item To penalize lateral position deviation, velocity deviation, and yaw angle deviation, ensuring tracking accuracy;

[0263] Formation Coordination Based on the PLF / TPL communication topology, penalties are imposed for arc length distance errors and speed differences with neighboring vehicles to ensure formation consistency.

[0264] Articulation penalty : Penalize the hinge angle deviation from the expected value and the hinge angular velocity to suppress the risk of head breakage;

[0265] Control smoothing term : Increase the penalty control quantity to ensure the actuator's stability;

[0266] drag efficiency Optimize formation drag reduction within safety constraints to improve power utilization efficiency.

[0267] Terminal cost item To ensure the asymptotic stability of the closed-loop system, P is the terminal weight matrix, which is solved using the discrete Riccati equation.

[0268] relaxation factor Used to ensure that optimization has a solution under extremely constrained conditions, it only applies to relative performance constraints such as drive torque and lateral position, and must not relax absolute safety boundaries such as TSSC and tire adhesion.

[0269] ④Constraints and Quadratic Programming Transformation

[0270] The complete constraints of the optimization problem are:

[0271]

[0272] In the formula, X f To ensure system stability, the objective function and constraints are rearranged into a standard quadratic programming form: (This is the set of feasible endpoints.)

[0273]

[0274] ⑤ Three types of trajectory definition and full process flow

[0275] Three types of states and control trajectories are clearly defined: the predicted trajectory is used for open-loop optimization and model linearization in the current cycle; the assumed trajectory is generated by rolling and shifting the optimal trajectory from the previous cycle, and broadcast to neighboring vehicles via V2V, serving as the external input benchmark for constructing the cooperative error term for neighboring vehicles; the optimal trajectory is the optimal solution obtained from solving the optimization problem, used to output the current control command and roll and shift to generate the predicted and assumed trajectories for the next cycle. Assumptions on terminal state update rules are designed, and the terminal feedback gain is solved using the discrete Riccati equation to ensure asymptotic convergence of the terminal state; the controller weight parameters satisfy the closed-loop stability design criteria, providing a quantitative theoretical basis for parameter tuning.

[0276] The assumed terminal state is updated according to the following rules:

[0277]

[0278] In the formula, Let the terminal state of the i-th vehicle be assumed in the current period. Let i be the set of neighbors of vehicle i. Let K be the desired arc length spacing vector between vehicles j and i. The terminal feedback gain K is given by the discrete algebraic Riccati equation. Solve for Q, where Q is a positive definite weighting matrix; this update rule guarantees that the predicted end-time state converges to the desired queue. The formation closed-loop stability is satisfied by the terminal feedback gain K. Guarantee D p =D+P,λ i (*) represents the matrix eigenvalues, which drive global formation consistency through local optima.

[0279] The formation closed-loop stability is satisfied by the terminal feedback gain K. Guarantee D p =D+P,λ i (*) represents the matrix eigenvalues, which drive global formation consistency through local optima.

[0280] ⑥ Online solution and constraint relaxation

[0281] The sparse QP solver is invoked online to solve the problem, using the optimal solution from the previous cycle as the initial value for hot start. If the solution encounters an anomaly of no feasible region, the relative hard constraints are relaxed and the soft constraint weights are increased in order of priority until a feasible solution is obtained, ensuring that the control output is not interrupted.

[0282] IV. Layered Collaborative Control Execution

[0283] It adopts a two-way collaborative architecture with upper and lower layers. The upper layer is a distributed MPC tracing layer, and the lower layer is a stability verification and adjustment layer.

[0284] The hierarchical collaborative control adopts a dual-time-scale architecture:

[0285] Upper-layer distributed MPC: Predicts road arc length intervals with a relatively long time scale in the time domain, with an update period of T. upper It is responsible for global trajectory tracking and formation coordination;

[0286] Lower-level differential brake regulator: The controlled variable is the hinged state, and the update cycle is... m≥2, is a positive integer, and is responsible for performing fast stability correction within the adjacent upper-level update interval.

[0287] upper level each The lower layer updates the reference trajectory once per cycle. Within each cycle, the lower layer performs differential braking judgment and intervention based on the latest upper layer reference trajectory and the current articulation state.

[0288] ① The upper-layer distributed controller adopts a synchronous distributed predictive control framework, defining the adjacency matrix of the formation communication topology:

[0289]

[0290] Neighbors set It supports dynamic switching between PLF (lead vehicle + leader vehicle only) and TPL (leading two vehicles + leader vehicle) topologies. Each vehicle independently solves its own optimization problem, using assumed trajectories from neighbors only through V2V interaction, driving global formation consistency through local optima.

[0291] The upper layer adopts an incremental augmented state model:

[0292]

[0293] The optimal trajectory is obtained for each vehicle. Then, discard the first segment (already executed) and proceed with the remaining segments. j=0,1,...,N p -1, as the next cycle Assuming trajectory at any moment The first N p The first segment is completed by the terminal state update rules; the hypothetical trajectory is broadcast to neighboring vehicles via V2V. The received neighbor hypothetical trajectories are substituted into the cooperative error term to complete optimization; the weighting coefficients of the cooperative error are determined by the communication topology adjacency matrix. Decide: The formation closed-loop stability is satisfied by the terminal feedback gain K. It drives global formation consistency through local optimization.

[0294] ② Lower-level differential braking and stabilizing regulator

[0295] The lower layer constructs a tractor-trailer coordinated differential system. Hinged controller. The hinge angle reference value (the hinge angle sequence optimized by S3) in the optimal trajectory output by the upper-level MPC solution is used as the reference input of the controlled variable; where γ ref The feedforward steady-state desired hinge angle, defined in step S23, serves as the hinge angle tracking benchmark in the cost function of S3. S42 uses the optimization result based on this benchmark as a reference input. The regulator uses the slip ratio difference U=ΔS between the left and right wheels as the control input and tracks the error using the hinge angle. Hinged angular velocity The difference in yaw rate between the tractor and the trailer is the controlled variable.

[0296] The state-space form of the articulated regulator is (subscript) (Represents the correlation matrix of the hinge regulator)

[0297]

[0298] in , For tractor-trailer yaw coupling disturbance, Solving using LMI (Linear Matrix Inequality) Output feedback controller To ensure that the closed-loop system is protected from disturbances To the controlled output of The gain is less than the given value.

[0299] Derivation of trailer differential braking torque based on slip ratio difference:

[0300]

[0301] In the formula, For the moment of inertia of the wheel, For the speed of the wheel center, The target slip ratio.

[0302] It adopts a tractor-trailer axle-coordinated differential braking architecture, applying equal and opposite braking forces to the left and right wheels of the same axle. Ideally, it only generates a corrective yaw moment, without introducing longitudinal deceleration into the entire vehicle and without interfering with the target speed of the convoy. Derivation of the equivalent control correction for differential braking:

[0303]

[0304] Where k δ k a Where B is the corresponding conversion gain, and r is the wheel pitch. eff This is the effective radius of the wheel. The residual longitudinal force generated by differential braking is compensated in real time by the upper-level speed controller.

[0305] The upper limit of braking intensity and braking force change rate is set to ensure ride comfort; the regulator has a lower priority than the ABS system and does not interfere with the vehicle's anti-lock braking safety logic.

[0306] ③ Level 3 instability threshold and bidirectional coordination

[0307] The stability region is divided using the hinge angle-hinge angular velocity phase plane method, and three levels of instability thresholds are set: stable region, early warning region, and danger region. Among them, γ... safe γ is the safety threshold for the hinge angle stability boundary. warn The instability warning thresholds are determined by combining the TSSC ellipsoidal constraint envelope with the hinge angle phase plane stability domain partitioning in step S22. Through dual-channel feedback of constraint margin and penalty weight to the upper layer, the stability margin adjustment coefficient β mapped to S24 and the hinge penalty weight Q from S32 are quantized and mapped to the stability margin adjustment coefficient β in S24 and the hinge penalty weight Q in S32. γ Horizontal oscillation penalty weight K ω .

[0308] Stable region and The lower layer does not interfere, while the upper layer performs full performance optimization; β is taken as the nominal value β. nom Q γ K ω Take the nominal weight.

[0309] Warning Zone and The lower layer feeds back to the upper layer to tighten the constraint boundary and amplify the stabilizing weights. The hinge angle deviation narrows linearly, Q γ K ω As the hinge angle deviation increases linearly, the specific mapping relationship is as follows: Where k β k Q To adjust the gain, the value range is (0,1); this correction continues until the articulated state returns to the stable region.

[0310] Danger Zone State crossing γ warn Upon triggering, the lower layer directly initiates differential braking intervention, reconstructs the following feedback gain, and simultaneously forces the upper layer to decelerate; β narrows to its minimum value. min Q γ K ω Magnify to 3 to 5 times the nominal value to prioritize driving stability.

[0311] Within the danger zone, further differentiated control is implemented based on the instability pattern: the rapid divergence of the hinge angle is used as the criterion. With the same number and If the yaw rate continues to increase, it is determined to be an articulated folding condition. In this case, differential braking of the tractor axle is applied first to quickly suppress the increase in the articulation angle. If the periodic fluctuation of the trailer yaw rate is used as the criterion (ω2 shows continuous oscillation), it is determined to be a trailer sway condition. In this case, differential braking of the trailer axle is applied first to specifically attenuate the trailer sway.

[0312] ④ Control output synthesis and execution

[0313] The final control output is synthesized in the following three-layer structure:

[0314] Baseline layer: Upper-layer MPC feedback control quantity The output is directly optimized by S3's scrolling mechanism;

[0315] Feedforward compensation layer: Multi-dimensional road alignment feedforward compensation amount in step S23 It is added to the reference layer in an additive manner to achieve active feedforward cancellation of curvature disturbance;

[0316] Safety correction layer: Lower layer differential braking correction amount The differential braking torque is derived from step ② and is superimposed in a weighted manner in the warning zone and the danger zone.

[0317] The synthesis form is:

[0318] Where the weighting coefficient λ brk The stability region λ is determined by the third-order instability threshold of S43. brk =0, warning zone follows

[0319] The danger zone λ increases linearly from 0 to 1. brk =1.

[0320] Physically limited by the actuator After being limited by the rate of change, the output is sent to the steering system, drive system, and braking system to complete the final control execution; the ABS anti-lock braking system has the highest priority—below the next level. When the brake command from the regulator causes the slip ratio of any wheel to exceed the ABS trigger threshold, the brake command for that axle is taken over by the ABS. The regulator retains braking on axles that have not triggered ABS.

Claims

1. A method for optimizing the platooning control of autonomous semi-trailer trucks under complex road alignments, characterized in that, The specific implementation steps are as follows: Step S1: Real-time acquisition of discrete coordinates, slope, and superelevation of the road ahead; collection of self-state information and state information of other trucks in the platoon; and establishment of vehicle coupled dynamics equations. Step S2: The curvature and slope linear parameters are transformed into the spatial domain through the chain rule, and the dynamic constraints in the rolling spatial prediction domain optimization are mapped to achieve feedforward suppression of instability risk. Step S3: Linearize the spatial domain nonlinear model and constraints, construct a multi-objective optimization function and transform it into a quadratic form for solution to obtain the optimal trajectory and control sequence; Step S4: A hierarchical collaborative control is adopted. The upper layer distributed MPC completes the collaborative control of path, speed and formation spacing; the lower layer determines the instability trend based on the articulated phase plane, the early warning zone feeds back to the upper layer to tighten the safety boundary, and the danger zone triggers braking intervention.

2. The method for optimizing the platooning control of autonomous semi-trailer trucks under complex road alignments according to claim 1, characterized in that, The specific implementation process of step S1 is as follows: Step S11: Obtain the discrete coordinate point sequence (X,Y) of the road reference path and the longitudinal slope using the vehicle-mounted high-precision map. Horizontal superelevation ; The vehicle acquires its own vehicle status information, including the longitudinal speed v of the tractor, through onboard sensors and an articulation angle acquisition unit. 1x Lateral velocity v 1y yaw rate Hinge angle γ, hinge angular velocity Trailer yaw rate Depend on The following components were synthesized: Tractor mass m1, trailer mass m2, and tractor yaw moment of inertia I. z1 Trailer yaw moment of inertia I z2 Tractor wheelbase l f Trailer wheelbase l r Distance from center of mass to traction pin l c1 l c2 Wheelbase B, center of gravity height h g The vehicle's physical parameters are provided by the preset vehicle parameter table in the vehicle controller; the tire side stiffness coefficient f is obtained by fitting tire test data. Obtain the status information of neighboring vehicles within the platoon through V2V communication, including the positions of the leading and convoy vehicles. j The speeds u of the leading and trailing vehicles j The yaw angle between the leading vehicle and the lead vehicle The articulation angle γ between the leading vehicle and the lead vehicle j Used for subsequent cooperative error term e i,coop The interaction between the calculation and the assumed trajectory; The current road adhesion coefficient μ is obtained in real time through an on-board road condition estimation algorithm, which serves as the basis for calculating the tire force boundary and the semi-trailer stability constraint (TSSC) stability boundary; a conservative safety value μ is adopted. safe : In the formula, μ min This is the minimum adhesion limit for the road surface; To estimate the adhesion coefficient in real time; k μ σ is the safety margin factor; μ To estimate the variance of the attachment; Fifth-order polynomial smoothing is applied to the discrete reference path points to obtain a continuously differentiable path function y=f(s). The curvature is then calculated using the arc length s as the independent variable. With rate of change of curvature : Curvature values ​​are extracted from the corresponding arc length intervals according to the prediction time domain range to form a look-ahead curvature sequence, which serves as the known external input parameter for model predictive control. Step S12: Construct a complete set of rigid body dynamic equations for the tractor and trailer, each with longitudinal, lateral, and yaw motions, using a Newton-Euler multibody framework; construct a zero-space projection matrix based on the hinge velocity constraint of the traction pin, eliminate the non-independent longitudinal and lateral motion components of the trailer, and reduce the dimensionality to obtain a fourth-order rigid body motion model containing only four independent physical degrees of freedom: longitudinal, lateral, and yaw motion of the tractor and yaw motion of the trailer; based on this, the hinge angle... Introduced as independent state variables, the state vector is combined to form a five-state coupled prediction model containing five state variables: the longitudinal velocity, lateral velocity, yaw rate of the tractor, the yaw rate of the trailer, and the articulation angle. For the yaw angle of the tractor unit, The trailer yaw angle is used; the five-state coupled prediction model incorporates the gravity components corresponding to road slope and superelevation to adapt to the stress characteristics of complex curved and sloping roads. The slope decomposition method is used to decouple the comprehensive slope angle into longitudinal climbing angle and lateral tilt angle, and the longitudinal and lateral decoupling calculation of the gravity component is completed. Based on the look-ahead curvature sequence, the steady-state sideslip angle, steady-state yaw rate and steady-state hinge angle of the curve are pre-calculated as the linearization reference working point. Tire lateral stiffness varies linearly with axle vertical load C i : C i =f·F Zi In the formula, f is the normalized lateral stiffness, F Zi The vertical load corresponds to the axle; the vertical load of each axle is calculated based on the total vehicle mass, axle load distribution, and lateral load transfer during curves. Step S13: Based on graph theory, complete the standardized modeling of the formation communication topology, define the adjacency matrix and in-degree matrix, and introduce the traction matrix to give the lead vehicle-navigator following topology PLF and the double lead vehicle following topology TPF; the matrix representation of the two communication topologies provides a unified mathematical framework for dynamic topology switching and stability analysis. Step S14: Establish a semi-trailer truck air resistance model that considers the correction of the platoon spacing, calculate the wind resistance force of the tractor and trailer respectively, embed the wind resistance into the longitudinal dynamic equation, and dynamically correct the wind resistance coefficient with the arc length distance between the vehicle and the vehicle in front. Construct a dynamic drag model related to the following distance, and calculate the resultant air resistance F of the whole vehicle. W : Dynamic drag reduction with exponential decay of drag coefficient : In the formula: ρ is the air density; A is the windward area; C d d is the drag coefficient of a single vehicle; s η is the arc length spacing of the workshop. d This represents the maximum drag reduction ratio; d is the attenuation characteristic length; min Minimum safe following distance; C d0 V is the standard drag coefficient for a single vehicle. x This represents the vehicle's longitudinal speed.

3. The method for optimizing the platooning control of autonomous semi-trailer trucks under complex road alignments according to claim 1, characterized in that, The specific implementation process of step S2 is as follows: Step S21: Perform the transformation from the time domain to the spatial domain based on the chain rule, using the complete Frenet relation: In the formula, s is the arc length of the road centerline. Let V be the arc length velocity. x V is the longitudinal velocity of the vehicle. y Let be the lateral velocity at the vehicle's center of gravity. e is the angle between the vehicle's heading and the road tangent. y This is a lateral positional deviation. Let f(x,u) represent the road curvature, be the time-domain form of the vehicle's nonlinear state-space equation, where x is the state vector and u is the control vector; set To avoid spatial domain singularity issues under low-speed conditions; after the transformation, all vehicle states, tracking errors, and constraints are mapped to the arc length coordinate system, and the expected vehicle spacing in the formation is defined as the arc length spacing along the road. After the conversion, the vehicle's dynamic state, tracking error, and constraints all use arc length s as the independent variable; The expected vehicle spacing within the formation is defined as the arc-length distance along the road. Neighboring vehicle states are obtained via V2V communication and directly aligned using arc-length coordinates, requiring no additional conversion. To ensure... There is a positive lower bound under low-speed operating conditions. make ,in ; Indicates the curvature of the road. The minimum permissible value for arc-length velocity; Using a spatial sampling step size Δs to perform forward Euler discretization on the above spatial domain differential equations, a nonlinear discrete state-space model is obtained: Where x(s) is the state vector of the current arc length step, and u(s) is the control input of the current arc length step. Let the state variable be the rate of change with respect to time. The arc-length velocity is determined by the complete Frenet relation; This discrete state-space model serves as the basic controlled object for linearization and rolling optimization in step S3. Step S22: The hard constraints are ordered from high to low priority as follows: TSSC includes yaw stability envelope and rollover LTR constraint, followed by tire attachment ellipse constraint, drive / brake torque constraint, and lateral position boundary constraint; among them, TSSC, with articulation angle and yaw rate difference between tractor and trailer as core variables, is the core safety boundary to prevent tipping and trailer swaying, and cannot be relaxed throughout the entire process. A look-ahead sequential dynamic constraint system is adopted. The constraint boundary of each arc length step in the prediction time domain is updated according to the following rules: the curvature and slope are linked to update the upper limit of lateral acceleration and the torque limit, the road adhesion coefficient is linked to update the tire force boundary and TSSC envelope range, and the lane width is linked to update the lateral position boundary. TSSC uses a normalized ellipsoid constraint form: In the formula, z s Let γ be the stable state vector, and γ be the hinge angle. For hinge angular velocity, P represents the difference in yaw rate between the tractor and trailer, LTR represents the lateral load transfer rate; s Let T be an ellipsoidal matrix that dynamically varies with velocity v, road surface adhesion coefficient μ, and vehicle mass m, where T represents the transpose. The safe speed for a vehicle in a curve is determined jointly by the lateral acceleration limit and the articulated stability boundary, with the lower bound of both being used: In the formula, a y,max The upper limit of lateral acceleration is determined jointly by road surface adhesion and rollover threshold; The speed limit is derived from the upper limit of lateral acceleration. Valid for a period of time. The upper limit of vehicle speed is derived from the hinge angle stability boundary and is negatively correlated with the curvature amplitude; Step S23: Design multi-dimensional steady-state feedforward compensation terms based on the entire look-ahead curvature sequence. These terms compensate for motion deviations caused by road curvature in advance from three dimensions: platooning speed, tractor steering, and semi-trailer articulation steady state. All feedforward quantities together constitute the steady-state feedforward benchmark, which is input to S3 as the initial reference for rolling optimization and the initial value for hot start. ① Combining forward curvature planning with the synchronous smooth speed curve of the entire fleet, upper and lower limits are set for acceleration and jerk to ensure synchronous speed of the formation driving under curves and reduce the impact of articulation in the workshop; ② Introduce an underspeed steering correction term to construct the steady-state steering feedforward, calculated using the following formula: In the formula δ ff (s) represents the steady-state steering feedforward; L represents the tractor wheelbase; K v V represents the understeer gradient, characterizing the correction of steering gain by vehicle speed; 1x (s) represents the longitudinal speed of the tractor; k γ γ is the hinge angle compensation coefficient, used to map the hinge angle to the front wheel steering angle compensation amount; ref (s) represents the steady-state desired hinge angle; ③ Abandoning the pure geometric hinge angle calculation method, a vehicle speed dynamics compensation coefficient is introduced to derive the steady-state expected hinge angle suitable for high-speed operating conditions: In the formula, The longitudinal distance from the center of gravity of the tractor unit to the traction pin. The longitudinal distance from the trailer's center of gravity to the draw pin; k on low adhesion coefficient road surfaces vγ Automatic adjustment to ensure that the feedforward compensation of the articulation angle does not exceed the tire force adhesion limit; at the same time, soft penalty constraints on the articulation angle and articulation angular velocity are added to the rolling optimization objective function, and the dynamic fluctuation of the articulation angle is further weakened by feedback control, and the two types of instability conditions, namely tractor folding and trailer swaying, are suppressed simultaneously. The aforementioned speed feedforward, steering feedforward, and articulation angle feedforward together constitute a feedforward compensation mechanism for curvature disturbances. This mechanism pre-corrects the reference trajectory and steady-state benchmark before predictive control roll optimization, thereby achieving proactive suppression of instability risks. Step S24: Construct a hierarchical constraint domain coordination mechanism, using the normalized hinged stability margin as the constraint index, and embedding feasible domain restrictions of the upper-level optimization problem. The constraint form is as follows: In the formula, To predict the normalized stability margin at step j in the time domain, M s,min,i (s) represents the minimum stability margin requirement for the current arc length. β is the actual value of the stability margin of the previous arc length step; β is the stability margin adjustment coefficient, which is a dual dynamic function of curvature and longitudinal slope. Increasing β on straight sections expands the economic optimization space, while automatically narrowing β on curved sections tightens the stability boundary.

4. The method for optimizing the platooning control of autonomous semi-trailer trucks under complex road alignments according to claim 3, characterized in that, The specific implementation process of step S3 is as follows: Step S31: In each control cycle, the optimal trajectory of the previous cycle after the rolling shift is used as the predicted trajectory, and the differential braking state correction of the previous cycle fed back in S42 is superimposed to update the initial state. The first-order Taylor expansion linearization is performed simultaneously on the nonlinear dynamic model in the spatial domain and all nonlinear TSSC stability constraints; the linearization error is checked in real time, and the steady-state operating point is updated if the error exceeds the limit. A fuzzy controller is constructed using curvature amplitude and curvature change rate as dual inputs, and the penalty weight matrix Q for prediction steps and hinge angle deviation is dynamically adjusted synchronously. γ Simultaneously update the stability margin coefficient β and wind resistance weight w based on the current curvature and slope. w Balancing control precision, computational efficiency, and driving stability; Step S32: Construct a multi-objective optimization function, integrating hard constraint boundary conditions and soft constraint penalty terms: In the formula, J i Indicates the first The total optimization cost function for the vehicle, N p N represents the prediction time-domain steps, j represents the vehicle, and N represents the number of prediction time-domain steps. i e represents the total number of neighboring vehicles. i,track For individual trajectory tracking error, e i,coop,l To account for the state coordination error with neighboring vehicle l, Δγ i The hinge angle deviation, Δμ i For the control increment, Q is the trajectory tracking error weight matrix, and F is the formation coordination error weight matrix. γ R is the hinge angle deviation penalty weight matrix, R is the control increment penalty weight matrix, and P is the terminal cost weight matrix; P w,i P is the power of vehicle air resistance. w,base As the reference power, The penalty weight for yaw oscillation, The yaw rate of the tractor unit. The yaw rate of the trailer. For the difference in yaw rate, This is the terminal state error vector. To predict the final time in the time domain, s represents the current arc length position. This indicates predicting the future t at time s. The position of the arc length; For yaw oscillation penalty term, weight The greater the curvature of the curve, the higher the stability penalty weight, and priority is given to suppressing the risk of trailer yaw. This is a relaxation factor penalty term; As the baseline weight for yaw penalty; The curvature sensitivity coefficient; Step S33: Organize all linearization constraints into inequality constraints, and use the optimal solution from the previous cycle to start QP solution; when there is no feasible region, the relaxation factor will automatically adjust the soft constraints first; if there is still no feasible solution, the relatively hard constraints will be relaxed step by step according to the constraint priority from low to high; the TSSC absolute safety hard constraints will not be relaxed under any circumstances. The solution space of the optimization problem within each control cycle is divided into three types of trajectory sequences with different lifecycles and interaction attributes: predicted trajectory, hypothetical trajectory, and optimal trajectory.

5. The method for optimizing the platooning control of autonomous semi-trailer trucks under complex road alignments according to claim 4, characterized in that, The predicted trajectory is defined as the open-loop state sequence formed by the rolling shift of the optimal trajectory of the previous cycle, and is stored in the local controller as the working base point for the linearization of the current cycle model and the initial value for the hot start of the optimization solution. The hypothetical trajectory is defined as a complete predicted time-domain sequence obtained by truncating, shifting, and supplementing the current period's optimal trajectory with terminal state update rules. This trajectory is broadcast to neighboring vehicles in the formation via a V2V communication link, serving as an external consistency benchmark for neighboring vehicles to construct cooperative error terms, thereby ensuring the compatibility of optimization propositions for each vehicle in distributed optimization. The optimal trajectory is defined as the sequence of feasible optimal solutions to the quadratic programming problem in the current cycle. The first segment of the control input is output to the actuator, and the remaining segments are used to update the predicted trajectory and the assumed trajectory for the next cycle after rolling shift. Assuming the terminal state update rule consists of a rolling shift operation, arc length coordinate alignment constraints, and terminal feasible set projection, its update form is as follows: In the formula, K is the terminal feedback gain, derived from the discrete algebraic Riccati equation. Solving for the controller weights, we find that they satisfy the positive definite closed-loop stability criterion, providing a quantitative theoretical basis for parameter tuning. For vehicles In the assumed terminal state of the next cycle, A s For discrete state matrices, For vehicles In the assumed terminal state of the current cycle, B s Let K be the discrete input matrix, and K be the terminal feedback gain matrix. In order to settle the score with the neighbor's vehicle, Let j be the assumed terminal state of the neighboring vehicle in the current period. Let i be the assumed terminal state of vehicle i in the current period; For vehicles The set of neighbors; Let represent the expected arc length spacing vector between vehicles j and i.

6. The method for optimizing the platooning control of automated semi-trailer trucks under complex road alignments according to claim 4, characterized in that, The specific implementation process of step S4 is as follows: Step S41: Adopt a synchronous distributed predictive control framework to support dynamic switching of PLF and TPL communication topologies; introduce a communication delay compensation mechanism; and adopt an incremental augmented state model at the upper layer. Let be the augmented state vector for the next arc-length step. Let Δs be the augmented state vector for the current arc-length step, and Δs be the spatial sampling step size. For the augmented state matrix, The augmented input matrix is ​​denoted by Δu(s), which is the control increment vector, ξ(s), which is the original state vector, and u(s-Δs), which is the control input of the previous cycle. The optimal trajectory is obtained for each vehicle. Then, discard the first segment and proceed with the remaining segments. Assuming the trajectory at time s+Δs in the next period The first N p Segment, j=0,1,...,N p -1, the final stage is completed by the terminal state update rule; the hypothetical trajectory is transmitted to neighboring vehicles via V2V broadcast, and the terminal state of each vehicle's hypothetical trajectory is updated and completed according to the rule described in step S3. The terminal feedback gain ensures that the predicted time domain terminal state asymptotically converges to the desired queue. Under the premise of communication topology connectivity and latency meeting the upper limit, it supports the compatibility and formation consistency of distributed optimization; the received neighbor hypothetical trajectories are substituted into the cooperative error term to complete the optimization. The weighting coefficient of the cooperative error is determined by the communication topology adjacency matrix: The formation closed-loop stability is satisfied by the terminal feedback gain K. Guarantee D p =D+P,λ i (*) represents the matrix eigenvalues, driving global formation consistency through local optima; A il Let A be the (i,l)th element of the communication topology adjacency matrix. il =1 indicates that vehicle i can receive the hypothetical trajectory information of vehicle l; , Let be the hypothetical trajectory state vectors of vehicle i and its neighboring vehicle l at arc length s, respectively; N is the desired arc length spacing vector between vehicles i and l; i Let i be the set of neighbors of vehicle i; This is the adjacency matrix of the communication topology. Let λ be the augmented in-degree matrix, where D is the in-degree matrix and P is the traction matrix; i (*) represents the eigenvalues ​​of the matrix, and δ is a positive number that guarantees stability margin, 0 < δ < 1; Step S42: Lower-level construction of tractor-trailer cooperative differential The articulated controller uses the articulated angle reference value in the optimal trajectory output by the upper-level MPC as the controlled variable reference input; the controller uses the slip ratio difference U=ΔS between the left and right wheels as the control input and the articulated angle tracking error as the control input. Hinged angular velocity Difference in yaw rate between tractor and trailer The controlled quantity; among which The feedforward steady-state desired hinge angle defined in step S23 is used as the hinge angle tracking benchmark in the cost function of step S3, and the optimization result of this benchmark is used as the reference input in S42. The state space form of the hinge regulator is as follows: subscript Represents the correlation matrix of the hinge regulator: in, , The time derivative of the state vector. Hinged angle, For hinge angular velocity, The difference in yaw rate between the tractor and trailer is represented by denoted as W; the yaw coupling disturbance between the tractor and trailer is represented by denoted as W. Solving using the Linear Matrix Inequality (LMI) The output feedback controller ensures that the closed-loop system is protected from disturbances. To the controlled output of The gain is less than the given value; For the control input of the slip ratio difference between the left and right wheels; A h For the state matrix of the hinged regulator, B h1 Let B be the perturbation input matrix. h2 To control the input matrix, C h D is the output matrix of the hinged regulator. h11 For the direct transfer matrix of the perturbation, D h12 To control the direct transfer matrix, the subscript h denotes the correlation matrix of the articulated regulator; the output feedback controller is solved using LMI to ensure the closed-loop system changes from disturbance W to the controlled output Z. The gain is less than the given value; Equal and opposite braking forces F are applied to the left and right wheels on the same axle. b,L F b,R This generates a corrective yaw moment M. z At the same time, it does not produce longitudinal deceleration of the entire vehicle: In the formula, B is the wheelbase, and F is the track width. b,L F b,R The braking forces of the left and right wheels on the same axle are M and M respectively. z To generate the corrective yaw moment, F x,brake This refers to the longitudinal braking force of the entire vehicle; when the braking forces of the left and right wheels are equal in magnitude and opposite in direction, F b,R =-F b,L F x,brake =0; Therefore, the equivalent control correction for differential braking is derived as follows: Where k δ k a This corresponds to the conversion gain; the additional longitudinal deceleration generated by differential braking is compensated in real time by the upper-level speed controller; Δδ brk , Δa x,brk These are the equivalent steering correction and the equivalent longitudinal acceleration correction, respectively. The differential braking effect is fed back to the upper-level MPC in the next cycle through three dimensions: First, the changes in longitudinal speed, hinge angle, and yaw rate caused by braking are used as state correction quantities to update the initial state of optimization in step S31; Second, the increase in longitudinal tire force occupied by differential braking is substituted into the tire adhesion ellipse constraint to correct the upper limit of available lateral force; Third, the total longitudinal braking force is embedded as a known disturbance quantity into the longitudinal dynamics feedforward and compensated in advance by the upper-level speed controller. Step S43: The stability region is divided using the hinge angle-hinge angular velocity phase plane method. Three levels of instability thresholds are set: stable region, early warning region, and danger region. The stability margin adjustment coefficient is quantized and mapped to the stability margin adjustment coefficient in S24 through a dual-channel feedback mechanism of constraint margin and penalty weight. The hinge penalty weight Q of S32 γ Horizontal oscillation penalty weight K ω ; Stable region: and The lower layer does not interfere, while the upper layer performs full performance optimization; β is taken as the nominal value β. nom Q γ K ω Take the nominal weight; Warning zone: and The lower layer feeds back to the upper layer to tighten the constraint boundary and amplify the stabilizing weights. Q narrows linearly with the hinge angle deviation. γ K ω As the hinge angle deviation increases linearly, the specific mapping relationship is as follows: Where k β k Q To adjust the gain, the value range is (0,1); β nom γ is the nominal value of the stability margin. safe γ is the safety threshold for the hinge angle. warn Q is the hinge angle warning threshold. γ,nom The nominal value of the hinge penalty weight; Danger Zone The lower layer directly initiates differential braking intervention, reconstructs the following feedback gain, and simultaneously forces the upper layer to decelerate; β is narrowed to its minimum value. min Q γ K ω Magnify the value to 3 to 5 times the nominal value to prioritize driving stability; Step S44, Control Output Synthesis and Execution: The final control output is synthesized as follows: The reference layer is the upper-layer MPC feedback control quantity. ; For the optimal front wheel steering angle of the upper-level MPC, The optimal longitudinal acceleration for the upper-layer MPC; The feedforward compensation layer is the multi-dimensional road alignment feedforward compensation amount in step S23. It is added to the base layer in an additive manner; δ ff For feedforward compensation steering amount, a x,ff For feedforward compensation of longitudinal acceleration; The safety correction layer is the differential braking correction amount of the lower layer. The warning zone and the danger zone are superimposed in a weighted manner, and the weight is determined by the third-level instability threshold in step S43; This is the differential braking steering correction amount. This is the longitudinal acceleration correction for differential braking; Synthetic steering command δ cmd And the synthetic longitudinal acceleration command a x,cmd for: Where λ brk For the braking intervention weight determined in step S43, the stable region is 0, the warning region increases linearly, and the danger region is 1. Physically limited by the actuator After being limited by the rate of change, the output is sent to the steering system, drive system, and braking system to complete the final control execution; the ABS anti-lock braking system has the highest priority, and the next layer... When the brake command from the regulator causes the slip ratio of any wheel to exceed the ABS trigger threshold, the brake command for that axle is taken over by the ABS. The regulator retains braking authority for axles that have not triggered ABS to ensure braking safety; where δ is the front wheel steering angle control value, δ max The maximum permissible front wheel steering angle; a x For longitudinal acceleration control, a x,min and a x,max These are the lower limit of longitudinal acceleration, i.e., the maximum braking deceleration, and the upper limit, i.e., the maximum acceleration capability.

7. The method for optimizing the platooning control of autonomous semi-trailer trucks under complex road alignments according to claim 1, characterized in that, The formation adopts a PLF / TPL switchable communication topology. The neighbor coordination error term in the objective function selects the corresponding neighbor vehicle according to the current communication topology, and drives global formation consistency through local optimization.

8. An automated semi-trailer truck platooning control optimization system for complex road alignments, comprising a processor, a memory, and a bus, wherein the memory stores machine-readable instructions executed by the processor; characterized in that, When the system is running, the processor communicates with the memory via a bus, and the machine-readable instructions are executed by the processor as described in any one of claims 1 to 7. This is an optimization method for autonomous driving semi-trailer truck platooning control under complex road alignments.

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