A multi-vehicle cooperative control method, system, medium and program product

Abstract

This invention discloses a multi-vehicle cooperative control method, system, medium, and program product. The method includes constructing a lateral and longitudinal coupled dynamic model for the multi-vehicle cooperative transportation system and extracting the model matrix of the lateral and longitudinal coupled dynamic model; constructing system constraint equations for the multi-vehicle cooperative transportation system with the cargo as the leader, including motion constraints and articulation constraints, and extracting the constraint matrix of the system constraint equations; obtaining the real-time state of the multi-vehicle cooperative transportation system; calculating the constraint forces of the multi-vehicle cooperative transportation system based on the model matrix of the lateral and longitudinal coupled dynamic model, the constraint matrix of the system constraint equations, and the real-time state; and calculating the actual control quantities of each vehicle based on the constraint forces of the multi-vehicle cooperative transportation system. This invention aims to solve the challenges of strong coupling, nonlinearity, and underactuation in existing multi-vehicle cooperative transportation systems, and improve the tracking performance of multi-vehicle cooperative transportation systems under topologically stable configurations.

Description

Technical Field

[0001] This invention relates to multi-vehicle cooperative control technology in the field of transportation, specifically to a multi-vehicle cooperative control method, system, medium, and program product. Background Technology

[0002] With the increasing demand for transporting large industrial components, traditional single-vehicle transportation modes face severe challenges in terms of safety, stability, and flexibility. Against this backdrop, Cooperative Transportation Systems (CTS), with their distributed cooperative control and load-bearing capabilities, have become an effective means of solving the problem of transporting large cargo. However, the nonlinearity, strong coupling, and underactuated characteristics of CTS make system topology stability and accurate trajectory tracking extremely challenging. With the rapid development of integrated molding technology for large components and smart logistics, CTS has become a key technology for the automated transportation of ultra-large, ultra-long, and ultra-heavy cargo. This technology, through a multi-vehicle combined transportation mode and a distributed drive architecture, achieves coordinated load-bearing and coordinated movement, significantly improving transportation efficiency and system robustness.

[0003] To achieve stable and reliable collaborative transportation, the control system of a multi-vehicle collaborative transportation system must simultaneously accomplish two core tasks: accurate trajectory tracking and strict maintenance of vehicle spacing, to prevent cargo damage due to internal force imbalance. Early research on multi-vehicle collaborative transportation systems mainly focused on controller design based on simplified models. These methods typically simplify the transportation unit into a single / dual integrator dynamic model and employ control architectures such as "leader-follower," "virtual structure," or fully distributed control to achieve collaborative transportation. For example, based on single-integral and distributed model predictive control, multiple robots have achieved autonomous alignment and collaborative handling at the edge of objects; decentralized behavior perception methods have enabled multiple robots to form a closed-loop collaborative transportation system in obstacle environments; and a combination of leader-follower and impedance control has addressed the slippage problem of underactuated robotic arms in loose grasping. These methods are simple in model and easy to implement, capable of performing basic formation and trajectory tracking tasks. However, integral models cannot characterize nonlinear features such as tire force saturation and longitudinal and lateral coupling, essentially ignoring the inherent dynamic coupling relationship between vehicles and cargo. This not only limits control accuracy but also makes it difficult to ensure the safety and integrity of cargo transportation under dynamic conditions. To overcome the aforementioned limitations, subsequent research has gradually shifted towards control methods based on dynamic models. The Udwadia-Kalaba (UK) equations, as an emerging constrained dynamics modeling method, allow for the use of redundant coordinates to simplify system descriptions. They are applicable to systems with both holistic and nonholonomic constraints and can explicitly analyze the generalized constraint forces required to satisfy those constraints. Yi Kui et al. established an underactuated coupled dynamic model based on the UK equations, realizing collaborative aerial lifting by a multi-rotor robot; Dai Yusheng et al. used the UK equations combined with a hierarchical decoupling architecture to achieve trajectory tracking and lateral stability control of a dual-articulated vehicle system. These methods are theoretically more complete and can better handle system coupling problems. However, most existing work still adopts a "distributed" control paradigm, treating the vehicle as an independent control unit, continuing the "vehicle-centric" control concept. This results in the need to design independent tracking controllers for each transport unit, creating indirectness with the ultimate goal of "safe and efficient delivery of goods," leading to a bloated and inefficient control architecture. Furthermore, cooperative transportation systems are essentially underactuated systems, and their dynamics exhibit strong nonlinearity and nonholonomic constraints. Traditional control methods, such as feedback control, model predictive control, and sliding membrane control, often rely on simplified or complex coordinate transformations of specific structures, lacking a universal constraint handling framework, which limits their applicability and scalability in diverse scenarios. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a multi-vehicle cooperative control method, system, medium and program product to address the above-mentioned problems in the prior art. The present invention aims to solve the challenges of strong coupling, nonlinearity, underactuation and parameter uncertainty in the existing multi-vehicle cooperative transportation system, and improve the tracking performance of the multi-vehicle cooperative transportation system under topological stability.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: A multi-vehicle cooperative control method includes the following steps: constructing a lateral and longitudinal coupled dynamic model for a multi-vehicle cooperative transportation system and extracting the model matrix of the lateral and longitudinal coupled dynamic model; constructing system constraint equations for the multi-vehicle cooperative transportation system with the cargo as the leader, including motion constraints and articulation constraints, and extracting the constraint matrix of the system constraint equations; obtaining the real-time state of the multi-vehicle cooperative transportation system; calculating the constraint force of the multi-vehicle cooperative transportation system based on the model matrix of the lateral and longitudinal coupled dynamic model, the constraint matrix of the system constraint equations, and the real-time state; and calculating the actual control quantity of each vehicle based on the constraint force of the multi-vehicle cooperative transportation system.

[0006] Optionally, the multi-vehicle cooperative transportation system includes n vehicles distributed in an equilateral polygon, with the n vehicles rigidly connected to the cargo at the center, and the center of gravity of the cargo located at the geometric center of the polygon; the functional expression of the constraint force of the multi-vehicle cooperative transportation system is: ; ; ; in, For the constraints of multi-vehicle cooperative transportation systems, For the binding force of goods, ~ These represent the constraint forces for vehicles 1 through n, respectively. Let T represent the constraint forces on vehicle i, where T in the superscript is the transpose of the matrix. ~ and ~ For vehicles 1 to n respectively X and Y Directional force, , , and For vehicle i and goods in X and Y Directional force, and The cargo acts on vehicle i respectively X and Y The direction of the force, i=1,2,…,n; and These are two virtual control components for vehicle i.

[0007] Optionally, the functional expression for calculating the actual control quantity of each vehicle based on the constraints of the multi-vehicle cooperative transportation system is as follows: ; in, Let i be the front wheel steering angle. The rear-wheel drive force of vehicle i, The longitudinal force of the front tires of vehicle i. Let be the lateral stiffness of the front tires of vehicle i. and Let be the longitudinal velocity and the lateral velocity of vehicle i, respectively. Let i be the yaw rate of vehicle i. The distance from the front axle to the center of gravity of vehicle i is given. The actual control parameters of vehicle i include the front wheel steering angle of vehicle i. and rear-wheel drive .

[0008] Optionally, when constructing a lateral and longitudinal coupled dynamic model for a multi-vehicle cooperative transportation system and extracting the model matrix of the lateral and longitudinal coupled dynamic model, the functional expression of the lateral and longitudinal coupled dynamic model constructed for any vehicle i is: ; in, Let be the inertia matrix of vehicle i. Let be the generalized acceleration vector of vehicle i. Let i be the Coriolis force matrix of vehicle i. Let be the input matrix for vehicle i. Let the constraint force be for vehicle i, and we have: ; ; ; ; ; ; in, and Let i be the mass and moment of inertia of vehicle i, respectively. , and These are the longitudinal acceleration, lateral acceleration, and yaw rate of vehicle i, respectively. Let i be the air resistance of vehicle i. Let be the lateral force on the rear tire of vehicle i. Let be the vertical force on the rear tire of vehicle i. Let i be the yaw rate of vehicle i. Let i be the yaw angle of vehicle i. Let be the distance from the center of gravity of vehicle i to the rear axle; when constructing a lateral and longitudinal coupled dynamic model for the multi-vehicle cooperative transportation system and extracting the model matrix of the lateral and longitudinal coupled dynamic model, the functional expression of the lateral and longitudinal coupled dynamic model constructed for the cargo is: ; in, Let be the inertia matrix of the cargo. Let be the generalized acceleration vector of the cargo. The Coriolis force matrix of the cargo, The input matrix is ​​for the goods. The binding force on the goods is: ; ; ; ; ; ; in, and These are the mass and moment of inertia of the cargo, respectively. , and These are the longitudinal acceleration, lateral acceleration, and yaw rate of the cargo, respectively. This is the desired distance between the center of gravity of the cargo and the vehicle. The lateral angle of the goods. and As intermediate variables; the functional expression for extracting the model matrix of the horizontal and vertical coupled dynamic model is: ; ; ; in, The system inertia matrix of a multi-vehicle cooperative transportation system. ~ Let be the inertia matrices of vehicles 1 to n, respectively. The system force matrix of a multi-vehicle cooperative transportation system. ~ These are the Coriolis force matrices for vehicles 1 to n. The system input matrix for a multi-vehicle cooperative transportation system. ~ These are the input matrices for vehicles 1 to n, respectively.

[0009] Optionally, when constructing system constraint equations for a multi-vehicle cooperative transportation system, with cargo as the lead vehicle and including motion constraints and articulation constraints, and extracting the constraint matrix of the system constraint equations, the system constraint equations for motion constraints include first-order and second-order constraint equations for desired travel path constraints and desired speed constraints; the system constraint equations for articulation constraints include first-order and second-order constraint equations for articulation constraints; the functional expressions for the first-order and second-order constraint equations for desired travel path constraints are as follows: The functional expressions for the first-order and second-order constraint equations of the desired driving path constraint are as follows: ; ; ; ; ; in, Let be the coefficient matrix of the desired driving path constraint. For a multi-vehicle cooperative transportation system, the generalized velocity vector is... For a multi-vehicle cooperative transportation system, the generalized acceleration vector is... and Position vector of multi-vehicle cooperative transportation system The first and second derivatives are calculated to obtain the result. , Let be the position vector of the goods. ~ Let be the position vectors of vehicles 1 to n. Let the matrix be the right-hand side of the first-order constraint of the desired driving path constraint. This is the matrix of the right-hand side terms of the second-order constraint of the desired driving path constraint. The expected route for the goods. Let X be the coordinate of the cargo in the X direction. Let X be the velocity of the cargo in the X direction; the functional expressions of the first-order and second-order constraint equations for the desired velocity constraint are: ; ; ; ; ; in, The coefficient matrix represents the desired velocity constraint. This is the matrix of the right-hand side of the first-order constraint for the desired velocity constraint. Let be the matrix of the right-hand side terms of the second-order constraint of the desired velocity constraint. The lateral angle of the goods. Let yaw rate be the angular velocity of the cargo. Let Y be the velocity of the cargo. For the desired speed; The functional expressions for the first-order and second-order constraint equations of the hinged constraint are as follows: ; ; ; ; ; in, This is the coefficient matrix of the hinge constraint. This is the matrix of the right-hand side terms of the second-order constraint of the hinged constraint. Let be the right-hand side term matrix of the second-order constraint of the hinged constraint; the functional expression for extracting the constraint matrix of the system constraint equation is: ; ; ; in, This is the coefficient matrix of the system's overall constraints. This is the matrix of the right-hand side terms of the second-order constraints of the system's total constraints. This is the matrix of the right-hand side terms of the first-order constraints of the system's total constraints.

[0010] Optionally, when acquiring the real-time status of the multi-vehicle cooperative transportation system, the real-time status includes the generalized position vector of the goods, the generalized velocity vector of the goods, the generalized position vectors of each vehicle, and the generalized velocity vectors of each vehicle: ; ; ; ; in, Let be the generalized position vector of the goods. , and These are the X-coordinate, Y-coordinate, and yaw angle of the cargo, respectively. Let be the generalized velocity vector of the cargo. , and These are the cargo's X-direction velocity, Y-direction velocity, and yaw rate, respectively. Let be the generalized position vector of vehicle i. , and These are the X-coordinate, Y-coordinate, and yaw angle of vehicle i, respectively. Let be the generalized velocity vector of vehicle i. , and These are the X-direction velocity, Y-direction velocity, and yaw rate of vehicle i, respectively.

[0011] Optionally, the functional expression for calculating the constraint force of the multi-vehicle cooperative transportation system based on the model matrix of the horizontal and vertical coupled dynamic model, the constraint matrix of the system constraint equation, and the real-time state is as follows: ; ; ; ; ; ; , , ; ; in, For the constraints of multi-vehicle cooperative transportation systems, , and These are the feedforward term, feedback term, and robust term that constitute a multi-vehicle cooperative transportation system. This is the coefficient matrix of the system's overall constraints. The system inertia matrix of a multi-vehicle cooperative transportation system. The system input matrix for a multi-vehicle cooperative transportation system. This is the matrix of the right-hand side terms of the second-order constraints of the system's total constraints. The system force matrix of a multi-vehicle cooperative transportation system. Here is the gain matrix. This represents the transformed constraint following error. To constrain the following error, This is the matrix of the right-hand side terms of the first-order constraints of the system's total constraints. To switch variables, The variable is used to determine the state. For functions used to estimate uncertainty, for basis functions, To estimate the coefficients, To estimate the first differential of the coefficients, and For design parameters, for norm, For a multi-vehicle cooperative transportation system, the generalized velocity vector is... for norm, for norm, This is the threshold parameter.

[0012] The present invention also provides a multi-vehicle cooperative control system, including a microprocessor and a memory interconnected thereto, wherein the microprocessor is programmed or configured to execute the multi-vehicle cooperative control method.

[0013] The present invention also provides a computer-readable storage medium storing a computer program or instructions that are programmed or configured to execute the multi-vehicle cooperative control method by a processor.

[0014] The present invention also provides a computer program product, including a computer program or instructions that are programmed or configured to execute the multi-vehicle cooperative control method via a processor.

[0015] Compared with the prior art, the present invention can mainly achieve the following beneficial effects: 1. The method of the present invention includes constructing a horizontal and vertical coupled dynamic model for a multi-vehicle cooperative transportation system, and calculating the constraint force of the multi-vehicle cooperative transportation system by combining the model matrix of the horizontal and vertical coupled dynamic model of the multi-vehicle cooperative transportation system. This method can overcome the shortcomings of traditional integral dynamic models in characterizing system coupling and providing accurate feedforward information.

[0016] 2. The method of the present invention includes constructing a multi-vehicle cooperative transportation system with the cargo as the lead motion constraint, calculating the actual control quantity of each vehicle based on the constraint force of the multi-vehicle cooperative transportation system, and the actual control quantity of each vehicle is the control quantity with the cargo as the lead. By adopting a cargo-centric control strategy, it is possible to get rid of the "vehicle-centric" indirect control mode and reduce the system control complexity and design burden.

[0017] 3. The method of the present invention includes an explicit control law based on constraint following control theory. By constructing system constraint equations with motion constraints and articulation constraints for a multi-vehicle cooperative transportation system and extracting the constraint matrix of the system constraint equations, the system trajectory tracking error can be asymptotically converged. It also has good constraint handling versatility and scenario adaptability.

[0018] By combining the above-mentioned technical means, this invention can solve the challenges of strong coupling, nonlinearity, underactuation, and uncertainty in existing multi-vehicle cooperative transportation systems, improve the tracking performance of multi-vehicle cooperative transportation systems under topologically stable configurations, and is applicable to the general control of underactuated and fully driven multi-vehicle transportation systems. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of the basic process of the method in an embodiment of the present invention.

[0020] Figure 2 This is a schematic diagram of the structure of the three-vehicle cooperative transportation system in an embodiment of the present invention.

[0021] Figure 3This is a schematic diagram of some parameters of the three-vehicle cooperative transportation system in an embodiment of the present invention.

[0022] Figure 4 This is a schematic diagram showing the actual trajectory and the desired trajectory of the goods in an embodiment of the present invention.

[0023] Figure 5 This is a schematic diagram of the trajectories of the three vehicles in the three-vehicle cooperative control system of this invention.

[0024] Figure 6 This is a schematic diagram of the time history curve of trajectory tracking error in an embodiment of the present invention, wherein (a) is the time history curve of trajectory tracking error of cargo, and (b) to (d) are the time history curves of trajectory tracking error of vehicles 1 to 3, respectively.

[0025] Figure 7 This is a schematic diagram of the spacing error between vehicles 1 to 3 in an embodiment of the present invention.

[0026] Figure 8 The above are error distribution histograms of vehicles 1 to 3 in this embodiment of the invention, where (a) to (c) are error distribution histograms of vehicles 1 to 3, respectively.

[0027] Figure 9 This is a schematic diagram illustrating the changes in the orientation of goods and vehicles in an embodiment of the present invention.

[0028] Figure 10 This is a snapshot of the orientation of the goods and vehicles in an embodiment of the present invention. Detailed Implementation

[0029] To enable those skilled in the art to better understand the technical solutions of the present invention, the technical solutions of the present invention will be further described in detail below with reference to the accompanying drawings in the embodiments of the present invention.

[0030] like Figure 1 As shown, the multi-vehicle cooperative control method in this embodiment includes the following steps: Based on the Udwadia-Kalaba method, a lateral and longitudinal coupled dynamic model with the cargo as the leader is constructed for the multi-vehicle cooperative transportation system, and the model matrix of the lateral and longitudinal coupled dynamic model is extracted; system constraint equations with motion constraints and articulation constraints are constructed for the multi-vehicle cooperative transportation system, and the constraint matrix of the system constraint equations is extracted; the real-time state of the multi-vehicle cooperative transportation system is obtained; the constraint force of the multi-vehicle cooperative transportation system is calculated based on the model matrix of the lateral and longitudinal coupled dynamic model, the constraint matrix of the system constraint equations, and the real-time state; and the actual control quantity of each vehicle is calculated based on the constraint force of the multi-vehicle cooperative transportation system.

[0031] The multi-vehicle cooperative transportation system comprises n vehicles arranged in an equilateral polygon. These n vehicles are rigidly connected to cargo at the center of the polygon, and the center of gravity of the cargo is located at the geometric center of the polygon. The functional expression for the constraint forces of the multi-vehicle cooperative transportation system is: ; ; ; in, For the constraints of multi-vehicle cooperative transportation systems, For the binding force of goods, ~ These represent the constraint forces for vehicles 1 through n, respectively. Let T represent the constraint forces on vehicle i, where T in the superscript is the transpose of the matrix. ~ and ~ For vehicles 1 to n respectively X and Y Directional force, , , and For vehicle i and goods in X and Y Directional force, and The cargo acts on vehicle i respectively X and Y The direction of the force, i=1,2,…,n; and These are two virtual control components for vehicle i. For example... Figure 2 As shown, the multi-vehicle cooperative transportation system in this embodiment is specifically a three-vehicle cooperative transportation system. The three transport vehicles are arranged in an equilateral triangle and rigidly connected to the cargo at the center, enabling the three vehicles to cooperatively transport a single, rigid cargo. The center of gravity of the cargo is located at the geometric center of the triangle, and the desired distance between each vehicle and the center of gravity of the cargo is... D d This configuration aims to distribute the load evenly and improve transportation stability. For a three-vehicle cooperative transportation system, n=3, and the functional expression of the constraint force is: ; ; In this embodiment, the functional expression for calculating the actual control quantity of each vehicle based on the constraint force of the multi-vehicle cooperative transportation system is as follows: ; in, Let i be the front wheel steering angle. The rear-wheel drive force of vehicle i, The longitudinal force of the front tires of vehicle i. Let be the lateral stiffness of the front tires of vehicle i. and Let be the longitudinal velocity and the lateral velocity of vehicle i, respectively. Let i be the yaw rate of vehicle i. The distance from the front axle to the center of gravity of vehicle i is given. The actual control parameters of vehicle i include the front wheel steering angle of vehicle i. and rear-wheel drive .

[0032] Figure 3 This is a schematic diagram showing some parameters of the three-vehicle cooperative transportation system in this embodiment. According to Newton's laws, the equations of motion for each vehicle i are: ; in, and Let i be the mass and moment of inertia of vehicle i, respectively. , and They are respectively , and The second derivatives of represent the longitudinal acceleration, the lateral acceleration, and the yaw acceleration, respectively. , and These represent the longitudinal position, lateral position, and yaw angle of vehicle i, respectively. Input the front wheel steering angle. and These are the distances from the center of gravity of vehicle i to the front and rear axles, respectively. and These are the effects of the cargo on vehicle i. X , Y Force in direction, and These are the longitudinal and lateral forces on the front tires of vehicle i, respectively. and These are the longitudinal and lateral forces on the rear tires of vehicle i, respectively. Let be the air resistance of vehicle i. Through coordinate transformation, the correspondence between the lateral and longitudinal velocities in the vehicle coordinate system and the lateral and longitudinal velocities in the geodetic coordinate system can be obtained: ; in, and They are respectively and The first derivatives of represent the velocities of vehicle i in the X and Y directions, respectively; and These represent the longitudinal and lateral velocities of vehicle i, respectively. In the magic tire model, when the slip angle is small, the lateral tire model can be simplified to a linear tire model. The lateral forces of the front and rear tires are... and It is linearly related to the slip angles of the front and rear tires, respectively, and its expression is: ; in, , These are the lateral stiffness of the front and rear tires, respectively. , This refers to the slip angle of the front and rear tires.

[0033] Air resistance is proportional to the square of the vehicle's longitudinal velocity, and its calculation function is expressed as follows: ; in, This is a general proportionality coefficient, equal to the product of air density, air drag coefficient, and vehicle frontal area. Let the wind speed be denoted as . The calculation function expressions for the longitudinal and lateral forces of the front and rear tires are as follows: ; ; in, It is the acceleration due to gravity. The tire rolling resistance coefficient is the coefficient of friction of the tire. Let be the driving force (rear wheel driving force) of vehicle i. Based on this, a lateral and longitudinal coupled dynamic model for any vehicle i can be obtained using the Udwadia-Kalaba method. Specifically, in this embodiment, when constructing a lateral and longitudinal coupled dynamic model with cargo as the lead vehicle for a multi-vehicle cooperative transportation system and extracting the model matrix of the lateral and longitudinal coupled dynamic model, the functional expression of the lateral and longitudinal coupled dynamic model for any vehicle i is: ; in, Let be the inertia matrix of vehicle i. Let be the generalized acceleration vector of vehicle i. Let i be the Coriolis force matrix of vehicle i. Let be the input matrix for vehicle i. Let the constraint force be for vehicle i, and we have: ; ; ; ; ; ; in, and Let i be the mass and moment of inertia of vehicle i, respectively. , and These are the longitudinal acceleration, lateral acceleration, and yaw rate of vehicle i, respectively. Let i be the air resistance of vehicle i. Let be the lateral force on the rear tire of vehicle i. Let be the vertical force on the rear tire of vehicle i. Let i be the yaw rate of vehicle i. Let i be the yaw angle of vehicle i. Let be the distance from the center of gravity of vehicle i to the rear axle.

[0034] like Figure 2 As shown, in this embodiment, the cargo is modeled as a rigid body located at the center of an equilateral triangle, and its dynamics are described by translational and rotational equations. Let the mass of the cargo be... The moment of inertia about the vertical axis is Its position is described by the coordinates of its center of gravity and its yaw angle (heading angle). According to Newton's second law, the motion of the cargo's center of gravity depends on the resultant force exerted by the three vehicles at the connection point, and its dynamic model is as follows: ; Based on this, it is constructed in matrix form, so that when constructing the lateral and longitudinal coupled dynamics model with the cargo as the leader for the multi-vehicle cooperative transportation system in this embodiment and extracting the model matrix of the lateral and longitudinal coupled dynamics model, the functional expression of the lateral and longitudinal coupled dynamics model constructed for the cargo is: ; in, Let be the inertia matrix of the cargo. Let be the generalized acceleration vector of the cargo. The Coriolis force matrix of the cargo, The input matrix is ​​for the goods. The binding force on the goods is: ; ; ; ; ; ; in, and These are the mass and moment of inertia of the cargo, respectively. , and These are the longitudinal acceleration, lateral acceleration, and yaw rate of the cargo, respectively. This is the desired distance between the center of gravity of the cargo and the vehicle. The lateral angle of the goods. and It is an intermediate variable.

[0035] The functional expression for extracting the model matrix of the longitudinal and transverse coupled dynamic model is: ; ; ; in, The system inertia matrix of a multi-vehicle cooperative transportation system. ~ Let be the inertia matrices of vehicles 1 to n, respectively. The system force matrix of a multi-vehicle cooperative transportation system. ~ These are the Coriolis force matrices for vehicles 1 to n. The system input matrix for a multi-vehicle cooperative transportation system. ~ These are the input matrices for vehicles 1 to n, respectively.

[0036] In this embodiment, when constructing system constraint equations for motion constraints and articulation constraints for a multi-vehicle cooperative transportation system and extracting the constraint matrix of the system constraint equations, the system constraint equations for motion constraints include first-order and second-order constraint equations for desired travel path constraints and desired speed constraints, and the system constraint equations for articulation constraints include first-order and second-order constraint equations for articulation constraints; the functional expressions for the first-order and second-order constraint equations for desired travel path constraints are as follows: ; ; ; ; ; in, Let be the coefficient matrix of the desired driving path constraint. For a multi-vehicle cooperative transportation system, the generalized velocity vector is... For a multi-vehicle cooperative transportation system, the generalized acceleration vector is... and Position vector of multi-vehicle cooperative transportation system The first and second derivatives are calculated to obtain the result. , Let be the position vector of the goods. ~ Let be the position vectors of vehicles 1 to n. Let the matrix be the right-hand side of the first-order constraint of the desired driving path constraint. This is the matrix of the right-hand side terms of the second-order constraint of the desired driving path constraint. The expected route for the goods. Let X be the coordinate of the cargo in the X direction. The velocity of the cargo in the X direction; The functional expressions for the first-order and second-order constraint equations of the desired velocity constraint are as follows: ; ; ; ; ; in, The coefficient matrix represents the desired velocity constraint. This is the matrix of the right-hand side of the first-order constraint for the desired velocity constraint. Let be the matrix of the right-hand side terms of the second-order constraint of the desired velocity constraint. The lateral angle of the goods. Let yaw rate be the angular velocity of the cargo. Let Y be the velocity of the cargo. For the desired speed; The functional expressions for the first-order and second-order constraint equations of the hinged constraint are as follows: ; ; ; ; ; in, This is the coefficient matrix of the hinge constraint. This is the matrix of the right-hand side terms of the second-order constraint of the hinged constraint. Let be the right-hand side term matrix of the second-order constraint of the hinged constraint; the functional expression for extracting the constraint matrix of the system constraint equation is: ; ; ; in, This is the coefficient matrix of the system's overall constraints. This is the matrix of the right-hand side terms of the second-order constraints of the system's total constraints. This is the matrix of the right-hand side terms of the first-order constraints of the system's total constraints.

[0037] In this embodiment, when acquiring the real-time status of the multi-vehicle cooperative transportation system, the real-time status includes the generalized position vector of the goods, the generalized velocity vector of the goods, the generalized position vectors of each vehicle, and the generalized velocity vectors of each vehicle: ; ; ; ; in, Let be the generalized position vector of the goods. , and These are the X-coordinate, Y-coordinate, and yaw angle of the cargo, respectively. Let be the generalized velocity vector of the cargo. , and These are the cargo's X-direction velocity, Y-direction velocity, and yaw rate, respectively. Let be the generalized position vector of vehicle i. , and These are the X-coordinate, Y-coordinate, and yaw angle of vehicle i, respectively. Let be the generalized velocity vector of vehicle i. , and These are the X-direction velocity, Y-direction velocity, and yaw rate of vehicle i, respectively.

[0038] In this embodiment, the functional expression for calculating the constraint force of the multi-vehicle cooperative transportation system based on the model matrix of the horizontal and vertical coupling dynamics model, the constraint matrix of the system constraint equation, and the real-time state is as follows: ; ; ; ; ; ; , , ; ; in, For the constraints of multi-vehicle cooperative transportation systems, , and These are the feedforward term, feedback term, and robust term that constitute a multi-vehicle cooperative transportation system. This is the coefficient matrix of the system's overall constraints. The system inertia matrix of a multi-vehicle cooperative transportation system. The system input matrix for a multi-vehicle cooperative transportation system. This is the matrix of the right-hand side terms of the second-order constraints of the system's total constraints. The system force matrix of a multi-vehicle cooperative transportation system. Here is the gain matrix. This represents the transformed constraint following error. To constrain the following error, This is the matrix of the right-hand side terms of the first-order constraints of the system's total constraints. To switch variables, The variable is used to determine the state. For functions used to estimate uncertainty, for basis functions, To estimate the coefficients, To estimate the first differential of the coefficients, and For design parameters, for norm, For a multi-vehicle cooperative transportation system, the generalized velocity vector is... for norm, for norm, This is the threshold parameter.

[0039] To verify the effectiveness of the multi-vehicle cooperative control method in this embodiment, a high-fidelity numerical simulation of the three-vehicle cooperative control system was performed in the Matlab / Simulink (R2021b) environment. The simulation used a circular path tracking scenario with a radius of 100m as the baseline scenario. This scenario has continuous and constant steering requirements, comprehensively testing the system's cooperative control capability, configuration-preserving robustness, and dynamic performance. The simulation used a fixed step size of 0.01 s, and the parameters of the vehicles and cargo are shown in Table 1.

[0040] Table 1: Parameters of vehicles and cargo used in the simulation

[0041] The system's initial state was set to deviate from the desired trajectory and configuration: each vehicle's initial heading angle was 0 rad, longitudinal velocity was 1 m / s, lateral velocity was 0 m / s, and all control inputs were initially zero. To compare the performance of the method in this embodiment, a widely used PID controller was selected as the comparison scheme in this experiment. A circular desired trajectory was used in the experiment. Figure 4 This is a schematic diagram showing the actual trajectory and the desired trajectory of the goods in this embodiment. Figure 5 This is a schematic diagram showing the trajectories of the three vehicles (vehicle 1 to vehicle 3) in the three-vehicle cooperative control system according to the method of this embodiment. See also... Figure 4 and Figure 5 It can be seen that, under the drive of the UK constraint force within the 150s simulation period, all vehicles in this embodiment can converge quickly and track the desired trajectory with high precision. Figure 6 The time-history curves of the trajectory tracking errors for goods and individual vehicles are further displayed, such as... Figure 6 As shown in (a), the cargo tracking error reaches a steady state after approximately 8 seconds, with a maximum tracking error of less than 0.05 m and a steady-state error of less than 0.005 m. Figure 6 As shown in (c) to (d), the tracking errors of each vehicle exhibit similar high-precision characteristics, with the maximum error not exceeding 0.001 m. This result directly verifies the effectiveness of modeling the trajectory tracking target as a second-order servo constraint. In this embodiment, UK control modeling and solving are used to apply generalized constraints, ensuring the exponential convergence of the tracking error from a dynamic perspective and avoiding the error accumulation and oscillation problems that may exist in traditional cascaded control structures.

[0042] Maintaining an equilateral triangle configuration is fundamental to collaborative transport safety. Figure 7 The evolution of distance errors between each vehicle and the cargo center was demonstrated. Within a 300-second simulation period, all distance errors were strictly controlled within ±0.001 m. Specifically, the average absolute errors of the distances between vehicles 1, 2, and 3 and the cargo were 0.0005 m, 0.0003 m, and 0.0003 m, respectively, with the maximum errors not exceeding 0.0008 m. Compared to the system's expected distance of 3 m, this error level corresponds to a relative accuracy higher than 0.03%, indicating extremely high accuracy in configuration preservation. Figure 8 This is the error distribution histogram for vehicles 1 to 3 in this embodiment, where (a) to (c) are the error distribution histograms for vehicles 1 to 3, respectively. Figure 8 The error distribution histogram clearly shows that the error is highly concentrated near zero, approximately following a Gaussian distribution with a mean of zero, without significant shift or divergence. This proves that by introducing the geometric topological relationship into the system in the form of differential constraints with error feedback, not only is the configuration objective defined, but it is also endowed with asymptotic stability. Any tiny configuration deviation can generate a cooperative restoring force / torque in real time, ensuring that the system maintains the preset internal geometric relationship during dynamic motion.

[0043] Speed ​​and posture stability during transportation are important indicators for measuring control quality. Figure 9 This is a schematic diagram illustrating the changes in the orientation of goods and vehicles in an embodiment of the present invention, such as... Figure 9 As shown, within a simulation period of 125 seconds, the longitudinal velocity of each vehicle, under the control law, can smoothly converge to the desired value V without overshoot. des =5 m / s. With the initial velocity set at 1 m / s, the system exhibited good acceleration smoothness during startup. Both the speed-constrained vehicle and the unconstrained cargo reached steady state within 15 seconds, and the standard deviation of velocity fluctuation for all units was less than 0.02 m / s, demonstrating excellent anti-interference capability. Regarding attitude control, Figure 10 This is a snapshot of the orientation of goods and vehicles in an embodiment of the present invention, such as... Figure 10 As shown, the heading angles of the cargo and vehicles adjust rapidly after startup and align with the tangent direction of the circular path (i.e., the desired heading) after approximately 10 seconds. The cargo heading angle changes smoothly throughout the steady-state tracking phase, with its rate of change perfectly matching the path curvature, meeting the stringent requirements for attitude stability in the transportation of oversized cargo in practical engineering.

[0044] In summary, the multi-vehicle cooperative control method in this embodiment breaks through the traditional simplified integral model or single-degree-of-freedom decoupled modeling method. It designs topological configuration constraints to characterize the coupling relationship of the system, proposes a constraint-oriented hierarchical modeling method, and constructs a dynamic model of the underactuated multi-vehicle cooperative transportation system that can accurately describe the internal lateral and longitudinal coupling, providing more accurate feedforward information. By analyzing the correlation between the dynamic model of the underactuated multi-vehicle cooperative transportation system and the trajectory tracking constraints, this embodiment designs a feedforward controller based on the Udwadia-Kalaba equation that matches the constraints to the system, ensuring effective driving of the underactuated CTS. Furthermore, to cope with unavoidable initial deviations, a constraint force consisting of feedforward, feedback, and robust terms of the multi-vehicle cooperative transportation system is designed, thus forming a composite control framework of "nominal control-error correction," enhancing the robustness and reliability of the multi-vehicle cooperative transportation system in real-world environments. The system tracking error of the multi-vehicle cooperative control method in this embodiment exhibits global asymptotic convergence, theoretically providing a solid guarantee for the safe operation of the system under complex conditions. Numerical simulation further verified the performance of the multi-vehicle cooperative control method in this embodiment: under complex conditions such as underactuation and strong coupling, the system achieved a comprehensive control accuracy of centimeter-level trajectory tracking and millimeter-level configuration maintenance, which can solve the problem of high-precision and high-safety cooperative transportation operations in the transportation of large items.

[0045] Those skilled in the art will understand that the technical solutions provided by this invention can take the form of a method, a system, or a computer program product. Therefore, this invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this invention can provide a multi-vehicle cooperative control system including an interconnected microprocessor and a memory, the microprocessor being programmed or configured to execute the multi-vehicle cooperative control method. This invention can provide a computer-readable storage medium storing a computer program or instructions programmed or configured to execute the multi-vehicle cooperative control method via a processor. This invention can provide a computer program product including a computer program or instructions programmed or configured to execute the multi-vehicle cooperative control method via a processor. Furthermore, this invention can take the form of a computer program product embodied on one or more computer-readable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It should be understood that each block of a flowchart and / or block diagram, and combinations of blocks in a flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing device, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 The computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The functions specified in one or more boxes. These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable apparatus for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0046] The above description is merely a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should also be considered within the scope of protection of the present invention.

Claims

1. A multi-vehicle cooperative control method, characterized in that, The process includes the following steps: constructing a lateral and longitudinal coupled dynamic model for the multi-vehicle cooperative transportation system and extracting the model matrix of the lateral and longitudinal coupled dynamic model; constructing system constraint equations for the multi-vehicle cooperative transportation system with the cargo as the leader, including motion constraints and articulation constraints, and extracting the constraint matrix of the system constraint equations; obtaining the real-time state of the multi-vehicle cooperative transportation system; calculating the constraint forces of the multi-vehicle cooperative transportation system based on the model matrix of the lateral and longitudinal coupled dynamic model, the constraint matrix of the system constraint equations, and the real-time state; and calculating the actual control quantities of each vehicle based on the constraint forces of the multi-vehicle cooperative transportation system.

2. The multi-vehicle cooperative control method according to claim 1, characterized in that, The multi-vehicle cooperative transportation system includes n vehicles distributed in an equilateral polygon. These n vehicles are rigidly connected to cargo at the center, and the center of gravity of the cargo is located at the geometric center of the polygon. The functional expression for the constraint forces of the multi-vehicle cooperative transportation system is: ； ； ； in, For the constraints of multi-vehicle cooperative transportation systems, For the binding force of goods, ~ These represent the constraint forces for vehicles 1 through n, respectively. Let T represent the constraint forces on vehicle i, where T in the superscript is the transpose of the matrix. ~ and ~ For vehicles 1 to n respectively X and Y Directional force, , , and For vehicle i and goods in X and Y Directional force, and The cargo acts on vehicle i respectively X and Y The direction of the force, i=1,2,…,n; and These are two virtual control components for vehicle i.

3. The multi-vehicle cooperative control method according to claim 2, characterized in that, The functional expression for calculating the actual control quantity of each vehicle based on the constraint of the multi-vehicle cooperative transportation system is as follows: ； in, Let i be the front wheel steering angle. The rear-wheel drive force of vehicle i, The longitudinal force of the front tires of vehicle i. Let be the lateral stiffness of the front tires of vehicle i. and Let be the longitudinal velocity and the lateral velocity of vehicle i, respectively. Let i be the yaw rate of vehicle i. The distance from the front axle to the center of gravity of vehicle i is given. The actual control parameters of vehicle i include the front wheel steering angle of vehicle i. and rear-wheel drive .

4. The multi-vehicle cooperative control method according to claim 3, characterized in that, When constructing a lateral and longitudinal coupled dynamic model for a multi-vehicle cooperative transportation system and extracting the model matrix of the lateral and longitudinal coupled dynamic model, the functional expression of the lateral and longitudinal coupled dynamic model constructed for any vehicle i is: ； in, Let be the inertia matrix of vehicle i. Let be the generalized acceleration vector of vehicle i. Let i be the Coriolis force matrix of vehicle i. Let be the input matrix for vehicle i. Let the constraint force be for vehicle i, and we have: ； ； ； ； ； ； in, and Let i be the mass and moment of inertia of vehicle i, respectively. , and These are the longitudinal acceleration, lateral acceleration, and yaw rate of vehicle i, respectively. Let i be the air resistance of vehicle i. Let be the lateral force on the rear tire of vehicle i. Let be the vertical force on the rear tire of vehicle i. Let i be the yaw rate of vehicle i. Let i be the yaw angle of vehicle i. Let be the distance from the center of gravity of vehicle i to the rear axle; when constructing a lateral and longitudinal coupled dynamic model for the multi-vehicle cooperative transportation system and extracting the model matrix of the lateral and longitudinal coupled dynamic model, the functional expression of the lateral and longitudinal coupled dynamic model constructed for the cargo is: ； in, Let be the inertia matrix of the cargo. Let be the generalized acceleration vector of the cargo. The Coriolis force matrix of the cargo, The input matrix is ​​for the goods. The binding force on the goods is: ； ； ； ； ； ； in, and These are the mass and moment of inertia of the cargo, respectively. , and These are the longitudinal acceleration, lateral acceleration, and yaw rate of the cargo, respectively. This is the desired distance between the center of gravity of the cargo and the vehicle. The lateral angle of the goods. and As intermediate variables; the functional expression for extracting the model matrix of the horizontal and vertical coupled dynamic model is: ； ； ； in, The system inertia matrix of a multi-vehicle cooperative transportation system. ~ Let be the inertia matrices of vehicles 1 to n, respectively. The system force matrix of a multi-vehicle cooperative transportation system. ~ These are the Coriolis force matrices for vehicles 1 to n. The system input matrix for a multi-vehicle cooperative transportation system. ~ These are the input matrices for vehicles 1 to n, respectively.

5. The multi-vehicle cooperative control method according to claim 4, characterized in that, When constructing system constraint equations for a multi-vehicle cooperative transportation system, with cargo as the lead vehicle and including motion constraints and articulation constraints, and extracting the constraint matrix of the system constraint equations, the system constraint equations for motion constraints include first-order and second-order constraint equations for the desired travel path constraints and desired speed constraints of the cargo, and the system constraint equations for articulation constraints include first-order and second-order constraint equations for articulation constraints. The functional expressions for the first-order and second-order constraint equations of the desired driving path constraint are as follows: ； ； ； ； ； in, Let be the coefficient matrix of the desired driving path constraint. For a multi-vehicle cooperative transportation system, the generalized velocity vector is... For a multi-vehicle cooperative transportation system, the generalized acceleration vector is... and Position vector of multi-vehicle cooperative transportation system The first and second derivatives are calculated to obtain the result. , Let be the position vector of the goods. ~ Let be the position vectors of vehicles 1 to n. Let the matrix be the right-hand side of the first-order constraint of the desired driving path constraint. This is the matrix of the right-hand side terms of the second-order constraint of the desired driving path constraint. The expected route for the goods. Let X be the coordinate of the cargo in the X direction. Let X be the velocity of the cargo in the X direction; the functional expressions of the first-order and second-order constraint equations for the desired velocity constraint are: ； ； ； ； ； in, The coefficient matrix represents the desired velocity constraint. This is the matrix of the right-hand side of the first-order constraint for the desired velocity constraint. Let be the matrix of the right-hand side terms of the second-order constraint of the desired velocity constraint. The lateral angle of the goods. Let yaw rate be the angular velocity of the cargo. Let Y be the velocity of the cargo. For the desired speed; The functional expressions for the first-order and second-order constraint equations of the hinged constraint are as follows: ； ； ； ； ； in, This is the coefficient matrix of the hinge constraint. This is the matrix of the right-hand side terms of the second-order constraint of the hinged constraint. Let be the right-hand side term matrix of the second-order constraint of the hinged constraint; the functional expression for extracting the constraint matrix of the system constraint equation is: ； ； ； in, This is the coefficient matrix of the system's overall constraints. This is the matrix of the right-hand side terms of the second-order constraints of the system's total constraints. This is the matrix of the right-hand side terms of the first-order constraints of the system's total constraints.

6. The multi-vehicle cooperative control method according to claim 5, characterized in that, The process of acquiring the real-time status of the multi-vehicle cooperative transportation system includes the generalized position vector of the goods, the generalized velocity vector of the goods, and the generalized position vectors and generalized velocity vectors of each vehicle. ； ； ； ； in, Let be the generalized position vector of the goods. , and These are the X-coordinate, Y-coordinate, and yaw angle of the cargo, respectively. Let be the generalized velocity vector of the cargo. , and These are the cargo's X-direction velocity, Y-direction velocity, and yaw rate, respectively. Let be the generalized position vector of vehicle i. , and These are the X-coordinate, Y-coordinate, and yaw angle of vehicle i, respectively. Let be the generalized velocity vector of vehicle i. , and These are the X-direction velocity, Y-direction velocity, and yaw rate of vehicle i, respectively.

7. The multi-vehicle cooperative control method according to claim 6, characterized in that, The functional expression for calculating the constraint force of the multi-vehicle cooperative transportation system based on the model matrix of the horizontal and vertical coupled dynamic model, the constraint matrix of the system constraint equation, and the real-time state is as follows: ； ； ； ； ； ； ， ， ； ； in, For the constraints of multi-vehicle cooperative transportation systems, , and These are the feedforward term, feedback term, and robust term that constitute a multi-vehicle cooperative transportation system. This is the coefficient matrix of the system's overall constraints. The system inertia matrix of a multi-vehicle cooperative transportation system. The system input matrix for a multi-vehicle cooperative transportation system. This is the matrix of the right-hand side terms of the second-order constraints of the system's total constraints. The system force matrix of a multi-vehicle cooperative transportation system. Here is the gain matrix. This represents the transformed constraint following error. To constrain the following error, This is the matrix of the right-hand side terms of the first-order constraints of the system's total constraints. To switch variables, The variable is used to determine the state. For functions used to estimate uncertainty, for basis functions, To estimate the coefficients, To estimate the first differential of the coefficients, and For design parameters, for norm, For a multi-vehicle cooperative transportation system, the generalized velocity vector is... for norm, for norm, This is the threshold parameter.

8. A multi-vehicle cooperative control system, comprising a microprocessor and a memory interconnected, characterized in that, The microprocessor is programmed or configured to execute the multi-vehicle cooperative control method according to any one of claims 1 to 7.

9. A computer-readable storage medium storing a computer program or instructions, characterized in that, The computer program or instructions are programmed or configured to execute the multi-vehicle cooperative control method of any one of claims 1 to 7 via a processor.

10. A computer program product, comprising a computer program or instructions, characterized in that, The computer program or instructions are programmed or configured to execute the multi-vehicle cooperative control method of any one of claims 1 to 7 via a processor.

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