Unmanned double-vehicle collaborative transportation system and trajectory tracking control method thereof

Abstract

The invention provides an unmanned double-vehicle cooperative transportation system and a trajectory tracking control method thereof, on one hand, aiming at the difficulty that a double-vehicle cooperative transportation system model is complex, a modeling method of an integral dynamic model containing uncertainty is provided by combining system incomplete constraint with Lagrange mechanics; according to the designed hierarchical adaptive robust tracking controller, a control algorithm based on a constraint following theory in an upper layer can effectively overcome the influence of system parameter perturbation and external interference uncertainty, and a lower layer takes the minimum load stress as a target, so that effective distribution of driving force is realized. And on the other hand, a matched unmanned vehicle system transportation system is designed, an operation calculation unit, a positioning unit, an information perception unit, an execution unit, a power supply unit and a communication unit are integrated, the system composition is simpler, and efficient cooperative work among the units is ensured while the system cost is reduced.

Description

Technical Field

[0001] The present invention relates to the field of unmanned driving technology, and in particular to an unmanned driving dual-vehicle cooperative transportation system and a trajectory tracking control method thereof. Background Art

[0002] In the manufacturing sector, especially in the aviation and energy industries, transporting large components such as aircraft fuselages and wind turbine blades is a huge challenge. These components are often huge and heavy, and traditional transportation methods often cannot meet the needs. Therefore, collaborative transportation systems (CTS) have emerged, overcoming the problem of insufficient transportation capacity of a single carrier through the coordinated work of multiple vehicles. However, the current manually operated two-vehicle collaborative transportation system requires multiple drivers and operators, and the system structure is complex, the operation and coordination are difficult, and it is easy to cause damage to cargo or vehicles. In addition, manual operation is difficult to flexibly adjust under complex road conditions, resulting in poor passability and affecting transportation efficiency.

[0003] The development of autonomous driving technology has provided new technical solutions for two-vehicle cooperative transportation. Leveraging advanced sensors and intelligent algorithms, autonomous driving enables autonomous navigation and coordinated control of vehicles, thereby improving transportation efficiency and safety. However, trajectory tracking control, a key technology in autonomous driving, still faces numerous challenges in two-vehicle cooperative transportation systems. Trajectory tracking control not only relies on accurate vehicle dynamics models but also requires consideration of complex factors such as environmental uncertainty and real-time control inputs.

[0004] Existing control strategies for collaborative transport systems often focus on small robots or between carriers and robotic arms. These mobile robots have simple dynamic models, and control methods often adjust the carrier's speed and acceleration within the kinematic model without considering the internal dynamic characteristics of the components. For collaborative transport systems composed of heavy-duty vehicles, the payload is much larger than the mobile objects of these small robots indoors, and the model is more complex, making existing collaborative transport methods for mobile robots difficult to directly transfer and apply. Furthermore, heavy-duty vehicles require higher levels of anti-interference capability and robustness in complex environments, further increasing the difficulty of trajectory tracking control. Summary of the Invention

[0005] (1) Technical issues to be resolved

[0006] Based on this, the present invention provides an unmanned dual-vehicle cooperative transportation system and its trajectory tracking control method to solve the problems mentioned in the background technology, such as the difficulty of dynamic modeling caused by the complexity of the system model, and the poor accuracy and stability of system tracking caused by the characteristics of uncertain parameters, external unknown disturbances, nonlinearity and over-driving in trajectory tracking control.

[0007] (2) Technical solution

[0008] In order to achieve the above objectives, the present invention provides a trajectory tracking control method for an unmanned dual-vehicle cooperative transportation system, comprising:

[0009] S1: Based on the geometric constraints, motion constraints and Euler-Lagrange equations of the system, the system dynamics model is constructed to obtain the system dynamics model. The specific steps include:

[0010] S101: obtaining geometric constraints based on the positional relationship between the load and the carrier in the system;

[0011] The system includes a load and a carrier, the carrier includes carrier 1 and carrier 2 following carrier 1; the coordinate system and key nodes are defined as follows: OXY is the inertial coordinate system; P i xy (i = 0, 1, 2) is a conjoined coordinate system, where the subscripts i = 0, 1, and 2 represent the load, carrier 1, and carrier 2, respectively. In the conjoined coordinate system, x represents the longitudinal direction of the object, and y represents the transverse direction of the object. The object includes the load, carrier 1, and carrier 2. i (x pi ,y pi ), C i (x i ,y i ), Represents the center point, center of mass and heading angle of the object respectively; the center point of the carrier is the midpoint of the line connecting the front axle center and the rear axle center; the position information of the load, carrier 1 and carrier 2 can be used To express, you can also use To express; let q p =(q p1 ,q p0 ,q p2 ) T ,q c =(q c1 ,q c0 ,q c2 ) T ;

[0012] According to the positional relationship between the load and the two carriers, the geometric constraint equations of the dual-vehicle cooperative transport system are as follows:

[0013]

[0014] Where l0, l1, and l2 represent the distances from hinge point 1 to the load's center of mass, hinge point 1 to the center of mass of carrier 1, and hinge point 2 to the center of mass of carrier 2, respectively. Hinge point 1 is the center point of carrier 1; hinge point 2 is the center point of carrier 2. The load is a uniform rectangular rigid body, and its center point and center of mass are both the midpoint of the line connecting hinge point 1 and hinge point 2.

[0015] Taking the second derivative of the geometric constraint equation, we get the following formula:

[0016]

[0017] in,

[0018]

[0019]

[0020] There is one dot above the parameter for the first-order derivative, and two dots above the parameter for the second-order derivative;

[0021] S102: Obtain motion constraints based on the motion states of the load and the carrier in the system;

[0022] Assume that the x component of the load center velocity, the y component of the velocity and the angular velocity are v x0 、v y0 and w0; the x component of the velocity, the y component of the velocity and the angular velocity of the center point of carrier 1 are v x1 、v y1 and w1; the x component of the velocity, the y component of the velocity and the angular velocity of the center point of carrier 2 are v x2 、v y2 and w2; state vector u=(w1,v x0 ,v y0 ,w0,w2) T ; Then the motion constraint equation of the system is:

[0023]

[0024] in,

[0025]

[0026] According to the geometric relationship between the center of mass and the center point of the object, the conversion relationship between the center of mass and the center point is obtained as follows:

[0027]

[0028] Taking the derivative of the above formula, we get

[0029]

[0030] in,

[0031]

[0032] I3=eye(3) is the third-order identity matrix;

[0033] S103: Combining the geometric constraints, the motion constraints, and the Euler-Lagrange equations to obtain a system dynamics model;

[0034] The kinetic energy expression of the system with the center of mass as the reference point is:

[0035]

[0036] Wherein, subscript i=0, 1, 2 are used to represent the load, carrier 1, and carrier 2, respectively; and denote the longitudinal and transverse components of the center-of-mass velocity in the inertial coordinate system; is the angular velocity; m i For quality; J i is the moment of inertia;

[0037] Combining the geometric constraints, the motion constraints and the Euler-Lagrange equation, the dynamic model of the system is derived as follows:

[0038]

[0039] in,

[0040] M=diag[M1 M0 M2];

[0041] M i =diag[m i m i J i ];

[0042]

[0043] U=[F x1 F y1 M1 F x2 F y2 M2] T ;

[0044]

[0045] O 3×3 =zero(3) represents the third-order zero matrix; in the virtual control quantity U, F x1 、F y1 and M1 represent the longitudinal driving force, lateral driving force and torque of carrier 1 respectively, F x2 、F y2 and M2 represent the longitudinal driving force, lateral driving force and torque of carrier 2 respectively; λ is the Lagrange multiplier;

[0046] Order s c =Ts p ,get

[0047] The simplified system dynamics equation is as follows:

[0048]

[0049] in,

[0050]

[0051] Assuming that the above parameters consist of a nominal part and a time-varying uncertain part, the parameter matrix can be decomposed as follows:

[0052]

[0053] Where t represents time; q = q c represents the system state; σ represents the system uncertainty; and They are C(q,σ,t) and the nominal part; ΔC(·) and They are C(q,σ,t) and The uncertainty part;

[0054] make

[0055]

[0056] Therefore, we get

[0057] ΔD(q,σ,t)=D(q,t)K(q,σ,t)

[0058] Where I represents the identity matrix;

[0059] S2: constructing an adaptive robust controller based on the system dynamics model; the control items of the adaptive robust controller include a nominal system control item, a feedback item, and an adaptive item;

[0060] S3: Allocate the control items of the adaptive robust controller to each carrier of the system through a stress optimization algorithm to achieve driving force distribution.

[0061] On the other hand, the present invention also provides an unmanned dual-vehicle cooperative transportation system, which is based on a master vehicle, a slave vehicle and a load, and includes: an operation calculation unit, a positioning unit, an information perception unit, an execution unit, a power supply unit and a communication unit;

[0062] The operation calculation unit is located in the master vehicle and is used to process data from other units, solve the control quantity through the controller algorithm, and issue instructions to the execution unit. The operation calculation unit receives data from other units, including: master vehicle-load angle information, master vehicle obstacle and image information obtained by the master vehicle information perception unit; slave vehicle-load angle information, slave vehicle obstacle and image information obtained from the slave vehicle information perception unit through the communication unit; and the load coordinate position, negative acceleration and angular velocity information obtained from the positioning unit through the communication unit.

[0063] The positioning unit is located on the payload and is used to determine the payload's position and heading information, including the GPS global positioning system and the inertial measurement unit;

[0064] The information perception unit includes a laser radar, a camera, a millimeter-wave radar, and an angle sensor, which are located on the master vehicle and the slave vehicle respectively. The laser radar, the camera, and the millimeter-wave radar are used to identify and track static and dynamic obstacles around the collaborative transport system. The angle sensors are located at the hinges between the master vehicle and the load, and between the slave vehicle and the load, respectively, to sense the rotation angles of the master vehicle and the slave vehicle relative to the load. The laser radars are located at the front end of the master vehicle and the rear end of the slave vehicle, the cameras are located on all four sides of the master vehicle and the slave vehicle, and the millimeter-wave radars are located on the left and right ends of the front of the master vehicle and the left and right ends of the rear of the slave vehicle. The cameras provide real-time images for background monitoring. The laser radar located on top of the carrier can provide a longer detection distance and a wider field of view. The millimeter-wave radars located on the front side of the master vehicle and the rear side of the slave vehicle detect whether there are vehicles or obstacles around, provide support for front and rear collision warnings, and provide close-range protection.

[0065] The execution unit is used to execute the instructions of the operation computing unit and control the movement and steering of the master vehicle and the slave vehicle through the drive system and steering system. The drive system includes a motor control module and a brake control module. The motor control module has two modes: braking and driving. In driving mode, the motor control module adjusts the motor supply voltage and frequency to achieve precise control of the motor speed and direction. In braking mode, the execution unit coordinates the motor control module and the brake control module, using the motor brake module to efficiently convert the carrier's kinetic energy into electrical energy and feed it back to the battery of the power supply unit.

[0066] The power supply unit is used to provide the required energy for each unit of the dual-vehicle cooperative transportation system. The power supply unit is installed inside the carrier and the load, and is equipped with a power monitoring device. While controlling and protecting the power supply to all electrical equipment, it also transmits power consumption data and battery status to the operation and calculation unit through the communication unit.

[0067] The communication unit is used to connect the real-time communication between the master vehicle, the slave vehicle and the load through wired or wireless means; the communication unit transmits the angle information and environmental perception data collected by the slave vehicle information perception unit, the real-time operation status information of the slave vehicle execution unit, and the position information obtained by the load positioning unit to the master vehicle operation calculation unit, and sends the control instructions generated by the master vehicle operation calculation unit to the slave vehicle execution unit through the communication unit.

[0068] (3) Beneficial effects

[0069] As can be seen from the above technical solutions, the unmanned dual-vehicle cooperative transportation system and its trajectory tracking control method proposed in the present invention have the following beneficial effects:

[0070] 1. The overall dynamic modeling method of the uncertain dual-vehicle cooperative transportation system based on the combination of system nonholonomic constraints and Euler-Lagrange equations solves the problem of complex system vector relationships caused by the traditional method using Newtonian mechanics.

[0071] 2. A hierarchical adaptive robust tracking controller was designed. The control algorithm based on constraint following theory in the upper layer can effectively overcome the influence of system parameter perturbations and external interference uncertainties. The lower layer aims to minimize load stress, thereby realizing the system's tracking of the desired trajectory and the effective allocation of redundant driving forces.

[0072] 3. The dual-vehicle cooperative transportation system of the present invention integrates an operation calculation unit, a positioning unit, an information perception unit, an execution unit, a power supply unit and a communication unit, providing a complete supporting platform for the trajectory tracking control of the dual-vehicle cooperative transportation system, and has significant practicality. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] The features and advantages of the present invention will be more clearly understood by referring to the accompanying drawings, which are schematic and should not be construed as limiting the present invention in any way. In the accompanying drawings:

[0074] Figure 1 This is a schematic diagram of an unmanned dual-vehicle cooperative transportation system according to an embodiment of the present invention;

[0075] Figure 2 This is a schematic diagram of motion constraint analysis of a carrier 1 according to an embodiment of the present invention;

[0076] Figure 3 This is a schematic diagram of the principle of trajectory tracking control of an unmanned dual-vehicle cooperative transportation system by an adaptive robust controller according to an embodiment of the present invention;

[0077] Figure 4 This is an architecture diagram of the unmanned dual-vehicle cooperative transportation system according to an embodiment of the present invention. DETAILED DESCRIPTION

[0078] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0079] Example 1:

[0080] The dual-vehicle cooperative transport system of this embodiment includes a payload and two unmanned vehicles serving as carriers: carrier 1 (the master vehicle) and carrier 2 (the slave vehicle) following behind carrier 1. The carriers are equipped with front and rear axle steering and four-wheel distributed drive. The payload is a rigid cuboid, hinged to the base of the carriers via undamped hinges.

[0081] In order to minimize the complexity of the vehicle model in the design of the trajectory tracking controller and facilitate theoretical analysis, the two-vehicle cooperative transportation system is simplified as follows: (1) the pitch, roll, and vertical motion of the system are ignored; (2) it is assumed that the carriers (including carrier 1 and carrier 2) are symmetrical on the left and right, the steering angles of the left and right wheels are the same, and the left and right tires can be merged into one tire.

[0082] The trajectory tracking control method of the dual-vehicle cooperative transportation system of this embodiment includes:

[0083] S1: Based on the geometric constraints, motion constraints and Euler-Lagrange equations of the system, the system dynamics model is constructed to obtain the system dynamics model; specifically, it includes:

[0084] S101: obtaining geometric constraints based on the positional relationship between the load and the carrier in the system;

[0085] like Figure 1 As shown, the coordinate system and key nodes are defined as follows: OXY is the inertial coordinate system; P i xy (i = 0, 1, 2) is the conjoined coordinate system (in this article, the subscripts i = 0, 1, 2 are used to represent the load, carrier 1, and carrier 2, respectively). In the conjoined coordinate system, x represents the longitudinal direction of the object (i.e., the load, carrier 1, and carrier 2), and y represents the transverse direction of the object; P i (x pi ,y pi ), C i (x i ,y i ), Represent the center point, center of mass and heading angle of the object respectively. Among them, the center point of the carrier (i.e. carrier 1 and carrier 2) is the midpoint of the line connecting the center of the front axle and the center of the rear axle. Therefore, the position information of the load, carrier 1 and carrier 2 can be used To express, you can also use To express it. To facilitate the following derivation, let q p =(q p1 ,q p0 ,q p2 ) T ,q c =(q c1 ,q c0 ,q c2 ) T .

[0086] According to the positional relationship between the load and the two carriers, the geometric constraints of the dual-vehicle cooperative transport system are as follows:

[0087]

[0088] where l0, l1, and l2 represent the distances from hinge point 1 to the load's center of mass, hinge point 1 to the center of mass of carrier 1, and hinge point 2 to the center of mass of carrier 2, respectively. In this paper, the hinge point between the load and carrier 1 (hinge point 1) is the center of carrier 1; the hinge point between the load and carrier 2 (hinge point 2) is the center of carrier 2. The load is a uniform rectangular rigid body, and its center and center of mass are both the midpoint of the line connecting hinge point 1 and hinge point 2.

[0089] It can be seen that the system is subject to four independent constraints expressed in the analytical form of generalized coordinates in formula (1), so the generalized coordinates of the system's 9 degrees of freedom are Can be represented by independent generalized coordinates with 5 degrees of freedom express.

[0090] Taking the second derivative of formula (1), we get the following formula:

[0091]

[0092] in,

[0093]

[0094] A parameter with one dot above it represents a first-order derivative, and a parameter with two dots above it represents a second-order derivative.

[0095] S102: Obtain motion constraints based on the motion states of the load and the carrier in the system;

[0096] like Figure 2 As shown, let the x component of the load center velocity, the y component of the velocity and the angular velocity be v respectively. x0 、vy0 and w0; the x component of the velocity, the y component of the velocity and the angular velocity of the center point of carrier 1 are v x1 、v y1 and w1; the x component of the velocity, the y component of the velocity and the angular velocity of the center point of carrier 2 are v x2 、v y2 and w2; then the motion constraint of carrier 1 satisfies the following nonholonomic constraint equation:

[0097]

[0098] make Then there is

[0099]

[0100] Let the state vector u=(w1,v x0 ,v y0 ,w0,w2) T , similarly, the nonholonomic constraint (motion constraint) equation of the system can be obtained as:

[0101]

[0102] in,

[0103]

[0104] From a kinematics perspective, it is more convenient to use the center point as a reference point. However, to derive the dynamic equations, the center of mass must be used as the reference point for system trajectory tracking. The conversion relationship between the center of mass and the center point is:

[0105]

[0106] Taking the derivative of formula (5), we get

[0107]

[0108] S103: Combining the geometric constraints, the motion constraints and the Euler-Lagrange equations to obtain a system dynamics model.

[0109] The kinetic energy expression of the system with the center of mass as the reference point is:

[0110]

[0111] Wherein, subscript i=0, 1, 2 are used to represent the load, carrier 1, and carrier 2, respectively; and denote the longitudinal and transverse components of the center-of-mass velocity in the inertial coordinate system; is the angular velocity; m i For quality; J iis the moment of inertia. For example: Represents the longitudinal component of the center-of-mass velocity of carrier 1.

[0112] For a nonholonomic constrained system, the dynamic model described by the Euler-Lagrange equation can be expressed as

[0113]

[0114] Among them, B is the control transformation matrix, U is the virtual control quantity of the control input, is the constraint matrix, and λ is the Lagrange multiplier.

[0115] Derivation of formula (8) yields

[0116]

[0117] in,

[0118] M=diag[M1 M0 M2];

[0119] M i =diag[m i m i J i ];

[0120]

[0121] U=[F x1 F y1 M1 F x2 F y2 M2] T ;

[0122] O 3×3 =zero(3) represents the third-order zero matrix; in the virtual control quantity U, F x1 、F y1 and M1 represent the longitudinal driving force, lateral driving force and torque of carrier 1 respectively, F x2 、F y2 M2 and M3 represent the longitudinal driving force, lateral driving force and torque of the carrier 2 respectively. c By deriving formula (1), we can get:

[0123]

[0124] Order s c =Ts p , from formula (4) and (6) we can get

[0125]

[0126] Among them, sc is the matrix A c The basis matrix of the null space, A c s c =0.

[0127] Multiply both sides of formula (9) by And then put it into formula (2) to get the simplified system dynamics equation, as shown below:

[0128]

[0129] in,

[0130]

[0131] Assuming that the parameters in formula (12) consist of a nominal part and a time-varying uncertain part, the parameter matrix can be decomposed as follows:

[0132]

[0133] Where t represents time; q = q c represents the system state; σ represents the system uncertainty; and They are C(q,σ,t) and the nominal part; ΔC(·) and They are C(q,σ,t) and In addition, the parameter matrices of both the nominal and uncertain parts are continuous, and the uncertainty part is bounded.

[0134] To facilitate the following derivation, let

[0135]

[0136] Therefore, we can get

[0137] ΔD(q,σ,t)=D(q,t)K(q,σ,t) (14)

[0138] Where I represents the identity matrix.

[0139] S2: constructing an adaptive robust controller based on the system dynamics model; the control items of the adaptive robust controller include a nominal system control item, a feedback item, and an adaptive item;

[0140] The principle diagram of using adaptive robust controller to perform trajectory tracking control on dual-vehicle cooperative transportation system is as follows: Figure 3 As shown, specifically including:

[0141] S201: Calculate the actual error in trajectory tracking based on the actual position and expected trajectory of the system, and establish a trajectory tracking constraint equation;

[0142] The trajectory tracking problem is equivalent to making the heading angle error and position error of the system tend to 0. Therefore, the heading angle error Defined as the heading angle of the object (including payload, carrier 1 and carrier 2) and the desired heading angle The position error (e x0 ,e y0 ) is defined as the distance from the center of mass of the load to the desired trajectory point (a point in the desired trajectory), where e x0 and e y0 It is the longitudinal and transverse distance from the center of mass of the load to the desired trajectory point. It is specifically expressed as:

[0143]

[0144] in, Indicates the system state quantity; represents the desired state (trajectory). Taking the first-order derivative of formula (15), we get

[0145]

[0146] Among them, v xi represents the longitudinal component of the object's velocity at the desired trajectory point; c ri represents the curvature at the desired trajectory point.

[0147] In order to make the system follow the target trajectory, the heading angle error and position error (e x0 ,e y0 ) should satisfy: when t→∞, e x0 ,e y0 →0. Therefore, the following equality constraints are imposed on the system dynamics model:

[0148]

[0149] Where, h=diag[h1,h2,h2,h2,h3], h k (k=1,2,3) is a constant. Write formula (17) in matrix form, and we get

[0150]

[0151] in,

[0152] A=diag([1,1,1,1,1]);

[0153]

[0154] A is the abbreviation of A(q,t), and ζ is the abbreviation of ζ(q,t).

[0155] Converting formula (17) into the second-order derivative form with respect to time t, we can get

[0156]

[0157] in,

[0158]

[0159] b is the abbreviation of b(q,t) (other abbreviations in this article are similar).

[0160] The task of trajectory tracking control is to ensure that the load accurately and timely follows the target trajectory. To address unmodeled factors such as parameter uncertainty and external disturbances in the dual-vehicle cooperative transportation system during operation, an adaptive robust control algorithm based on the constraint-following approach is designed. The control terms of this algorithm mainly consist of a nominal system control term, a feedback term, and an adaptive term.

[0161] S202: Obtaining a nominal system control term based on the system dynamics model and the trajectory tracking constraint equation;

[0162] Design the nominal system control term without considering the uncertainty and initial error. Definition Then the nominal dynamic system formula (12) can be written as follows:

[0163]

[0164] At the same time, the second-order equality constraint formula (19) can be described as:

[0165]

[0166] in,

[0167] because and There is a one-to-one correspondence, and the constraints of formula (19) and formula (21) are equivalent, so about The equation of equation (21) is consistent.

[0168] Substituting formula (20) into formula (21), we get

[0169]

[0170] definition Substituting into formula (22) we can get

[0171]

[0172] The above equation can be regarded as an equality constraint about U. The nominal dynamic system equation (12) is about The prerequisite for the controllability of the constraints is consistent with equation (20).

[0173] From formula (23), the constraint control quantity that meets the requirements is

[0174]

[0175] Where s is any vector satisfying the order.

[0176] If the system is free of uncertainty and initially satisfies Equation (18), then the constrained control variable U0 can be used to ensure that the nominal system follows the equality constraint. However, in practice, unknown uncertainties often exist, and initial errors may also exist. Therefore, the control algorithm needs to be further designed to address these unknown uncertainties and initial errors.

[0177] The designed adaptive robust controller is as follows:

[0178]

[0179] where p1, p2, and p3 represent the nominal system control term, feedback term, and adaptive term, respectively; and

[0180] S203: Construct feedback items and adaptive items;

[0181] In the actual control process, due to the existence of initial posture error and velocity error, the system cannot strictly meet the constraints of formula (18), so the system constraint following error is defined as:

[0182]

[0183] In order to suppress the impact of initial pose error and velocity error on the system, it is necessary to add feedback terms to compensate for the dynamic response of the system, as shown below:

[0184]

[0185] in, P=eye(5); k0 is an adjustable parameter and k0>0.

[0186] In order to ensure that the virtual control variable U can satisfy the uniform boundedness and uniform ultimate boundedness of the system, the following assumptions are made:

[0187] Assumption 1: Let W = PADEM -1 A-1 P -1 , there is an unknown constant ρ Ω >-1, so

[0188]

[0189] Among them, λ m Represents the matrix W+W T The eigenvalue of .

[0190] Assumption 2: There exists an unknown constant vector a and a known function So that:

[0191]

[0192] Hypothesis 3: Based on Hypothesis 2, for each There is a function π can be linearly decomposed with respect to a as follows:

[0193]

[0194] Where a is the adaptive coefficient and satisfies L 1,2 ∈R and L 1,2 >0,L 1,2 Indicates L1 and L2. These two parameters have no special meaning and are used to adjust The change equation.

[0195] Based on the above assumptions, for a given boundary constant ε>0, we have

[0196]

[0197] in,

[0198]

[0199] S3: Allocate the control items of the adaptive robust controller to each carrier of the system through a stress optimization algorithm to achieve driving force distribution.

[0200] Since the unmanned dual-vehicle cooperative transport system is an overdrive system, For a full row rank matrix, the virtual control quantity U needs to be allocated, let

[0201]

[0202] Then there is

[0203]

[0204] Where w is any vector that satisfies the order.

[0205] Taking the minimum stress on the load as the distribution optimization goal, the objective function is as follows:

[0206]

[0207] Where θ represents the cost function of the external force on the load; is the resultant force acting on the load in the X direction of the inertial coordinate system; is the resultant force on the load in the Y direction of the inertial coordinate system; T1 and T2 are the horizontal and vertical decomposition matrices of the driving force of carrier 1 and carrier 2 respectively; F f1 and F f2 are the external resistances experienced by carrier 1 and carrier 2 respectively.

[0208] Quadratic programming can be used to solve the above optimization problem to achieve driving force distribution.

[0209] Example 2:

[0210] like Figure 4 As shown, the dual-vehicle cooperative transportation system of this embodiment is based on a master vehicle (carrier 1), a slave vehicle (carrier 2) and a load, and includes: an operation calculation unit, a positioning unit, an information perception unit, an execution unit, a power supply unit and a communication unit.

[0211] The operation calculation unit, located in the master vehicle, contains one or more computing platforms. It processes data from other units, solves control variables using controller algorithms, and issues instructions to the execution unit. Data received by the operation calculation unit from other units includes: master vehicle-load angle information, master vehicle obstacle and image information acquired via the master vehicle's information sensing unit; slave vehicle-load angle information, slave vehicle obstacle and image information acquired from the slave vehicle's information sensing unit via the communication unit; and the load's coordinate position, negative acceleration, and angular velocity information acquired from the positioning unit via the communication unit.

[0212] The positioning unit is located on the payload and is used to determine the payload's position and heading information, including the GPS global positioning system and the inertial measurement unit (IMU);

[0213] The information perception unit includes lidar, cameras, millimeter-wave radar, and angle sensors, located on both the master and slave vehicles. The lidar, cameras, and millimeter-wave radar are used to identify and track static and dynamic obstacles around the coordinated transport system. Angle sensors, located at the joints between the master vehicle and the payload, and the slave vehicle and the payload, respectively, sense the rotational angle of the master and slave vehicles relative to the payload. Lidars are located at the front of the master vehicle and the rear of the slave vehicle, respectively. Cameras are located on all four sides of the vehicles (including vehicle 1 and vehicle 2, i.e., the master and slave vehicles). Millimeter-wave radars are located at the front and left ends of the master vehicle and the rear and left and right ends of the slave vehicle. The cameras provide real-time images for background monitoring. The lidar, located on top of the vehicles, offers a long detection range and a wide field of view. Millimeter-wave radars, located on the front and rear sides of the master vehicle and the slave vehicle, detect nearby vehicles or obstacles, supporting forward and backward collision warnings and providing close-range protection. This multi-layered perception system ensures that the dual-vehicle coordinated transport system accurately perceives its surroundings in various driving scenarios.

[0214] The execution unit is responsible for executing the instructions from the computational unit, controlling the movement and steering of the master and slave vehicles through the drive and steering systems. The drive system includes a motor control module and a brake control module. The motor control module has two modes: braking and driving. In driving mode, the motor control module precisely controls the motor speed and steering by adjusting the motor's supply voltage and frequency. In braking mode, the execution unit coordinates the motor control module and the brake control module, prioritizing the motor brake module to efficiently convert the carrier's kinetic energy into electrical energy and feed it back to the power supply unit's battery, thereby achieving energy recovery and utilization and improving the system's energy efficiency.

[0215] The power supply unit provides energy to each unit in the dual-vehicle cooperative transport system. Installed within both the carrier and the load, the power supply unit is equipped with a power monitoring device. While controlling and protecting the power supply to all electrical devices, it also transmits power usage data and battery status to the operational computing unit via the communication unit.

[0216] The communication unit is used to connect the master vehicle, slave vehicles, and loads for real-time communication via wired or wireless connections. Specifically, the communication unit transmits angle information and environmental perception data collected by the slave vehicle's information sensing unit, real-time operating status information from the slave vehicle's execution unit, and position information obtained by the load's positioning unit to the master vehicle's operation calculation unit. It also sends control instructions generated by the master vehicle's operation calculation unit to the slave vehicle's execution unit via the communication unit.

[0217] The unmanned dual-vehicle cooperative transportation system designed by the present invention based on the trajectory tracking control method integrates an operation calculation unit, a positioning unit, an information perception unit, an execution unit, a power supply unit and a communication unit. The system composition is streamlined, which can ensure efficient collaborative work between various units while reducing costs.

[0218] The above description is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with this technical field can easily think of changes or replacements within the technical scope disclosed by the present invention, which should be covered by the scope of protection of the present invention.

Claims

1. A trajectory tracking control method for an unmanned dual-vehicle cooperative transportation system, characterized in that: include: S1: Based on the geometric constraints, motion constraints and Euler-Lagrange equations of the system, the system dynamics model is modeled to obtain the system dynamics model; The specific steps include: S101: obtaining geometric constraints based on the positional relationship between the load and the carrier in the system; The system includes a load and a carrier, the carrier includes carrier 1 and carrier 2 following carrier 1; the coordinate system and key nodes are defined as follows: OXY is the inertial coordinate system; P i xy (i = 0, 1, 2) is a conjoined coordinate system, where the subscripts i = 0, 1, and 2 represent the load, carrier 1, and carrier 2, respectively. In the conjoined coordinate system, x represents the longitudinal direction of the object, and y represents the transverse direction of the object. The object includes the load, carrier 1, and carrier 2. i (x pi ,y pi ), C i (x i ,y i ), Represents the center point, center of mass and heading angle of the object respectively; the center point of the carrier is the midpoint of the line connecting the front axle center and the rear axle center; the position information of the load, carrier 1 and carrier 2 can be used To express, you can also use To express; let q p =(q p1 ,q p0 ,q p2 ) T ,q c =(q c1 ,q c0 ,q c2 ) T ; According to the positional relationship between the load and the two carriers, the geometric constraint equations of the dual-vehicle cooperative transport system are as follows: Where l0, l1, and l2 represent the distances from hinge point 1 to the load's center of mass, hinge point 1 to the center of mass of carrier 1, and hinge point 2 to the center of mass of carrier 2, respectively. Hinge point 1 is the center point of carrier 1; hinge point 2 is the center point of carrier 2. The load is a uniform rectangular rigid body, and its center point and center of mass are both the midpoint of the line connecting hinge point 1 and hinge point 2. Taking the second derivative of the geometric constraint equation, we get the following formula: in, There is one dot above the parameter for the first-order derivative, and two dots above the parameter for the second-order derivative; S102: Obtain motion constraints based on the motion states of the load and the carrier in the system; Assume that the x component of the load center velocity, the y component of the velocity and the angular velocity are v x0 、v y0 and w0; the x component of the velocity, the y component of the velocity and the angular velocity of the center point of carrier 1 are v x1 、v y1 and w1; the x component of the velocity, the y component of the velocity and the angular velocity of the center point of carrier 2 are v x2 、v y2 and w2; state vector u=(w1,v x0 ,v y0 ,w0,w2) T ; Then the motion constraint equation of the system is: in, According to the geometric relationship between the center of mass and the center point of the object, the conversion relationship between the center of mass and the center point is obtained as follows: Taking the derivative of the above formula, we get in, I3=eye(3) is the third-order identity matrix; S103: Combining the geometric constraints, the motion constraints, and the Euler-Lagrange equations to obtain a system dynamics model; The kinetic energy expression of the system with the center of mass as the reference point is: Wherein, subscript i=0, 1, 2 are used to represent the load, carrier 1, and carrier 2, respectively; and denote the longitudinal and transverse components of the center-of-mass velocity in the inertial coordinate system; is the angular velocity; m i For quality; J i is the moment of inertia; Combining the geometric constraints, the motion constraints and the Euler-Lagrange equation, the dynamic model of the system is derived as follows: in, M=diag[M1 M0 M2]; M i =diag[m i m i J i ]; U=[F x1 F y1 M1 F x2 F y2 M2] T ; O 3×3 =zero(3) represents the third-order zero matrix; in the virtual control quantity U, F x1 、F y1 and M1 represent the longitudinal driving force, lateral driving force and torque of carrier 1 respectively, F x2 、F y2 and M2 represent the longitudinal driving force, lateral driving force and torque of carrier 2 respectively; λ is the Lagrange multiplier; Order s c =Ts p ,get The simplified system dynamics equation is as follows: in, Assuming that the above parameters consist of a nominal part and a time-varying uncertain part, the parameter matrix can be decomposed as follows: Where t represents time; q = q c represents the system state; σ represents the system uncertainty; and They are C(q,σ,t) and the nominal part; ΔC(·) and They are C(q,σ,t) and The uncertainty part; make Therefore, we get ΔD(q,σ,t)=D(q,t)K(q,σ,t) Where I represents the identity matrix; S2: constructing an adaptive robust controller based on the system dynamics model; the control items of the adaptive robust controller include a nominal system control item, a feedback item, and an adaptive item; S3: Allocate the control items of the adaptive robust controller to each carrier of the system through a stress optimization algorithm to achieve driving force distribution.

2. The method according to claim 1, characterized in that The S2 specifically includes: S201: Calculate the actual error in trajectory tracking based on the actual position and expected trajectory of the system, and establish a trajectory tracking constraint equation; S202: Obtaining a nominal system control term based on the system dynamics model and the trajectory tracking constraint equation; S203: Construct feedback items and adaptive items.

3. The method according to claim 2, characterized in that The S201 specifically includes: The heading angle error Defined as the heading angle of the object and the desired heading angle The position error (e x0 ,e y0 ) is defined as the distance from the center of mass of the load to the desired trajectory point, where e x0 and e y0 is the longitudinal and lateral distance from the center of mass of the load to the desired trajectory point; the actual error in trajectory tracking is specifically expressed as: in, Indicates the system state quantity; Indicates a desired state; Taking the derivative of the above formula, we get Among them, v xi represents the longitudinal component of the object's velocity at the desired trajectory point; c ri represents the curvature at the desired trajectory point; The following equality constraints are imposed on the system dynamics model: Where, h=diag[h1,h2,h2,h2,h3], h k (k=1,2,3) is a constant; write the above formula into matrix form, and we get in, A=diag([1,1,1,1,1]); A is the abbreviation of A(q,t), ζ is the abbreviation of ζ(q,t); Convert the above formula into the second-order derivative form with respect to time t, and we get in, b is the abbreviation of b(q,t).

4. The method according to claim 3, characterized in that The S202 specifically includes: defining Then the nominal dynamic system formula is written as follows: The derived second-order equality constraint formula is described as: in, After deduction, we get definition Substituting into the above formula we get Then the constraint control quantity that meets the requirements is Where s is any vector satisfying the order; The designed adaptive robust controller is as follows: where p1, p2, and p3 represent the nominal system control term, feedback term, and adaptive term, respectively; and 5. The method according to claim 4, characterized in that In S203, the step of constructing feedback items specifically includes: The system constraint following error is defined as: The feedback items are as follows: in, P=eye(5); k0 is an adjustable parameter and k0>

0.

6. The method according to claim 5, characterized in that In S203, the step of constructing the adaptive term specifically includes: Make the following assumptions: Assumption 1: Let W = PADEM -1 A -1 P -1 , there is an unknown constant ρ Ω >-1, so Among them, λ m Represents the matrix W+W T The characteristic value of Assumption 2: There exists an unknown constant vector a and a known function So that: Hypothesis 3: Based on Hypothesis 2, for each There is a function π can be linearly decomposed with respect to a as follows: Where a is the adaptive coefficient and satisfies L 1,2 ∈R and L 1,2 >0,L 1,2 Indicates L1 and L2. These two parameters have no special meaning and are used to adjust The change equation of Based on the above assumptions, for a given boundary constant ε>0, we have in, 7. The method according to claim 6, characterized in that The S3 specifically includes: make Then there is Where w is any vector that satisfies the order; Taking the minimum stress on the load as the distribution optimization goal, the objective function is as follows: in, represents the cost function of the external force on the load; is the resultant force acting on the load in the X direction of the inertial coordinate system; is the resultant force on the load in the Y direction of the inertial coordinate system; T1 and T2 are the horizontal and vertical decomposition matrices of the driving force of carrier 1 and carrier 2 respectively; F f1 and F f2 are the external resistances experienced by carrier 1 and carrier 2 respectively.

8. The method according to claim 7, characterized in that The optimization problem in S3 is solved using quadratic programming.

9. An unmanned dual-vehicle cooperative transportation system, characterized in that: Running the method according to any one of claims 1 to 8, the system is based on a master vehicle, a slave vehicle and a load, and includes: an operation calculation unit, a positioning unit, an information perception unit, an execution unit, a power supply unit and a communication unit; The operation calculation unit is located in the master vehicle and is used to process data from other units, solve the control quantity through the controller algorithm, and issue instructions to the execution unit. The operation calculation unit receives data from other units, including: master vehicle-load angle information, master vehicle obstacle and image information obtained by the master vehicle information perception unit; slave vehicle-load angle information, slave vehicle obstacle and image information obtained from the slave vehicle information perception unit through the communication unit; and the load coordinate position, negative acceleration and angular velocity information obtained from the positioning unit through the communication unit. The positioning unit is located on the payload and is used to determine the payload's position and heading information, including the GPS global positioning system and the inertial measurement unit; The information perception unit includes a laser radar, a camera, a millimeter-wave radar, and an angle sensor, which are located on the master vehicle and the slave vehicle respectively. The laser radar, the camera, and the millimeter-wave radar are used to identify and track static and dynamic obstacles around the collaborative transport system. The angle sensors are located at the hinges between the master vehicle and the load, and between the slave vehicle and the load, respectively, to sense the rotation angles of the master vehicle and the slave vehicle relative to the load. The laser radars are located at the front end of the master vehicle and the rear end of the slave vehicle, the cameras are located on all four sides of the master vehicle and the slave vehicle, and the millimeter-wave radars are located on the left and right ends of the front of the master vehicle and the left and right ends of the rear of the slave vehicle. The cameras provide real-time images for background monitoring. The laser radar located on top of the carrier can provide a longer detection distance and a wider field of view. The millimeter-wave radars located on the front side of the master vehicle and the rear side of the slave vehicle detect whether there are vehicles or obstacles around, provide support for front and rear collision warnings, and provide close-range protection. The execution unit is used to execute the instructions of the operation computing unit and control the movement and steering of the master vehicle and the slave vehicle through the drive system and steering system. The drive system includes a motor control module and a brake control module. The motor control module has two modes: braking and driving. In driving mode, the motor control module adjusts the motor supply voltage and frequency to achieve precise control of the motor speed and direction. In braking mode, the execution unit coordinates the motor control module and the brake control module, using the motor brake module to efficiently convert the carrier's kinetic energy into electrical energy and feed it back to the battery of the power supply unit. The power supply unit is used to provide the required energy for each unit of the dual-vehicle cooperative transportation system. The power supply unit is installed inside the carrier and the load, and is equipped with a power monitoring device. While controlling and protecting the power supply to all electrical equipment, it also transmits power consumption data and battery status to the operation and calculation unit through the communication unit. The communication unit is used to connect the real-time communication between the master vehicle, the slave vehicle and the load through wired or wireless means; the communication unit transmits the angle information and environmental perception data collected by the slave vehicle information perception unit, the real-time operation status information of the slave vehicle execution unit, and the position information obtained by the load positioning unit to the master vehicle operation calculation unit, and sends the control instructions generated by the master vehicle operation calculation unit to the slave vehicle execution unit through the communication unit.

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