A Variable Cross-Section Tube MPC Trajectory Tracking Control Method Considering Uncertainty of Truck Load

Abstract

The present invention discloses a variable cross-section Tube MPC trajectory tracking control method considering the uncertainty of truck load, and the steps are as follows: establish a three-degree-of-freedom model considering the yaw motion, lateral motion and roll motion of the truck under load uncertainty; perform disturbance separation on the three-degree-of-freedom model considering load uncertainty based on the Tube invariant set theory to establish a nominal model; collect on-vehicle sensor information and design a variable cross-section Tube based on the system state; calculate the nominal front wheel angle based on the nominal model; design an auxiliary controller based on the variable cross-section Tube and calculate the additional front wheel angle; combine the nominal front wheel angle and the additional front wheel angle to output a front wheel angle command to the steering system to make the truck track the target trajectory. The present invention collects the truck driving state signals in real time through sensors, adjusts the front wheel angle control strategy of the controller based on the current state of the vehicle, and reduces the influence of variable load on the trajectory tracking performance of the truck.

Description

Technical Field

[0001] The present invention belongs to the technical field of vehicle dynamics, and particularly relates to a variable cross-section Tube MPC trajectory tracking control method considering the uncertainty of truck load. Background Art

[0002] The mass of the goods transported by the truck each time varies greatly, which causes large changes in the vehicle's steering performance and rollover characteristics. At present, unmanned trucks generally use MPC (Model Predictive Control) for trajectory tracking control; however, these MPC algorithms generally set the internal vehicle model parameters according to the fully loaded state of the truck, without considering the impact of load changes on the vehicle's dynamic characteristics.

[0003] For example, compared with the fully loaded state, the front wheelbase, the height of the center of mass of the sprung mass, and the tire cornering stiffness of the vehicle in the unloaded state result in the truck being more difficult to roll over than in the fully loaded state. If the MPC algorithm does not consider the load change, it will calculate a rollover danger area much larger than the actual one, resulting in a conservative output steering angle during the trajectory tracking process and reducing the tracking accuracy. In addition, it is difficult to accurately obtain the front wheelbase, the height of the center of mass of the sprung mass, and the tire cornering stiffness under different loads, so it is very difficult to update the model parameters of MPC in real time based on the load.

[0004] Therefore, the present invention proposes a variable cross-section Tube MPC trajectory tracking control method considering the uncertainty of truck load. With the goal of trajectory tracking accuracy, considering the influence of variable load, the shape of the Tube is updated in real time according to the vehicle state according to the variable cross-section Tube algorithm; combining the terminal sliding mode control algorithm and the variable cross-section Tube to design an auxiliary controller to keep the vehicle state always within the variable cross-section Tube, so as to ensure the stability of the truck during driving, improve the convergence speed, and effectively improve the trajectory tracking accuracy of the truck under uncertain load. Summary of the Invention

[0005] Aiming at the deficiencies of the above-mentioned prior art, the purpose of the present invention is to provide a variable cross-section Tube MPC trajectory tracking control method considering the uncertainty of truck load, so as to solve the problems of the decline in path tracking accuracy and stability caused by the uncertainty of the mass of the goods transported by the truck each time in the prior art.

[0006] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0007] A variable cross-section Tube MPC trajectory tracking control method considering the uncertainty of truck load of the present invention comprises the following steps:

[0008] 1) Design a variable cross-section Tube based on vehicle state;

[0009] 11) Establish a three-degree-of-freedom model considering the yaw motion, lateral motion, and roll motion of the truck under load uncertainty;

[0010] 12) Based on the Tube invariant set theory, perform disturbance separation on the three-degree-of-freedom model considering load uncertainty to establish a nominal model;

[0011] 13) Collect the information of vehicle-mounted sensors and design a variable cross-section Tube based on the system state;

[0012] 2) Calculate the front wheel steering angle of the truck based on the variable cross-section Tube;

[0013] 21) Calculate the nominal front wheel steering angle based on the nominal model;

[0014] 22) Design an auxiliary controller based on the variable cross-section Tube and calculate the additional front wheel steering angle;

[0015] 23) Combine the nominal front wheel steering angle and the additional front wheel steering angle to output a front wheel steering angle command to the steering system, enabling the truck to track the target trajectory.

[0016] Furthermore, in step 11), the front axle distance greatly affected by the load, the distance from the center of mass of the sprung mass to the roll axis, and the tire cornering stiffness are taken as uncertain parameters to construct a three-degree-of-freedom dynamic model of a heavy truck considering load uncertainty, and its expression is as follows:

[0017]

[0018]

[0019]

[0020] In the formula, \(k\) is the running time, \(A\) is the system matrix, \(B\) is the control matrix, \(x(k)\) is the system state, \(u(k)\) is the control input, is the range of state variables, \(\Pi\) is the range of control inputs, \(W\) is the range of disturbances, \(n\) is the dimension of state variables, \(\Delta K\) f is the disturbance of the front wheel cornering stiffness, \(\Delta K\) r is the disturbance of the rear wheel cornering stiffness, \(\Delta a\) is the disturbance of the front axle distance, \(\Delta h\) s is the disturbance of the distance from the center of mass of the sprung mass to the roll axis, \(v\) y is the lateral vehicle speed, \(\omega\) r is the yaw angular velocity, is the roll angle of the sprung mass, \(I\) x is the moment of inertia of the sprung mass about the \(x\)-axis, \(K\) f is the front wheel cornering stiffness, \(K\) r is the rear wheel cornering stiffness, \(m\) is the vehicle mass, \(m\) s is the sprung mass, \(h\) sis the distance from the sprung mass to the roll axis, a is the front axle distance, b is the rear axle distance, is the roll stiffness, is the roll damping, u is the vehicle speed, I z is the moment of inertia about the z-axis, δ is the front wheel steering angle, w(ΔK f , ΔK r , Δa, Δh s ) is the equivalent parameter set disturbance caused by the load change; and, the above parameters are initialized according to the values in the fully loaded state of the truck.

[0021] Further, in step 12), a nominal model is established by separating the disturbance:

[0022]

[0023] where, is the nominal state variable, is the nominal control variable;

[0024] The Tube invariant set ensures that the state trajectory of the actual vehicle dynamics system is within the Tube sequence X:={x(1), x(2),..., x(N)} centered on the state trajectory of the nominal model without disturbance, and its expression is as follows:

[0025]

[0026] where, is the Tube invariant set, that is, the width of the Tube;

[0027] Let be the invariant set of the system, then there is the following mathematical relationship:

[0028]

[0029] Further, in step 13), the sensor information includes: yaw rate sensor information, lateral acceleration sensor information, front wheel steering angle sensor information, and vehicle speed sensor information.

[0030] Further, the method for designing a variable cross-section Tube based on the system state in step 13) is as follows:

[0031] Determine the difference between the current load and the full load by measuring the angular velocity and the front wheel steering angle. The calculation method of the yaw rate gain is as follows:

[0032]

[0033]

[0034] Calculate the difference between the current yaw rate gain and the yaw rate gain under full load, so as to characterize the difference degree Δ between the current load and the full load. The expression is as follows:

[0035]

[0036] Wherein, is the current yaw rate gain, is the yaw rate gain under full load;

[0037] Calculate the variable cross-section Tube cross-section gain coefficient α based on the difference degree Δ:

[0038]

[0039] Wherein, Δ max is the maximum deviation of the yaw rate gain, which is related to the vehicle model;

[0040] Update the cross-section of the Tube in real time according to the variable cross-section Tube cross-section gain coefficient:

[0041]

[0042] Wherein, is the current Tube invariant set, is the maximum Tube invariant set, is the minimum Tube invariant set;

[0043] Combine Equation (3) and Equation (10) to obtain the current Tube cross-section;

[0044]

[0045] Furthermore, the method for calculating the nominal front wheel angle in step 21) is as follows:

[0046] Calculate the optimal angle by taking the error between the reference lateral distance and the actual lateral distance and the front wheel angle as the optimization quantities. The expression is as follows:

[0047]

[0048] Wherein, R, P and Q are weight coefficients, N is the prediction step length, is the reference lateral distance at the k-th moment for the i-th prediction step length, which is given by the upper-level autonomous driving strategy; is the predicted lateral distance at the k-th moment for the i-th prediction step length, is the predicted front wheel angle at the k-th moment for the i-th prediction step length, is the front wheel angle at the N-th prediction step length.

[0049] Furthermore, the method for calculating the additional front wheel angle in step 22) is as follows:

[0050] Substitute Equation (10) into Equation (11) to obtain the error system state equation:

[0051]

[0052] where is the error state, is the control law of the auxiliary controller;

[0053] Design a sliding mode surface function based on the error system:

[0054]

[0055] where γ is a scheduling parameter, γ > 0; both p and q are scheduling parameters and are positive odd numbers, p > q;

[0056] The control law of the auxiliary controller designed based on the sliding mode surface Equation (14) is:

[0057]

[0058] where 1 < p / q < 2, η > 0. By making the upper bound of the disturbance of the sliding mode control law consistent with the farthest distance from the state Tube boundary at the k-th moment to the nominal state, the control law of the auxiliary controller can make the system converge to the nominal state within the state Tube, as shown in the following equation:

[0059]

[0060] where D is the upper bound of the disturbance.

[0061] Furthermore, the specific value of the front wheel steering angle command output to the steering system by combining the nominal front wheel steering angle and the additional front wheel steering angle in step 23) is:

[0062]

[0063] Input the calculated u(k) into the steering system and execute it.

[0064] Advantages of the present invention:

[0065] The present invention collects the truck driving state signals in real time through sensors, adjusts the front wheel steering angle control strategy of the controller based on the current state of the vehicle, and reduces the influence of variable load on the trajectory tracking performance of the truck.

[0066] 1. Separate the nominal model from the dynamic model containing interference terms through the Tube invariant set, and calculate the most ideal nominal steering angle through MPC with the trajectory tracking error and output steering angle as the objectives, effectively eliminating the influence of parameter perturbations caused by variable load on the calculation of the ideal steering angle.

[0067] 2. Update the Tube cross-sectional shape in real time based on the current vehicle state, reduce the conservatism of the Tube MPC method, and improve the trajectory tracking accuracy while ensuring the stability of the truck.

[0068] 3. Update the disturbance upper bound of the auxiliary controller in real time based on the variable cross-section of the Tube, enabling the auxiliary controller to calculate the additional steering angle that best suits the current state, thereby improving the convergence speed of trajectory tracking. Description of the Drawings

[0069] Figure 1 It is the schematic diagram of the method of the present invention. Detailed Embodiment

[0070] For the convenience of those skilled in the art to understand, the present invention will be further described below in conjunction with the embodiments and the drawings. The content mentioned in the embodiments does not limit the present invention.

[0071] Refer to Figure 1 As shown, a variable cross-section Tube MPC trajectory tracking control method for a truck considering load uncertainty of the present invention is as follows:

[0072] 1) Design a variable cross-section Tube based on the vehicle state;

[0073] 11) Establish a three-degree-of-freedom model considering the yaw motion, lateral motion, and roll motion of the truck under load uncertainty;

[0074] Take the front axle distance, the distance from the center of mass of the sprung mass to the roll axis, and the tire cornering stiffness, which are greatly affected by the load, as uncertain parameters, and construct a three-degree-of-freedom dynamic model of a heavy truck considering load uncertainty. Its expression is as follows:

[0075]

[0076]

[0077]

[0078] In the formula, k is the running time, A is the system matrix, B is the control matrix, x(k) is the system state, u(k) is the control input, is the range of state variables, Π is the range of control inputs, W is the range of disturbances, n is the dimension of state variables, ΔK f is the disturbance of the front wheel cornering stiffness, ΔK r is the disturbance of the rear wheel cornering stiffness, Δa is the disturbance of the front axle distance, Δh s is the disturbance of the distance from the center of mass of the sprung mass to the roll axis, v y is the lateral vehicle speed, ω r is the yaw angular velocity, is the roll angle of the sprung mass, I x is the moment of inertia of the sprung mass about the x-axis, K f is the cornering stiffness of the front wheels, K r is the cornering stiffness of the rear wheels, m is the vehicle mass, m s is the sprung mass, h s is the distance from the sprung mass to the roll axis, a is the front wheelbase, b is the rear wheelbase, is the roll stiffness, is the roll damping, u is the vehicle speed, I z is the moment of inertia about the z-axis, δ is the front wheel steering angle, w(ΔK f , ΔK r , Δa, Δh s ) is the equivalent parameter set perturbation caused by load changes; and, the above parameters are initialized according to the values in the fully-loaded state of the truck.

[0079] 12) Based on the Tube invariant set theory, perform perturbation separation on the three-degree-of-freedom model considering load uncertainty to establish a nominal model;

[0080] Among them, the nominal model is established by separating perturbations:

[0081]

[0082] Among them, is the nominal state variable, is the nominal control variable;

[0083] The Tube invariant set ensures that the state trajectory of the actual vehicle dynamics system is within the Tube sequence X:={x(1),x(2),...,x(N)} centered on the state trajectory of the nominal model without interference, and its expression is as follows:

[0084]

[0085] Among them, is the Tube invariant set, that is, the width of the Tube;

[0086] Let be the invariant set of the system, then the following mathematical relationship exists:

[0087]

[0088] 13) Collect vehicle sensor information and design a variable cross-section Tube based on the system state;

[0089] The sensor information includes: yaw rate sensor information, lateral acceleration sensor information, front wheel steering angle sensor information, and vehicle speed sensor information.

[0090] The method for designing a variable cross-section Tube based on the system state is as follows:

[0091] Judge the difference between the current load and the full load by the measured angular velocity and the front wheel angle. The calculation method of the yaw angular velocity gain is as follows:

[0092]

[0093]

[0094] Calculate the difference between the current yaw angular velocity gain and the yaw angular velocity gain under full load, so as to characterize the difference degree Δ between the current load and the full load. Its expression is as follows:

[0095]

[0096] Wherein, is the current yaw angular velocity gain, is the yaw angular velocity gain under full load;

[0097] Calculate the variable cross-section Tube section gain coefficient α based on the difference degree Δ:

[0098]

[0099] Wherein, Δ max is the maximum deviation of the yaw angular velocity gain, which is related to the vehicle model;

[0100] Update the cross-section of the Tube in real time according to the variable cross-section Tube section gain coefficient:

[0101]

[0102] Wherein, is the current Tube invariant set, is the maximum Tube invariant set, is the minimum Tube invariant set;

[0103] Combine Equation (3) and Equation (10) to obtain the current Tube cross-section;

[0104]

[0105] 2) Calculate the front wheel angle of the truck based on the variable cross-section Tube;

[0106] 21) Calculate the nominal front wheel angle based on the nominal model;

[0107] The method for calculating the nominal front wheel angle is as follows:

[0108] To improve the trajectory tracking accuracy and avoid rollover accidents, the optimal steering angle is calculated with the error between the reference lateral distance and the actual lateral distance, and the front wheel steering angle as the optimization variables. The expression is as follows:

[0109]

[0110] where R, P, and Q are weight coefficients, N is the prediction step length, is the reference lateral distance at the k-th moment and the i-th prediction step length, which is given by the upper-level autonomous driving strategy, is the predicted lateral distance at the k-th moment and the i-th prediction step length, is the predicted front wheel steering angle at the k-th moment and the i-th prediction step length, is the front wheel steering angle at the N-th prediction step length.

[0111] 22) Design an auxiliary controller based on the variable cross-section Tube and calculate the additional front wheel steering angle;

[0112] The role of the auxiliary control is to calculate an appropriate control law based on the error between the nominal model state and the actual system state, so that the actual system state is always within the Tube centered on the nominal model state, thereby ensuring the stability and control accuracy of the system;

[0113] Substitute Equation (10) into Equation (11) to obtain the error system state equation:

[0114]

[0115] where, is the error state, is the control law of the auxiliary controller;

[0116] Design a sliding mode surface function based on the error system:

[0117]

[0118] where γ is a scheduling parameter, γ > 0; p and q are both scheduling parameters and positive odd numbers, p > q;

[0119] The control law of the auxiliary controller designed based on the sliding mode surface Equation (14) is:

[0120]

[0121] where 1 < p / q < 2, η > 0. By making the upper bound of the disturbance of the sliding mode control law consistent with the farthest distance from the state Tube boundary at the k-th moment to the nominal state, the control law of the auxiliary controller can make the system converge to the nominal state within the state Tube, as shown in the following equation:

[0122]

[0123] where D is the upper bound of the disturbance.

[0124] 23) Combine the nominal front wheel steering angle and the additional front wheel steering angle to output a front wheel steering angle command to the steering system, so that the truck tracks the target trajectory;

[0125] The specific value of the front wheel steering angle command output to the steering system by combining the nominal front wheel steering angle and the additional front wheel steering angle is:

[0126]

[0127] Input the calculated u(k) into the steering system and execute it.

[0128] The specific application scenarios of the present invention are numerous. The above description is only the preferred embodiment of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements can be made, and these improvements should also be regarded as the protection scope of the present invention.

Claims

1. A variable cross-section Tube MPC trajectory tracking control method considering the uncertainty of truck load, characterized in that The steps are as follows: 1) Design a variable cross-section Tube based on vehicle state, specifically including: 11) Establish a three-degree-of-freedom model considering the yaw motion, lateral motion, and roll motion of the truck under uncertain loads; 12) Based on the Tube invariant set theory, perform perturbation separation on the three-degree-of-freedom model considering load uncertainty to establish a nominal model; 13) Collect vehicle sensor information and design a variable cross-section Tube based on the system state; 2) Calculate the front wheel angle of the truck based on the variable cross-section Tube, specifically including: 21) Calculate the nominal front wheel angle based on the nominal model; 22) Design an auxiliary controller based on the variable cross-section Tube and calculate the additional front wheel angle; 23) Combine the nominal front wheel angle and the additional front wheel angle to output a front wheel angle command to the steering system, enabling the truck to track the target trajectory; In step 11), the front axle distance, the distance from the center of mass of the sprung mass to the roll axis, and the tire cornering stiffness, which are greatly affected by the load, are used as uncertain parameters to construct a three-degree-of-freedom dynamic model of a heavy truck considering load uncertainty; The method for designing a variable cross-section Tube based on the system state in step 13) is as follows: Judge the difference between the current load and the full load by the measured angular velocity and front wheel angle. The calculation method of the yaw angular velocity gain is as follows: where a is the front wheelbase, b is the rear wheelbase, m is the vehicle mass, K f is the cornering stiffness of the front wheels, K r is the cornering stiffness of the rear wheels, and v is the vehicle speed; Calculate the difference between the current yaw angular velocity gain and the yaw angular velocity gain under full load, so as to characterize the difference Δ between the current load and the full load. Its expression is as follows: Among them, is the current yaw rate gain, is the yaw rate gain under full load; Calculate the cross-section gain coefficient α of the variable cross-section Tube based on the difference degree Δ; Among them, Δ max is the maximum deviation of the yaw rate gain; Update the cross-section of the Tube in real time according to the cross-section gain coefficient of the variable cross-section Tube; Among them, is the current Tube invariant set, is the maximum Tube invariant set, is the minimum Tube invariant set; Current Tube cross-section: where x(k) is the system state, is the nominal state variable.

2. The variable cross-section Tube MPC trajectory tracking control method considering the uncertainty of the truck load according to claim 1, characterized in that, In step 11), the front axle distance, the distance from the center of mass of the sprung mass to the roll axis, and the tire cornering stiffness, which are greatly affected by the load, are used as uncertain parameters to construct a three-degree-of-freedom dynamic model of a heavy truck considering load uncertainty. Its expression is as follows: u(k) = δ where k is the running time, A is the system matrix, B is the control matrix, x(k) is the system state, u(k) is the control input, is the range of state variables, Π is the range of control inputs, W is the range of disturbances, n is the dimension of state variables, ΔK f is the disturbance of the front wheel cornering stiffness, ΔK r is the disturbance of the rear wheel cornering stiffness, Δa is the disturbance of the front axle distance, Δh s is the disturbance of the distance from the center of mass of the sprung mass to the roll axis, v y is the lateral vehicle speed, ω r is the yaw rate, is the roll angle of the sprung mass, I x is the moment of inertia of the sprung mass about the x-axis, K f is the front wheel cornering stiffness, K r is the rear wheel cornering stiffness, m is the vehicle mass, m s is the sprung mass, h s is the distance from the sprung mass to the roll axis, a is the front axle distance, b is the rear axle distance, is the roll stiffness, is the roll damping, v is the vehicle speed, I z is the moment of inertia about the z-axis, δ is the front wheel steering angle, w(ΔK f , ΔK r , Δa, Δh s ) is the equivalent parameter set disturbance caused by load changes.

3. The variable cross-section Tube MPC trajectory tracking control method considering the uncertainty of the truck load according to claim 2, wherein, In step 12), a nominal model is established by separating perturbations: wherein, is the nominal state variable, is the nominal control variable; The Tube invariant set ensures that the state trajectory of the actual vehicle dynamic system is within a Tube sequence X:={x(1),x(2),...,x(N)} centered on the state trajectory of the nominal model without interference. Its expression is as follows: Among them, is the Tube invariant set; Let be an invariant set of the system, then the following mathematical relationship exists:

4. The variable cross-section Tube MPC trajectory tracking control method considering the uncertainty of the truck load according to claim 3, characterized in that The method for calculating the nominal front wheel angle in step 21) is as follows: Calculate the optimal angle with the error between the reference lateral distance and the actual lateral distance and the front wheel angle as the optimization quantities. Its expression is as follows: wherein, R, P and Q are weight coefficients, and N is the prediction step length, is the reference lateral distance at the k-th moment for the i-th prediction step length; is the predicted lateral distance at the k-th moment for the i-th prediction step length, is the predicted front wheel steering angle at the k-th moment for the i-th prediction step length, is the front wheel steering angle for the N-th prediction step length.

5. The variable cross-section Tube MPC trajectory tracking control method considering the uncertainty of the truck load according to claim 4, characterized in that The method for calculating the additional front wheel angle in step 22) is as follows: Substitute equation (10) into equation (11) to obtain the error system state equation: Among them, is the error state, is the control law of the auxiliary controller; Design a sliding mode surface function based on the error system; Where γ is a scheduling parameter, γ>0; p and q are both scheduling parameters and are positive odd numbers, p>q; The control law for designing an auxiliary controller based on the sliding mode surface (14) is: Where 1<p / q<2, η>0. By making the upper bound of the perturbation of the sliding mode control law consistent with the farthest distance from the state Tube boundary at the k-th moment to the nominal state, the control law of the auxiliary controller can make the system converge to the nominal state within the state Tube, as follows: Where D is the upper bound of the perturbation.

6. The variable cross-section Tube MPC trajectory tracking control method considering the uncertainty of the truck load according to claim 5, characterized in that The specific value of the front wheel steering angle command output to the steering system by combining the nominal front wheel steering angle and the additional front wheel steering angle in step 23) is as follows: Input the calculated u(k) into the steering system and execute it.

7. The variable cross-section Tube MPC trajectory tracking control method considering the uncertainty of the truck load according to claim 1, characterized in that, The sensor information in step 13) includes: yaw rate sensor information, lateral acceleration sensor information, front wheel steering angle sensor information, and vehicle speed sensor information.

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