Virtual Reference Trajectory Tracking Control Method for Wheeled Mobile Robots Against Sliding Interference

Abstract

The present invention discloses a virtual reference trajectory tracking control method for a wheeled mobile robot against sliding interference. First, a global rectangular coordinate system is established in the motion plane of the mobile robot, and then the odometer kinematic model and the actual kinematic model of the wheeled mobile robot are respectively described, and the kinematic model of the desired trajectory is given; then, based on the difference between the odometer pose and the actual pose of the wheeled mobile robot, the sliding interference of the wheeled mobile robot is estimated by using a tracking differentiator; then, the estimated value of the sliding interference is fused with the reference trajectory to obtain a virtual reference trajectory; finally, a controller is designed and the control parameters are adjusted to make the odometer pose of the wheeled mobile robot track the virtual reference trajectory, so that the actual pose of the wheeled mobile robot tracks the reference trajectory. The present invention has a simple form and strong practicability, and can effectively achieve accurate tracking of the reference trajectory by the wheeled mobile robot under the condition of sliding interference, and has a very broad engineering application prospect.

Description

Technical Field

[0001] The present invention relates to a virtual reference trajectory tracking control method for a wheeled mobile robot against sliding interference, belonging to the technical field of motion control of wheeled mobile robots. Background Technique

[0002] In the past few decades, wheeled mobile robots have been widely used in more and more practical engineering applications due to their advantages such as simple structure, flexible operation, etc., such as exploration, transportation, security, and target search. Trajectory tracking control technology, as one of the basic and core tasks in the motion control of wheeled mobile robots, has considerable research and application value.

[0003] At present, several control methods have been used for the trajectory tracking control of wheeled mobile robots. The literature (Z. Chen, Y. Liu, W. He, H. Qiao, H. Ji. Adaptive-Neural-Network-Based Trajectory Tracking Control for a Nonholonomic Wheeled Mobile Robot With Velocity Constraints[J]. IEEE Transactions on Industrial Electronics, vol. 68, no. 6, pp. 5057-5067, 2021) designed a trajectory tracking controller based on neural network for the kinematic model of wheeled mobile robots. The literature (K. Singhal, V. Kumar, K. Rana. Robust trajectory tracking control of non-holonomic wheeled mobile robots using an adaptive fractional order parallel fuzzy PID controller[J]. Journal of the Franklin Institute, Vol. 359, no. 9, pp. 4160-4215, 2022) designed a trajectory tracking control algorithm for wheeled mobile robots using the sliding mode control method. The literature (Y. Chen, Z. Li, H. Kong. Model Predictive Tracking Control of Nonholonomic Mobile Robots With Coupled Input Constraints and Unknown Dynamics[J]. IEEE Transactions on Industrial Informatics, vol. 15, no. 6, pp. 3196–3205, 2019) designed a trajectory tracking controller for constrained wheeled mobile robots using the model predictive control method.

[0004] None of the above-mentioned methods consider the trajectory tracking control problem of wheeled mobile robots under skidding disturbances. Skidding disturbances seriously affect the trajectory tracking performance of wheeled mobile robots. References (D. Chwa. Fuzzy Adaptive Tracking Control of Wheeled Mobile Robots With State-Dependent Kinematic and Dynamic Disturbances[J]. IEEE Transactions on Fuzzy Systems, vol. 20, no. 3, pp. 587–593, 2012) and (M. Chen. Disturbance Attenuation Tracking Control for Wheeled Mobile Robots With Skidding and Slipping[J], IEEE Transactions on Industrial Electronics, vol. 64, no. 4, pp. 3359–3368, 2017) both consider the influence of skidding disturbances and respectively propose a fuzzy adaptive algorithm and a robust tracking control scheme based on a disturbance observer to compensate for the disturbances, achieving global ultimate boundedness of the closed-loop system. It should be noted that in the above two works, even if the skidding disturbances are accurately estimated, the distance and yaw angle tracking errors cannot converge to zero. The reason for this limitation is that it is difficult to completely compensate for the lateral skidding disturbances.

[0005] To achieve complete compensation for skidding disturbances and thus better trajectory tracking performance, the present invention proposes a virtual reference trajectory tracking control method that incorporates disturbance compensation into the reference trajectory to compensate for skidding disturbances. On the one hand, the skidding disturbance estimation method proposed by the present invention is simple in form and convenient for practical engineering use. On the other hand, the scheme proposed by the present invention achieves complete compensation for skidding disturbances, making up for the deficiencies of existing schemes. Summary of the Invention

[0006] Object of the Invention: Based on the odometry kinematic model and the actual kinematic model of a wheeled mobile robot, a virtual reference trajectory tracking control method is proposed, which can achieve complete compensation for skidding disturbances and thus enable the wheeled mobile robot to accurately track the reference trajectory.

[0007] Technical Solution: To achieve the object of the present invention, the present invention adopts the following technical solution: A virtual reference trajectory tracking control method for a wheeled mobile robot resistant to skidding disturbances, the steps include:

[0008] Step 1: Establish a global rectangular coordinate system in the plane and describe the kinematic models of the wheeled mobile robot in the global coordinate system, including the odometer kinematic model and the actual kinematic model. The pose of the odometer kinematic model (hereinafter referred to as the odometer pose) is obtained by the wheel encoder, and the pose of the actual kinematic model (hereinafter referred to as the actual pose) is obtained by a high-precision positioning device. In addition, the kinematic equation of the reference trajectory needs to be given;

[0009] Step 2: Subtract the odometer pose mentioned in Step 1 from the actual pose to obtain the pose difference, and use a tracking differentiator to differentiate the pose difference to obtain the estimated values of the sliding disturbances (longitudinal and lateral sliding disturbances);

[0010] Step 3: Fuse the sliding disturbances obtained in Step 2 with the reference trajectory to obtain a virtual reference trajectory;

[0011] Step 4: Define a tracking error model and design a trajectory tracking controller to make the odometer pose of the wheeled mobile robot track the virtual reference trajectory, so that the actual pose of the wheeled mobile robot tracks the reference trajectory.

[0012] Specifically, in Step 1, first establish a global rectangular coordinate system, and then describe the odometer kinematic model and the actual kinematic model of the wheeled mobile robot in the global rectangular coordinate system respectively. The odometer kinematic model of the wheeled mobile robot is described as:

[0013]

[0014]

[0015]

[0016] where, [x o , y o T is the odometer position of the wheeled mobile robot, θ o is the odometer yaw angle, υ is the odometer speed, and ω is the odometer angular velocity. The odometer speed υ and the angular velocity ω are obtained by the wheel encoder. The odometer pose of the wheeled mobile robot is obtained by integrating the odometer speed. and are the derivatives of x o , y o and θ o with respect to time respectively.

[0017] The actual kinematic model of the wheeled mobile robot is described as:

[0018]

[0019]

[0020]

[0021] wherein, [x a , y a T is the actual position of the wheeled mobile robot, and a is the actual yaw angle. The actual pose is obtained by a high-precision positioning device. and are the derivatives of x a , y a and θ a with respect to time, respectively. δ x and δ y are the longitudinal slip disturbance and the lateral slip disturbance, respectively.

[0022] The reference trajectory of the wheeled mobile robot can be described as:

[0023]

[0024]

[0025]

[0026] wherein, [x r , y r T is the desired position, θ r is the desired yaw angle, υ r and ω r are the desired linear velocity and the desired angular velocity, respectively. and are the derivatives of x r , y r and θ r with respect to time, respectively.

[0027] Furthermore, in the second step, differentiating the difference between the odometry pose and the actual pose can obtain an estimated value of the slip disturbance. Define the difference between the odometry pose and the actual pose:

[0028] d x = x o - x a

[0029] d y = d o - d a

[0030] wherein, d x and d y are the coordinate differences between the odometry pose and the actual pose in the X and Y directions of the global coordinate system, respectively. Then, d x and d​​y are used as the inputs of the tracking differentiator respectively. The outputs of the tracking differentiator and and are the estimated values of d x , d y , δ x and δ y respectively.

[0031] The tracking differentiator adopted in the present invention is:

[0032] fh = fhan(c1(k) - s(k), c2(k), r, h0)

[0033] c1(k + 1) = c1(k) + hc2(k)

[0034] c2(k + 1) = c2(k) + hfh

[0035] wherein, s(k), c1(k) and c2(k) are the input signal, the tracking signal and the differential signal respectively. h0 and r are the sampling time and the fast factor respectively. h = nh0, n is a positive integer. For the specific form of the fhan function, please refer to "Active Disturbance Rejection Control Technology" (Han Jingqing, Active Disturbance Rejection Control Technology, National Defense Industry Press, 2008).

[0036] Under the action of the above tracking differentiator, there exists a time T such that when t → T, there is

[0037] Furthermore, in the third step, the estimated value of the sliding disturbance obtained in the second step is fused with the reference trajectory to obtain a virtual reference trajectory:

[0038]

[0039]

[0040]

[0041]

[0042]

[0043]

[0044]

[0045] wherein, x υr and y υr are the positions of the virtual reference trajectory, θ υris its yaw angle, υ υr and ω υr are respectively the linear velocity and angular velocity of the virtual reference trajectory.

[0046] Furthermore, in the fourth step, a tracking error model is established for the odometry kinematic model and the virtual reference trajectory, and then a controller is designed such that the odometry kinematic model tracks the virtual reference trajectory, so that the actual pose of the mobile robot tracks the reference trajectory. First, define the tracking error:

[0047]

[0048] Then, taking the derivative of both sides of the equation gives the tracking error model:

[0049]

[0050]

[0051]

[0052] For the above tracking error model, design the following trajectory tracking controller:

[0053] υ = k1e ox + υ υr cose oθ

[0054]

[0055] where k1, k2, and k3 are all controller gains and are all positive numbers.

[0056] Under the action of the above controller, the odometry kinematic pose of the wheeled mobile robot can track the virtual reference trajectory, so that the actual pose of the wheeled mobile robot tracks the reference trajectory.

[0057] Beneficial effects: Compared with the existing technical solutions for anti-slip interference of wheeled mobile robots, the present invention has the following technical effects:

[0058] (1) The virtual reference trajectory tracking control method proposed by the present invention can achieve complete compensation for the slip interference of the wheeled mobile robot, so that the wheeled mobile robot can accurately track the reference trajectory.

[0059] (2) The design principle of the virtual reference trajectory method proposed by the present invention is simple, and the compensation for slip interference can be achieved only by modifying the reference trajectory, without modifying the original trajectory tracking controller, so it is convenient to apply in actual engineering.

[0060] (3) The present invention proposes a virtual reference trajectory tracking control method for wheeled mobile robots, which has achieved remarkable effects in MATLAB numerical simulations, trajectory tracking experiments of wheeled mobile robots based on STM32 and TX2 boards, and experimental platforms with camera positioning functions. Description of the Drawings

[0061] Figure 1 It is a schematic diagram of the kinematic model of a wheeled mobile robot, where (a) is a schematic diagram of the odometer kinematic model and (b) is a schematic diagram of the actual kinematic model;

[0062] Figure 2 It is a schematic diagram of the virtual reference trajectory tracking control method;

[0063] Figure 3 It is the MTALAB numerical simulation curve graph of the circular trajectory tracking of the method proposed by the present invention. Among them, (a) is the simulation X-Y plane trajectory graph, (b) is the simulation distance and yaw angle tracking error response curve graph, and (c) is the simulation control input graph;

[0064] Figure 4 It is the visualization experimental result curve graph of the circular trajectory tracking of the method proposed by the present invention based on a wheeled mobile robot with STM32 and TX2 boards and an experimental platform with camera positioning function. Among them, (a) is the experimental X-Y plane trajectory graph, (b) is the experimental distance and yaw angle tracking error response curve graph, and (c) is the experimental control input graph. Detailed Implementation Manner

[0065] Step 1: First, establish a global rectangular coordinate system, such as Figure 1 the XOY coordinate system in. Then, describe the odometer kinematic model and the actual kinematic model of the wheeled mobile robot in the global rectangular coordinate system, as Figure 1 shown. The odometer kinematic model of the wheeled mobile robot is described as:

[0066]

[0067]

[0068]

[0069] where, [x o , y o T is the odometer position of the wheeled mobile robot, θ o is the odometer yaw angle, υ is the odometer speed, and ω is the odometer angular velocity. The odometer speed υ and angular velocity ω are obtained through wheel encoders. The pose of the wheeled mobile robot is obtained by integrating the speed. and are the derivatives of x o , y o and θ o with respect to time, respectively.

[0070] The actual kinematic model of the wheeled mobile robot is described as:

[0071]

[0072]

[0073]

[0074] where [x a , y a T is the actual position of the wheeled mobile robot, and θ a is the actual yaw angle. The actual pose is obtained by a high-precision positioning device. and are the derivatives of x a , y a and θ a with respect to time, respectively. δ x and δ y are the longitudinal slip disturbance and the lateral slip disturbance, respectively.

[0075] The reference trajectory of the wheeled mobile robot is given as:

[0076]

[0077]

[0078]

[0079] where [x r , y r T is the desired position, θ r is the desired yaw angle, υ r and ω r are the desired linear velocity and the desired angular velocity, respectively. and are the derivatives of x r , y r and θ r with respect to time, respectively.

[0080] Step 2: Differentiating the difference between the odometry pose and the actual pose can obtain the estimated value of the slip disturbance. Define the difference between the odometry pose and the actual pose:

[0081] d x = x o-x a

[0082] d y = d o -d a

[0083] where d x and d y are the coordinate differences between the odometer pose and the actual pose in the X and Y directions of the global coordinate system, respectively. Then, d x and d y are used as the inputs of the tracking differentiator, respectively. The outputs of the tracking differentiator and and are the estimated values of d x , d y , δ x and δ y , respectively.

[0084] The tracking differentiator adopted in the present invention is:

[0085] fh = fhan(c1(k) - s(k), c2(k), r, h0)

[0086] c1(k + 1) = c1(k) + hc2(k)

[0087] c2(k + 1) = c2(k) + hfh

[0088] where s(k), c1(k), and c2(k) are the input signal, the tracking signal, and the differential signal, respectively. h0 and r are the sampling time and the fast factor, respectively. h = nh0, where n is a positive integer. The specific form of the fhan function can be found in "Active Disturbance Rejection Control Technology" (Han Jingqing, Active Disturbance Rejection Control Technology, National Defense Industry Press, 2008).

[0089] Step 3: Fuse the sliding interference estimated value obtained in Step 2 with the reference trajectory to obtain the virtual reference trajectory (as shown in Figure 2 ):

[0090]

[0091]

[0092]

[0093]

[0094]

[0095]

[0096]

[0097] where x υr and y υr are the positions of the virtual reference trajectory, and θ υr is its yaw angle, and υ υr and ω υr are the linear velocity and angular velocity of the virtual reference trajectory, respectively.

[0098] Step 4: Establish a tracking error model for the odometry kinematic model and the virtual reference trajectory, and then design a controller so that the odometry pose tracks the virtual reference trajectory, thereby enabling the actual pose of the mobile robot to track the reference trajectory, as Figure 2 shown. First, define the tracking error:

[0099]

[0100] Then, taking the derivative of both sides of the equation gives the tracking error model:

[0101]

[0102]

[0103]

[0104] For the above tracking error model, design the following trajectory tracking controller:

[0105] υ = k1e ox + υ υr cos e oθ

[0106]

[0107] where k1, k2, and k3 are all controller gains and are all positive numbers.

[0108] Under the action of the above controller, the odometry kinematic pose of the wheeled mobile robot can track the virtual reference trajectory, thereby enabling the actual pose of the wheeled mobile robot to track the reference trajectory.

[0109] To verify the effectiveness of the virtual reference trajectory tracking control method proposed in the present invention, simulations and experiments were carried out on the wheeled mobile robot tracking a circular trajectory under the condition of sliding interference.

[0110] In the simulation, the sampling period was set to 0.001 s. The initial position of the reference trajectory was: [x r (0), y r (0)] T= [0.65, 0] T m, θ r (0) = π / 2 rad, and its linear velocity and angular velocity are respectively set as: v r = 0.65 m / s, ω r = 1 rad / s. The sliding interference is set as: [δ x , δ y T = [0.03sin(0.5t + π / 4), 0.05cos(0.3t)] T m / s. The initial pose of the wheeled mobile robot is: [x o (0), y o (0)] T = [x a (0), y a (0)] T = [0.8, -0.1] T m, θ o (0) = θ a (0) = 1.9 rad. The parameters of the tracking differentiator are set as: [r, n] T = [100, 1.5] T . The controller gains are set as: [k1, k2, k3] T = [1.5, 1.2, 1.3] T .

[0111] The simulation results are as Figure 3 shown. Figure 3 (a) is the trajectory diagram of the wheeled mobile robot and the reference trajectory in the XOY plane. Figure 3 (b) is the distance and yaw angle tracking error response of the wheeled mobile robot. It can be seen from Figure 3 (b) that the distance and yaw angle tracking errors of the wheeled mobile robot can converge to 0. Figure 3 (c) is the control input of the wheeled mobile robot.

[0112] To further verify the effectiveness of the virtual reference trajectory tracking control method proposed in the present invention, a circular trajectory experiment verification is now carried out based on a wheeled mobile robot on STM32 and TX2 boards and an experimental platform with camera positioning function.

[0113] The initial position of the experimental circular trajectory is set as: [x r (0), y r (0)] T = [0.65, 0] T m, θ r (0) = π / 2 rad, and its linear velocity and angular velocity are respectively set as: v r = 0.65 m / s, ω r ​= 1 rad / s. The initial pose of the wheeled mobile robot is: [x o (0), y o (0)] T = [x a (0), y a (0)] T = [0.86, -0.026] T m, θ o (0) = θ a (0) = 3.02 rad. The parameters of the tracking differentiator are set as: [r, n] T = [100, 3] T . The controller gains are set as: [k1, k2, k3] T = [1.1, 0.9, 1] T .

[0114] The experimental results are as Figure 4 shown. Figure 4 (a) is the trajectory diagram of the wheeled mobile robot and the reference trajectory on the XOY plane. Figure 4 (b) is the distance and yaw angle tracking error response of the wheeled mobile robot. Figure 4 (c) is the control input of the wheeled mobile robot.

[0115] The above embodiments are only for explaining the technical idea of the present invention, and the protection scope of the present invention cannot be limited thereby. It should be noted that any improvement made to the technical solution based on the technical idea of the present invention falls within the protection scope of the present invention.

Claims

1. A virtual reference trajectory tracking control method for a wheeled mobile robot to resist sliding interference, characterized in that, It includes the following steps: Step 1: Establish a global rectangular coordinate system in a plane, and describe the kinematic models of the wheeled mobile robot in the global rectangular coordinate system, including the odometer kinematic model and the actual kinematic model; the pose of the odometer kinematic model is obtained by the wheel encoder, and the pose of the actual kinematic model is obtained by a high-precision positioning device; in addition, the kinematic equation of the reference trajectory needs to be given; Step 2: Subtract the pose of the odometer kinematic model from the pose of the actual kinematic model mentioned in Step 1 to obtain the pose difference, and then use a tracking differentiator to differentiate the pose difference to obtain an estimated value of the sliding disturbance, where the sliding disturbance includes longitudinal and lateral sliding disturbances; Step 3: Fuse the sliding disturbance obtained in Step 2 with the reference trajectory to obtain a virtual reference trajectory; Step 4: Define the tracking error and describe the tracking error model, and then design a controller to make the pose of the odometer kinematic model of the wheeled mobile robot track the virtual reference trajectory, so that the pose of the actual kinematic model of the wheeled mobile robot tracks the reference trajectory.

2. The virtual reference trajectory tracking control method for a wheeled mobile robot to resist sliding interference according to claim 1, characterized in that, In Step 1, first establish a global rectangular coordinate system, and then describe the odometer kinematic model and the actual kinematic model of the wheeled mobile robot in the global rectangular coordinate system respectively; the odometer kinematic model of the wheeled mobile robot is described as: Among them, [x o , y o T is the odometer position of the wheeled mobile robot, θ o is the odometer yaw angle, v is the odometer speed, and ω is the odometer angular velocity; the odometer speed v and the angular velocity ω are obtained through wheel encoders; the pose of the kinematic model of the wheeled mobile robot is obtained by integrating the odometer speed; and are the derivatives of x o , y o and θ o with respect to time, respectively;​ The actual kinematic model of the wheeled mobile robot is described as: Among them, [x a , y a T is the actual position of the wheeled mobile robot, and θ a is the actual yaw angle; the pose of the actual kinematic model is obtained through a high-precision positioning device; and are the derivatives of x a , y a and θ a with respect to time respectively; δ x and δ y are the longitudinal slip interference and the lateral slip interference respectively;​ The reference trajectory of the wheeled mobile robot is described as: where, [x r , y r T is the desired position, θ r is the desired yaw angle, v r and ω r are the desired linear velocity and the desired angular velocity respectively; and are the derivatives of x r , y r and θ r with respect to time respectively.​ 3. The virtual reference trajectory tracking control method for a wheeled mobile robot to resist sliding interference according to claim 2, characterized in that, In Step 2, differentiating the difference between the pose of the odometer kinematic model and the pose of the actual kinematic model can obtain an estimated value of the sliding disturbance; define the difference between the pose of the odometer kinematic model and the pose of the actual kinematic model: d x = x o - x a d y = y o -y a where d x and d y are the coordinate differences in the X and Y directions of the pose of the odometry kinematic model and the pose of the actual kinematic model, respectively; then d x and d y are used as the inputs to the tracking differentiator respectively; the tracking differentiator outputs and and are the estimated values of d x , d y , δ x and δ y , respectively; The tracking differentiator adopted is: fh = fhan(c1(k) - s(k), c2(k), r, h0) c1(k + 1) = c1(k) + hc2(k) c2(k + 1) = c2(k) + hfh where s(k), c1(k), and c2(k) are the input signal, the tracking signal, and the differential signal respectively; h0 and r are the sampling time and the fast factor respectively; h = nh0, and n is a positive integer.

4. The virtual reference trajectory tracking control method for a wheeled mobile robot to resist sliding interference according to claim 3, characterized in that, In the third step, the sliding interference estimation value obtained in the second step is fused with the reference trajectory to obtain a virtual reference trajectory: where x vr and y vr are the positions of the virtual reference trajectory, θ vr is its yaw angle, v vr and ω vr are the linear velocity and angular velocity of the virtual reference trajectory, respectively.

5. The virtual reference trajectory tracking control method for a wheeled mobile robot to resist sliding interference according to claim 4, characterized in that, In Step 4, establish a tracking error model for the odometer kinematic model and the virtual reference trajectory, and then design a controller to make the odometer kinematic model track the virtual reference trajectory, so that the pose of the actual kinematic model of the mobile robot tracks the reference trajectory; first, define the tracking error: Then, taking the derivative of both sides of the equation gives the tracking error model: For the above tracking error model, design the following trajectory tracking controller: v = k1e ox + v vr cos e oθ where k1, k2, and k3 are all controller gains and are all positive numbers; Under the action of the above controller, the odometer kinematic pose of the wheeled mobile robot can track the virtual reference trajectory, so that the pose of the actual kinematic model of the wheeled mobile robot tracks the reference trajectory.

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