Anti-slip robust self-adaptive trajectory tracking control system of submarine cable laying robot

Abstract

The invention discloses an anti-slip robust adaptive trajectory tracking control system of a submarine cable laying robot, belongs to the field of trajectory tracking control of submarine cable laying robots, and designs a novel adaptive robust controller by combining adaptive control with a sliding mode control theory. According to the controller, by constructing a slip parameter adaptive law and an anti-interference adaptive law based on a sliding mode, on-line compensation of the caterpillar band slip rate is achieved on the kinematics level, meanwhile, a robust control item is designed on the dynamics level to restrain model uncertainty and external environment disturbance, and control torque closer to reality is output. According to the method, track slipping, external interference and system uncertainty can be effectively dealt with, the stable speed and robustness of the system are improved, and accurate and rapid tracking control over the track of the submarine cable laying robot is achieved.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of trajectory tracking control of seabed cable-laying robots, and particularly relates to a skid-resistant robust adaptive trajectory tracking control system of a seabed cable-laying robot. BACKGROUND

[0002] Exploiting seabed resources is a new way to improve the strategic resource guarantee capability of China. Unlike ordinary ground vehicles, seabed cable-laying robots need to adapt to the high pressure, low temperature and extremely unstable terrain of the deep sea. Seabed cable-laying robots work in the deep-sea soft soil environment, and the soil shear strength is extremely low, with fluid stirring characteristics. Moreover, there are great differences between seabed cable-laying robots and ordinary ground vehicles in terms of running environment, control method, load, vehicle configuration / size, etc. The seabed cable-laying mobile mechanism has the characteristics of large ground contact pressure, large traction, good stability and strong obstacle crossing ability, which is very suitable for seabed environment. However, as a multi-input and multi-output strong nonlinear system, the seabed cable-laying robot has high uncertainty in the complex underwater environment, which makes it difficult to achieve control of its motion.

[0003] The seabed cable-laying robot walks on the extremely soft seabed, and its walking power comes from the mutual shearing action between the track and the soft seabed. Due to the inherent soil mechanics characteristics of soft soil, the track of the seabed cable-laying robot will produce a certain amount of skid during seabed operation. The change of skid rate will directly affect the seabed walking dynamic performance of the seabed cable-laying robot. At the same time, the seabed cable-laying robot needs to walk according to the pre-set path during seabed operation. However, due to the influence of laying deviation, seabed soft seabed current and other factors, there is a certain deviation between the actual walking path of the seabed cable-laying robot and the predetermined path. Therefore, when operating in the complex environment of soft seabed, problems such as sinking, tilting and skidding are prone to occur. Therefore, it is of great significance to study the trajectory tracking control of seabed cable-laying robots on soft soil surface. At present, although there are many control technologies used in adaptive cruise control systems for cars. However, the existing technology still has the following problems: Firstly, in the control method for robot track skid, although some research has considered skid compensation control, it basically stays at the kinematics level, and the control input is not in the form of actual control torque.

[0004] Secondly, most of the existing control methods only consider research under ideal conditions, without considering other external interference factors such as seabed current. SUMMARY

[0005] In order to solve the problems in the prior art, the adaptive control method is combined with the sliding mode control theory, and an anti-slip robust adaptive trajectory tracking control system of a submarine cable laying robot is provided, so that adaptive trajectory tracking control of the submarine cable laying robot system is realized.

[0006] The anti-interference adaptive robust control system of the submarine cable laying robot comprises: A pose error module is configured to calculate a pose error signal between an actual pose of the robot and a reference trajectory. A speed control auxiliary input module is configured to receive the pose error signal between the actual pose of the robot and the reference trajectory, and generate a virtual desired linear speed control signal and a desired angular speed control signal . A speed controller module is connected to the speed control auxiliary input module, configured to convert the desired linear speed control signal and the desired angular speed control signal into desired speed control signals of left and right tracks . ; A sliding parameter adaptive law module is configured to estimate unknown slip parameters of the left and right tracks based on the pose error signal and the desired speed control signal , and input the unknown slip parameters and to the speed controller module, so as to effectively compensate for track slip. An equivalent control law module is configured to calculate total control torque based on a sliding surface , the desired speed control signals of the left and right tracks , and a robot system dynamics model. A sliding mode adaptive law module is configured to generate a robust compensation control torque by an adaptive law, so as to compensate for the total control torque , obtain a compensated total control torque , and input the compensated total control torque to a submarine cable laying robot system dynamics model, so as to drive the left and right tracks of the robot.

[0007] Further, the kinematics model of the submarine cable laying robot system is described by the following differential equation, which is represented as: (1) wherein x and y are two-dimensional coordinate positions of the submarine cable laying robot, and theta is an azimuth angle of the submarine cable laying robot.​​​ This represents the velocity of the submarine cable-laying robot in the horizontal direction of the global coordinate system. This represents the velocity of the submarine cable-laying robot along the vertical axis of the global coordinate system. This represents the angular velocity of the submarine cable-laying robot. The forward velocity of the robot's left track. The forward velocity of the robot's right track. This refers to the slippage of the left track caused by the soft, rarefied soil surface of the seabed. This refers to the slippage of the right track caused by the soft, rarefied soil surface of the seabed. Let be the distance between the left and right tracks of the robot; the dynamic model of the submarine cable-laying robot system is represented as follows: (2) in, It is the velocity vector; This represents the total control torque vector. and These are the torque control inputs for the left and right tracks of the submarine cable-laying robot; Represents the external disturbance vector; This represents the friction coefficient vector of the submarine cable-laying robot. It involves centripetal force and the Coriolis matrix, and when the center of mass coincides with the centroid, In this application, ;matrix , , and vectors The specific form is as follows:

[0008] in, This indicates the total mass of the submarine cable-laying robot underwater. This represents the rotational inertia of the submarine cable-laying robot underwater. To facilitate the calculation of the slip parameter adaptive law to compensate for track slippage, the slippage law is... Can be transformed into .

[0009] Furthermore, in the speed controller module, the desired speed control signals for the left and right tracks... , Represented as: .

[0010] Furthermore, estimate the unknown slip parameters. and , is represented as:

[0011] , , , , , , , wherein, and are design parameters, the tracking error of the subsea cable-laying robot current pose relative to the desired pose in the subsea cable-laying robot local coordinate system can be expressed as three error signals, the expression form of which is:

[0012] and are two-dimensional coordinate positions of the reference trajectory, is the reference azimuth angle calculated by the reference signal and

[0013] Further, in the velocity control auxiliary input module, the calculation of the virtual desired linear velocity control signal and the desired angular velocity control signal is as follows:

[0014] wherein, is a control gain, represents the linear velocity of the reference trajectory, represents the angular velocity of the reference trajectory, and the calculation expression is:

[0015] Further, in the equivalent control law module, the sliding mode surface is represented as follows: , wherein, is a normal number; the tracking error includes the left track velocity error signal and the left track velocity error signal ; is represented as: .

[0016] Further, according to the sliding mode surface , the desired velocity control signals of the left and right tracks , and the robot system dynamics model, the total control torque , specifically as follows: Assume , then , since , the tracking error converges to zero asymptotically, i.e. ; The derivative of the sliding surface with respect to time is written as: ; The selected sliding surface is a necessary condition for the system to remain on it, and according to the formula and the robot system dynamics model formula (2), the total control torque is obtained:

[0017] where, , , , , and are the natural values of the intermediate variables and , representing the total uncertainty; On this basis, the total control torque is re-expressed as: Further, the robust compensation control torque generated by the adaptive law is expressed as: .

[0018] Further, for compensation of the total control torque , the compensated total control torque is obtained, which is expressed as:

[0019] Further, assuming that the total uncertainty has an optimal upper bound , the adaptive parameter is designed as an estimate of the optimal upper bound , and the adaptive parameter is used instead of the fixed gain , and the compensated total control torque is further expressed as:

[0020] where the saturation function ; ; is a small positive number, represents the left track speed error, represents the right track speed error; adaptive parameter is represented as: .

[0021] Compared with the prior art, the present application has the following beneficial effects: First, in the track tracking control method of the submarine cable laying robot, the slip compensation control is added, which more truly restores the slip factor of the robot when working on the seabed, and the simulation result shows effective tracking effect.

[0022] Second, in the present application, the influence of interference factors such as submarine current and modeling uncertainty on the submarine cable laying robot is considered, so it is more universal and convincing than previous research. BRIEF DESCRIPTION OF DRAWINGS

[0023] The present application has a total of Figure 10 Zhang, Figure 1 is an anti-interference adaptive robust control schematic diagram of the submarine cable laying robot for track slip compensation.

[0024] Figure 2 is a robot two-dimensional plane track tracking effect diagram.

[0025] Figure 3 is a position and direction angle error curve diagram of the robot.

[0026] Figure 4 is a robot control torque input signal curve diagram.

[0027] Figure 5 is a robot left track speed tracking effect diagram.

[0028] Figure 6 is a robot right track speed tracking effect diagram.

[0029] Figure 7 is an adaptive item curve diagram.

[0030] Figure 8 is an adaptive item curve diagram.

[0031] Figure 9 is an adaptive parameter curve diagram.

[0032] Figure 10It is an adaptive parameter Line graph. Detailed Implementation

[0033] The invention will now be further described with reference to the accompanying drawings. For example... Figure 1 As shown, the anti-slip robust adaptive trajectory tracking control system for the submarine cable-laying robot of the present invention aims to achieve accurate trajectory tracking of the submarine cable-laying robot under conditions of unknown slippage, ocean currents, and modeling uncertainties. The anti-slip robust adaptive trajectory tracking control system for the submarine cable-laying robot of the present invention includes a pose error module, a velocity control auxiliary input module, a velocity controller module, a sliding parameter adaptive law module, an equivalent control law module, and a sliding mode adaptive law module. The sliding mode-based anti-interference adaptive law module and the dynamic equivalent control module together constitute the robust control system. The output of the robust control system is connected to the system dynamics model, and then to the input of the kinematic model.

[0034] First, the pose error module will use the given reference trajectory signal. The actual pose information of the robot fed back from the system's kinematics module By comparison, the robot pose error signal is calculated. .in, This indicates the reference position of the submarine cable-laying robot in the horizontal direction of the global coordinate system. This indicates the reference position of the submarine cable-laying robot along the vertical axis of the global coordinate system. The reference azimuth angle representing the movement of the submarine cable-laying robot. This represents the error in the direction of movement of the submarine cable-laying robot in its local coordinate system. This represents the error in the direction perpendicular to the direction of travel within the local coordinate system of the submarine cable-laying robot. This indicates the azimuth error during the movement of the submarine cable-laying robot. Pose error signal The signal is fed to the speed control auxiliary input module, which analyzes and processes the pose error information to generate the desired robot kinematic commands, i.e., the virtual desired linear velocity control signal. With angular velocity control signal The virtual desired linear velocity is controlled by the speed controller module. With angular velocity control signal Perform coordinate transformation to generate left and right track speed control signals. Left and right track speed control signals As a kinematic control objective, it is fed into subsequent modules to calculate the left and right track speed errors and the overall control law module.

[0035] To solve the problem of track slipping, the control system of the application introduces a slip parameter adaptive law module. The slip parameter adaptive law module receives the expected speed command generated by the speed controller auxiliary module , and combines the actual pose and reference pose signals fed back from the system kinematics model to generate a pose error signal . Track slipping will cause the actual motion trajectory of the robot to deviate from the prediction of its theoretical kinematics model, which is called "kinematics model mismatch". The degree of this mismatch is determined by a set of unknown "slip parameters" . The unknown slip parameters of the left and right tracks are identified and estimated online by the adaptive law . The unknown slip parameters and are used to compensate for the kinematics model mismatch caused by slipping in real time. Next, enter the dynamics control layer of the control system of the application. The dynamics control layer consists of an equivalent control law module and a sliding mode adaptive law module to form a robust controller. The equivalent control law module calculates the total control torque in the ideal undisturbed case according to the sliding surface, the expected left and right track speed command , and the dynamics model of the robot, which is also the nominal control torque. The sliding mode adaptive law module is designed to deal with model uncertainty and external disturbances (such as ocean currents). The sliding mode adaptive law module constructs a sliding surface s based on the tracking error as a measure of the deviation of the system state from the expected value, and designs a robust compensation control torque with the structure ; In this structure, is the dynamic gain, which determines the strength of the compensation torque. The "adaptive law" clearly defines the update mechanism of the gain : it takes the sliding surface variable as input, and when increases (i.e. the system deviates seriously), the adaptive law will increase the gain correspondingly, so as to generate a stronger compensation torque to suppress disturbances.

[0036] In this way, by adjusting the gain in real time through the adaptive law, the controller can dynamically generate a compensation torque with appropriate strength, thereby achieving strong suppression of uncertain factors, while avoiding the chattering problem that may be caused by a fixed gain .

[0037] Finally, the total control torque is compensated by the robust compensation control torque with the correction term to form the final compensated total control torque . The compensated total control torque The system dynamics model is applied to the left and right tracks of the robot, thereby forming a closed-loop control on the actual motion of the robot, so that the robot accurately and quickly tracks the preset reference trajectory. The design goal of the application is to combine the sliding parameter adaptive law with the adaptive robust dynamics control based on the sliding mode, so that the control system can not only effectively compensate for the track slip at the kinematics level, but also effectively suppress external disturbances and model uncertainties at the dynamics level, output more actual driving torque, and achieve high-precision and high-robustness trajectory tracking performance.

[0038] The modules in the control system of the application are specifically introduced as follows: A, the seabed cable-laying robot system model includes a system kinematics model and a system dynamics model, wherein the seabed cable-laying robot system kinematics model is described by the following differential equation:

[0039] wherein, is the two-dimensional coordinate position of the seabed cable-laying robot, is the azimuth angle of the movement of the seabed cable-laying robot; represents the horizontal direction velocity of the seabed cable-laying robot in the global coordinate system, represents the vertical direction velocity of the seabed cable-laying robot in the global coordinate system, represents the angular velocity of the seabed cable-laying robot, is the forward linear velocity of the left track of the robot, is the forward linear velocity of the right track of the robot, is the slip law of the left track due to the seabed soft soil surface, is the slip law of the right track due to the seabed soft soil surface, is the distance between the left and right tracks of the robot; the seabed cable-laying robot system dynamics model is represented as follows: (2)

[0040] wherein, is the velocity vector; represents the total control torque vector, and are the torque control inputs of the left and right tracks of the seabed cable-laying robot respectively; represents the external disturbance vector; represents the friction coefficient vector of the seabed cable-laying robot; is the centripetal force and the Coriolis matrix, and when the mass center coincides with the geometric center, , here we take ; the matrix , , and the vector The specific form is as follows: , , ,

[0041] wherein, represents the total mass of the undersea cable laying robot under water; represents the moment of inertia of the undersea cable laying robot under water, in order to facilitate calculation of the slip parameter adaptive law to compensate for the track slip, the slip law can be converted into .

[0042] B, slip parameter adaptive law module:

[0043] In practice and are not measurable or difficult to calculate, so the parameters in the speed controller module need to be estimated to achieve compensation control, that is

[0044] wherein, , , , , , , , , represents the estimated value of , represents the estimated value of .

[0045] C, speed control auxiliary input module: Under the action of the following speed control auxiliary input, the trajectory tracking error of the undersea cable laying robot will converge to zero.

[0046]

[0047] wherein, is a control gain.

[0048] D, sliding surface and equivalent control law module PI type sliding surface is selected: wherein is a normal number, the rate of error convergence to zero is directly related to the change of this parameter, speed error signal. However, it should be noted that the control torque increases with The increase in the control torque can cause chattering phenomenon. The goal of the design of the sliding surface is to guide the system to reach the sliding surface from an external point in a finite time and to remain on the sliding surface in the subsequent time.

[0049] Assume , , the tracking error asymptotically converges to zero, i.e. . The derivative of the sliding surface with respect to time can be written as: . Considering the chosen sliding surface, is a necessary condition for the system to remain on it. Bringing the equations and into the system dynamics model, the expression of the total control torque can be obtained: The total control torque in the above equation is the nominal control torque; E, sliding adaptive law module The total control torque is able to keep the system on the sliding surface if all the system parameters are known. However, due to the inaccuracy of the mass and moment of inertia measurements or their variations, due to the modeling uncertainties and the presence of uncertainties on the slip parameters and external disturbances entering the system, the system always has uncertainties and the performance of the total control torque may become insufficient.

[0050] Set the intermediate variables and as follows: Then the system dynamics model is simplified as: (3) where and are the natural values of the intermediate variables and , the total uncertainty includes the disturbances and uncertainties in the system, the total uncertainty is described as; , (4) where is the value due to the system uncertainties, to ensure that the system can reach and remain on the sliding surface despite the presence of uncertainties, the final control law introduces a reaching term .

[0051] ​

[0052] represents a fixed gain, represents a sign function, represents an intermediate variable , and

[0053] Based on the above equations (3) and (4), the total control torque is re-expressed as follows: This term is derived from the simplified system dynamics. In order to ensure the system converges to the sliding surface even in the presence of uncertainties and external disturbances, we additionally design a robust compensation term . Therefore, the complete sliding mode controller is the superposition of these two parts, i.e., the total control torque is defined as:

[0054] In the sliding mode control, in order to guarantee the robustness of the system to the total uncertainty , the fixed gain of the reaching control law must be greater than the upper bound of the uncertainty, i.e., However, it is very difficult to accurately estimate this upper bound. If the value of is too large, the discontinuity of the sign function will cause severe chattering phenomenon; on the contrary, if the value of is insufficient, the sliding mode reaching condition cannot be guaranteed, which may lead to system instability.

[0055] To solve this inherent contradiction, this paper introduces an adaptive law to estimate the upper bound of the total uncertainty online. Here, it is assumed that there exists an optimal (i.e., the smallest) upper bound , and an adaptive parameter is designed as an estimate of the optimal upper bound . Through the designed adaptive update law, the adaptive parameter can dynamically adjust according to the system state, thereby replacing the dependence on the fixed gain , achieving the purpose of suppressing uncertainties while effectively weakening chattering. The adaptive capability has been used To reduce the chattering phenomenon, a saturation function is used; which is defined as:

[0056] where It is a small positive number. This indicates the left track speed error. This indicates the speed error of the right track.

[0057] It is an adaptive term with an update law. It is the estimation error.

[0058]

[0059] in, and It is a positive adaptive gain and is highly dependent on uncertainty. The upper bound value, Indicates the optimal upper bound The optimal estimate.

[0060] The present invention relates to an anti-slip robust adaptive trajectory tracking control system for a submarine cable-laying robot. This system introduces an adaptive robust controller based on sliding mode control (SMC) to handle problems related to unknown uncertainties and disturbances. Simulation results show that the proposed controller exhibits good performance in handling slippage, external disturbances, and uncertainties, thereby reducing tracking errors and converging to zero more quickly. Simulation results are as follows: Figures 2-10 As shown. Figure 2 Based on the actual task requirements, this is a two-dimensional planar trajectory tracking curve of the submarine cable-laying robot. The graph shows that the submarine cable-laying robot can achieve trajectory tracking tasks quite well. Figure 3 It is the relative distance error signal between the submarine cable-laying robot and the following trajectory. and relative angle error signal The graph shows that the three error signals can quickly converge to near zero. Figure 4 The two signals represent the left and right track torque input signals of the robot, respectively. and The curve graph shows that the introduced adaptive robust control can overcome the influence of disturbance uncertainties. Figures 5-6 These represent the tracking effect of the left and right track speed signals, respectively. Figures 7-8 These represent the sliding mode adaptive law; Figures 9-10 These represent the adaptive laws for the slippage parameters of the left and right tracks, respectively. As can be seen from the simulation results above, the designed trajectory tracking controller for the submarine cable-laying robot can quickly achieve stability under interference environments such as track slippage, modeling uncertainties, and ocean currents, ultimately fulfilling the expected requirements for the trajectory tracking task of the submarine cable-laying robot.

[0061] This invention is not limited to this embodiment. Any equivalent concept or modification within the technical scope disclosed in this invention shall be included within the protection scope of this invention.

Claims

1. An adaptive trajectory tracking control system, characterized in that, include: The pose error module is used to calculate the pose error signal between the actual pose of the submarine cable laying robot and the reference trajectory. The speed control auxiliary input module is used to receive the pose error signal between the actual pose of the submarine cable-laying robot and the reference trajectory, and to generate a virtual desired linear velocity control signal. and desired angular velocity control signal ; The speed controller module, connected to the speed control auxiliary input module, is used to input the desired linear velocity control signal. and desired angular velocity control signal Converted into desired speed control signals for the left and right tracks , ; The sliding parameter adaptive law module is used to control the position error signal and the desired velocity based on the position error signal and the desired velocity control signal. , Estimate the unknown slip parameters of the left and right tracks. and and the unknown slippage parameters and Input to the speed controller module; The equivalent control law module is used to determine the sliding surface. The desired speed control signal for the left and right tracks , The dynamic model of the submarine cable-laying robot system was used to calculate the total control torque. ; The sliding mode adaptive law module is used to generate robust compensation control torque through adaptive laws. Regarding the total control torque Compensation is performed to obtain the total control torque after compensation. This data is then input into the dynamic model of the submarine cable-laying robot system to drive the robot's left and right tracks.

2. The adaptive trajectory tracking control system according to claim 1, characterized in that, The kinematic model of the submarine cable-laying robot system is described by the following differential equation: （1） in, This represents the two-dimensional coordinates of the submarine cable-laying robot. The azimuth angle for the movement of the submarine cable-laying robot; This represents the velocity of the submarine cable-laying robot in the horizontal direction of the global coordinate system. This represents the velocity of the submarine cable-laying robot along the vertical axis of the global coordinate system. This represents the angular velocity of the submarine cable-laying robot. The forward velocity of the robot's left track. The forward velocity of the robot's right track. This refers to the slippage of the left track caused by the soft, rarefied soil surface of the seabed. This refers to the slippage of the right track caused by the soft, rarefied soil surface of the seabed. This is the distance between the left and right tracks of the robot. The dynamic model of the submarine cable-laying robot system is represented as follows: （2） in, It is the velocity vector; This represents the total control torque vector. and These are the torque control inputs for the left and right tracks of the submarine cable-laying robot; Represents the external disturbance vector; This represents the friction coefficient vector of the submarine cable-laying robot. It involves centripetal force and the Coriolis matrix, and when the center of mass coincides with the centroid, Take here ;matrix , , and friction coefficient vector The specific form is as follows: ； ； in, This indicates the total mass of the submarine cable-laying robot underwater. This represents the rotational inertia of the submarine cable-laying robot underwater. To facilitate the calculation of the slip parameter adaptive law to compensate for track slippage, the slippage law is... Transform into .

3. The adaptive trajectory tracking control system according to claim 2, characterized in that, In the speed controller module, the desired speed control signals for the left and right tracks. , ; The desired speed control signal vector is represented as follows: 。 4. The adaptive trajectory tracking control system according to claim 3, characterized in that, Estimate unknown slip parameters and Specifically, it is expressed as: ； ； in, , , , , , , , ;in, and All represent positive design parameters; the tracking error of the subsea cable-laying robot's current pose relative to its desired pose is expressed in the subsea cable-laying robot's local coordinate system as three error signals: ； and It is the two-dimensional coordinate position of the reference trajectory. It is by and The calculated reference azimuth angle is expressed as: ; This represents the error of the tracked robot in the horizontal X direction of the global coordinate system. Let represent the error of the tracked robot in the Y-axis direction of the global coordinate system. This represents the reference azimuth error of the tracked robot's movement. This represents the desired angular velocity control signal.

5. The adaptive trajectory tracking control system according to claim 4, characterized in that, In the speed control auxiliary input module, the virtual desired linear velocity control signal and desired angular velocity control signal The calculation is as follows: ； ； in, To control the gain, Represents the linear velocity of the reference trajectory. This represents the angular velocity of the reference trajectory.

6. The adaptive trajectory tracking control system according to claim 5, characterized in that, In the equivalent control law module, the sliding surface , means as follows: ， in, It is a positive constant; The tracking error is represented as: ， in, This indicates the left track speed error signal. This indicates the speed error signal of the right track.

7. The adaptive trajectory tracking control system according to claim 6, characterized in that, According to the sliding surface The desired speed control signal for the left and right tracks , Based on the robot system dynamics model, the total control torque is calculated as follows: Assumption ,but ,because Tracking error Eventually converges asymptotically to zero, that is This indicates that once the system state reaches the sliding surface, the tracking error can automatically converge; Sliding surface The derivative with respect to time is written as: ； This reflects the tendency of the system state to deviate from the sliding surface. To keep the system on the sliding surface, its rate of change must be zero. Then, according to the formula... And from the robot system dynamics model (2), the total control torque is obtained: in, , ; , It is an intermediate variable and The natural value, Indicates overall uncertainty; Based on this, the total control torque is re-expressed as: 。 8. The adaptive trajectory tracking control system according to claim 7, characterized in that, The robust compensation control torque is generated through an adaptive law. , means as follows: ； in, It is a symbolic function.

9. The adaptive trajectory tracking control system according to claim 8, characterized in that, Used for the total control torque Compensation is performed to obtain the total control torque after compensation. , is represented as: 。 10. The adaptive trajectory tracking control system according to claim 9, characterized in that, Assume overall uncertainty There exists an optimal upper bound. Design adaptive parameters As the optimal upper bound The estimate uses adaptive parameters. Replace fixed gain The total control torque after compensation Further expressed as: ； Wherein, saturation function ; ； It is a small positive number. This indicates the left track speed error. Indicates the right track speed error; Adaptive parameters Represented as: 。

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