Trajectory control method and system for mobile device based on anti-input saturation

Abstract

The present invention provides a trajectory control method and system for a mobile device based on anti-input saturation, comprising: obtaining a desired trajectory of a mobile device; obtaining a dynamic trajectory of the mobile device according to the obtained desired trajectory and a preset trajectory control model; wherein the trajectory control model is a fractional-order iterative learning control model including an input saturation function; in the fractional-order iterative learning control model, the control amount of the dynamic model of the fractional-order trajectory tracking system for the current iteration is equal to the product of the gain matrix and the tracking error and the sum of the input saturation function; the saturation function includes the control amount of the dynamic model of the fractional-order trajectory tracking system for the next iteration after the current one, and the input saturation amount of the control amount; the tracking error is the difference between the dynamic trajectory and the desired trajectory; the present invention solves the tracking problem in the fractional-order tracking control system under the condition of input saturation during the control process of the mobile device.

Description

Technical Field

[0001] The present invention belongs to the technical field of trajectory tracking, and in particular, relates to a trajectory control method and system for a mobile device based on anti-input saturation. Background Art

[0002] When solving complex trajectory tracking, the existing technology has solved the control problem in the strictly repetitive fractional-order trajectory tracking system. The proposed iterative controller not only has low design requirements and can repair the impact of system disturbances on tracking, but also can observe the frequency domain characteristics of the controller. Ultimately, it can ensure that the tracking error of the fractional-order tracking system is controlled within the ideal range after a certain number of iterations. It has strong practicality and observability.

[0003] The inventors found that when tracking the trajectory of a mobile device, although the use of an ordinary iterative learning control algorithm can effectively achieve complete tracking of the trajectory, the premise is that the system must meet the strict repetitive requirements. The system can iterate infinitely without input saturation. The tracking problem in the presence of input saturation in the fractional-order tracking control system is not solved. Summary of the invention

[0004] In order to solve the above problems, the present invention proposes a trajectory control method and system for a mobile device based on anti-input saturation. The present invention solves the tracking problem in a fractional-order tracking control system under input saturation during the control process of the mobile device.

[0005] In order to achieve the above object, the present invention is implemented through the following technical solutions:

[0006] In a first aspect, the present invention provides a trajectory control method for a mobile device based on anti-input saturation, comprising:

[0007] obtaining a desired trajectory of a mobile device;

[0008] According to the acquired desired trajectory and the preset trajectory control model, the dynamic trajectory of the mobile device is obtained;

[0009] Among them, the trajectory control model is a fractional-order iterative learning control model including an input saturation function; in the fractional-order iterative learning control model, the control quantity of the dynamic model of the fractional-order trajectory tracking system in the current iteration is equal to the product of the gain matrix and the tracking error and the sum of the input saturation function; the saturation function includes the control quantity of the dynamic model of the fractional-order trajectory tracking system for the next iteration after the current one, and the input saturation quantity of the control quantity; the tracking error is the difference between the dynamic trajectory and the expected trajectory.

[0010] Furthermore, the control objective of the trajectory control module is to make the tracking error zero through iterative calculation.

[0011] Furthermore, the dynamic model of the fractional-order trajectory tracking system is:

[0012] D α x k (s) = g(x k ,t)+A(x(t),t)sat(u k (t),u k *);

[0013] Among them, D α x k (s) is the α-order derivative defined by Caputo, where α∈[0,1] is the order; A(x(t), t)∈R n×m , g(x k ,t) is an uncertain function, which is differentiable everywhere, A(x(t),t) is the input perturbation matrix, x, t are variables; it satisfies |g(x1,t)-g(x2,t)|≤L|x1-x2|, L is the Lipschitz constant; sat(u k (t),u k *) is a saturation function.

[0014] Furthermore, the expected trajectory is an expected trajectory in an expected trajectory model, and the expected trajectory model is:

[0015]

[0016] Among them, D α x k (s) is the α-order derivative defined by Caputo, where α∈[0,1] is the order; g(x d ,t) is an uncertain function, g(x d ,t) is differentiable everywhere and satisfies the Lipschitz condition; u d (t) is the expected input of the system; x d (t) is the desired state of the system; is a saturation function.

[0017] Furthermore, in the initial state, the expected trajectory and the dynamic trajectory are both zero.

[0018] In a second aspect, the present invention further provides a mobile device, which adopts the trajectory control method of the mobile device based on anti-input saturation as described in the first aspect.

[0019] Furthermore, the mobile device is a robot.

[0020] In a third aspect, the present invention further provides a trajectory control system for a mobile device based on anti-input saturation, comprising:

[0021] The data acquisition module is configured to: obtain a desired trajectory of the mobile device;

[0022] The control module is configured to: obtain a dynamic trajectory of the mobile device according to the acquired desired trajectory and a preset trajectory control model;

[0023] Among them, the trajectory control model is a fractional-order iterative learning control model including an input saturation function; in the fractional-order iterative learning control model, the control quantity of the dynamic model of the fractional-order trajectory tracking system for the current iteration is equal to the product of the gain matrix and the tracking error and the sum of the input saturation function; the saturation function includes the control quantity of the dynamic model of the fractional-order trajectory tracking system for the next iteration after the current one, and the input saturation quantity of the control quantity; the tracking error is the difference between the dynamic trajectory and the expected trajectory, and the control objective of the trajectory control model is to make the tracking error zero.

[0024] In a fourth aspect, the present invention further provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the trajectory control method for a mobile device based on anti-input saturation as described in the first aspect.

[0025] In a fifth aspect, the present invention further provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the steps of the trajectory control method for a mobile device based on anti-input saturation are implemented as described in the first aspect.

[0026] Compared with the prior art, the present invention has the following beneficial effects:

[0027] In the present invention, when a mobile device is controlled using a fractional-order calculus control system, the system input saturation limitation can be eliminated on the basis of ensuring consistency in the entire tracking process after a certain number of iterations. By setting an input saturation function in the controller, the tracking problem in the fractional-order tracking control system under input saturation conditions is solved. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] The drawings in the specification that constitute a part of this embodiment are used to provide a further understanding of this embodiment. The schematic embodiments of this embodiment and their descriptions are used to explain this embodiment and do not constitute improper limitations on this embodiment.

[0029] Figure 1 This is a flow chart of Embodiment 1 of the present invention;

[0030] Figure 2 This is a schematic diagram of the structure of the system in Example 1 of the present invention;

[0031] Figure 3is a system error convergence diagram of the fractional-order iterative learning controller when there is no input saturation in Example 1 of the present invention;

[0032] Figure 4 This is a tracking simulation result diagram of the fractional-order anti-input saturation fractional-order iterative learning trajectory tracking control method of Example 1 of the present invention

[0033] Figure 5 This is a diagram of error convergence simulation results of the fractional-order anti-input saturation fractional-order iterative learning trajectory tracking control method of Example 1 of the present invention. DETAILED DESCRIPTION

[0034] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0035] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present application belongs.

[0036] Embodiment 1:

[0037] like Figure 1 As shown, this embodiment provides a trajectory control method for a mobile device based on anti-input saturation, including:

[0038] obtaining a desired trajectory of a mobile device;

[0039] According to the acquired desired trajectory and the preset trajectory control model, the dynamic trajectory of the mobile device is obtained;

[0040] Among them, the trajectory control model is a fractional-order iterative learning control model including an input saturation function; in the fractional-order iterative learning control model, the control amount of the dynamic model of the fractional-order trajectory tracking system at the current iteration is equal to the product of the gain matrix and the tracking error and the sum of the input saturation function; the saturation function includes the control amount of the dynamic model of the fractional-order trajectory tracking system for the next iteration after the current one, and the input saturation amount of the control amount; the tracking error is the difference between the dynamic trajectory and the expected trajectory

[0041] In this embodiment, the trajectory control model can be understood as a controller, and the controller can be:

[0042]

[0043] Where sat(.) represents the input saturation function, Φ is the gain matrix of the fractional-order iterative learning controller, such that k∈N + is the number of iterations; α∈[0,1] is the α-order derivative defined by Caputo; u k(t) is the control variable of the kth iteration of the dynamic model of the fractional-order trajectory tracking system with input saturation, u k-1 (t) is the control quantity of the k-1th iteration of the dynamic model of the fractional-order trajectory tracking system with input saturation; u*(t) represents the input saturation of the control quantity; e k (t) = y d (t)-y k (t) is the tracking error, which is the difference between the output dynamic trajectory of the dynamic model of the fractional-order trajectory tracking system with input saturation and the expected trajectory in the expected trajectory model, y d (t) is the expected trajectory, y k (t) Dynamic trajectory.

[0044] Analysis of complex tracking trajectories can form a nonlinear uncertain dynamic system with multiple inputs and outputs:

[0045] D α x k (s) = g(x k ,t)+A(x(t),t)sat(u k (t),u k *) (1)

[0046] Among them, D α x k (s) is the α-order derivative under Caputo’s definition, where α∈[0,1] is the order; A(x(t),t)∈R n×m , g(x k ,t) is an uncertain function, which is differentiable everywhere, A(x(t),t) is the input perturbation matrix, x, t are variables; it satisfies |g(x1,t)-g(x2,t)|≤L|x1-x2|, L is the Lipschitz constant; sat(u k (t),u k *) is a saturation function and is defined as:

[0047]

[0048] Define the trajectory of a fractional calculus system that transforms a complex known path into a desired trajectory model, and then design a dynamic system to track the trajectory. The desired trajectory is defined as:

[0049]

[0050] Among them, α∈[0,1] is the α-order derivative defined by Caputo; g(x d ,t) is differentiable almost everywhere, g(x d ,t) is an uncertain function and satisfies the Lipschitz condition, u d(t) is the expected input of the system, x d (t) is the desired state of the system.

[0051] In this embodiment, for the nonlinear uncertain dynamic system (1), a fractional-order iterative learning controller with resistance to input saturation is designed so that the output of the system (1) can track the expected trajectory of the system (3).

[0052] The implementation process of the controller is:

[0053] S1. Define the fractional-order Lyaponov function

[0054]

[0055] For a system with input saturation, t∈[0,T], a fractional-order iterative learning controller with anti-input saturation is designed so that V k (t)>0, k=1,2,…,N, the control problem of fractional-order path tracking is transformed into the stability control problem of the tracking error system in the time interval t∈[0,T]; λ is a positive real number, T is the matrix transpose, is the Caputo fractional integral, δu k =u d -u k .

[0056] S2. The controller can be designed as:

[0057]

[0058] The controller relies on the input and output information of systems (1) and (3); the controller's gain matrix does not require information of the path tracking dynamic model.

[0059] S3. Analysis of convergence conditions for achieving output consistency in input saturated fractional-order tracking systems;

[0060] To make the system converge Convergence condition satisfies Δe k (t) = e k+1 (t)-e k (t)<0, we can obtain that there exists a Lyaponov function V k (t)>0, Thus, the convergence range of the controller can be obtained:

[0061] This embodiment provides a convergence condition that can ensure output consistency of a fractional-order tracking system based on Lyapunov theory.

[0062] S4, solving the initial state learning matrix and iterative learning gain matrix;

[0063] Assuming that the initial state learning matrix is ​​consistent with the expected initial value, the gain matrix Φ is designed to satisfy V k (t)>0, k=1,2,…,N holds true, thus obtaining a controller that satisfies the convergence condition.

[0064] When designing the gain matrix in the anti-input saturation fractional-order iterative learning controller, MATLAB and other software can be used to verify whether the convergence conditions are met; thereby verifying the controller's ability to repair the input saturation system.

[0065] In order to verify the system and controller in this embodiment, this embodiment carried out a simulation experiment, specifically:

[0066] In the complex trajectory tracking process of the robot with input saturation, the expected trajectory y d (t) = sin(3πt), the initial state is x k (0) = x d (0) = 0, t∈[0,2π]. In order to track the desired trajectory of the wheeled robot more accurately, the multi-input and multi-output nonlinear uncertain dynamic tracking system is defined as follows based on the input and output information of the robot's running trajectory:

[0067] D α x k (s) = 3xsin(t) + sat(u k (t),5.7)

[0068] The designed frequency domain iterative learning controller is

[0069]

[0070] Define the system output error as |e k (t)|, Figure 2 It is the system error convergence diagram of the fractional-order iterative learning controller when there is no input saturation;

[0071] According to the known information, the Lyaponov function V k (t)>0, Available Satisfy the convergence condition.

[0072] Figure 3 This is a tracking simulation result diagram of the fractional-order anti-input saturation fractional-order iterative learning trajectory tracking control method; Figure 4 This is a diagram of error convergence simulation results of the fractional-order anti-input saturation fractional-order iterative learning trajectory tracking control method provided in an embodiment of the present disclosure.

[0073] Based on the method of this embodiment, a fractional-order tracking system based on anti-input saturation can also be provided, including a controller, an input device and a moving device, and the controller can be a fractional-order iterative learning controller.

[0074] The mobile device is connected to the controller, and the controller is configured to track the desired trajectory of the mobile device. The mobile device can be a vehicle, an aircraft, or a robot, as long as it meets the requirements of the mobile device connected to the controller in this embodiment.

[0075] Embodiment 2:

[0076] This embodiment provides a mobile device, which adopts the trajectory control method of the mobile device based on anti-input saturation as described in Embodiment 1; the mobile device may be a robot.

[0077] Embodiment 3:

[0078] This embodiment provides a trajectory control system for a mobile device based on anti-input saturation, including:

[0079] The data acquisition module is configured to: obtain a desired trajectory of the mobile device;

[0080] The control module is configured to: obtain a dynamic trajectory of the mobile device according to the acquired desired trajectory and a preset trajectory control model;

[0081] Among them, the trajectory control model is a fractional-order iterative learning control model including an input saturation function; in the fractional-order iterative learning control model, the control quantity of the dynamic model of the fractional-order trajectory tracking system for the current iteration is equal to the product of the gain matrix and the tracking error and the sum of the input saturation function; the saturation function includes the control quantity of the dynamic model of the fractional-order trajectory tracking system for the next iteration after the current one, and the input saturation quantity of the control quantity; the tracking error is the difference between the dynamic trajectory and the expected trajectory, and the control objective of the trajectory control model is to make the tracking error zero.

[0082] The working method of the system is the same as the trajectory control method of the mobile device based on anti-input saturation in Example 1, and will not be repeated here.

[0083] Embodiment 4:

[0084] This embodiment provides a computer-readable storage medium on which a computer program is stored. When the program is executed by a processor, the steps of the trajectory control method of a mobile device based on anti-input saturation are implemented as described in Embodiment 1.

[0085] Embodiment 5:

[0086] This embodiment provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps of the trajectory control method for a mobile device based on anti-input saturation are implemented as described in Embodiment 1.

[0087] The above description is only a preferred embodiment of the present embodiment and is not intended to limit the present embodiment. For those skilled in the art, the present embodiment may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present embodiment shall be included in the protection scope of the present embodiment.

Claims

1. A trajectory control method for a mobile device based on anti-input saturation, characterized in that: include: obtaining a desired trajectory of a mobile device; According to the acquired desired trajectory and the preset trajectory control model, the dynamic trajectory of the mobile device is obtained; Wherein, the trajectory control model is a fractional-order iterative learning control model including an input saturation function; in the fractional-order iterative learning control model, the control amount of the dynamic model of the fractional-order trajectory tracking system at the current iteration is equal to the product of the gain matrix and the tracking error and the sum of the input saturation function; the saturation function includes the control amount of the dynamic model of the fractional-order trajectory tracking system for the next iteration after the current one, and the input saturation amount of the control amount; the tracking error is the difference between the dynamic trajectory and the desired trajectory; The dynamic model of the fractional-order trajectory tracking system is: D α x k (s)=g(x k ,t)+A(x(t),t)sat(u k (t),u k *); Among them, D α x k (s) is the α-order derivative under Caputo’s definition, where α∈[0,1] is the order; A(x(t),t)∈R n×m ,g(x k ,t) is an uncertain function, differentiable everywhere, A(x(t),t) is the input perturbation matrix, x, t are variables; satisfies g(x1,t)-g(x2,t)|≤Lx1-x2|, L is the Lipschitz constant; sat(u k (t),u k *) is the saturation function; The expected trajectory is the expected trajectory in the expected trajectory model, and the expected trajectory model is: Among them, α∈[0,1] is the α-order derivative defined by Caputo; g(x d ,t) is an uncertain function, which is differentiable almost everywhere and satisfies the Lipschitz condition, u d (t) is the expected input of the system, x d (t) is the desired state of the system.

2. The trajectory control method of a mobile device based on anti-input saturation as claimed in claim 1, characterized in that: The control objective of the trajectory control module is to make the tracking error zero through iterative calculation.

3. The trajectory control method of a mobile device based on anti-input saturation as claimed in claim 1, characterized in that: In the initial state, the desired trajectory and the dynamic trajectory are both zero.

4. A mobile device, characterized in that The trajectory control method of a mobile device based on anti-input saturation as described in any one of claims 1 to 3 is adopted.

5. The mobile device according to claim 4, wherein: The mobile device is a robot.

6. A trajectory control system for a mobile device based on anti-input saturation, characterized in that: include: The data acquisition module is configured to: obtain a desired trajectory of the mobile device; The control module is configured to: obtain a dynamic trajectory of the mobile device according to the acquired desired trajectory and a preset trajectory control model; Wherein, the trajectory control model is a fractional-order iterative learning control model including an input saturation function; in the fractional-order iterative learning control model, the control amount of the dynamic model of the fractional-order trajectory tracking system at the current iteration is equal to the product of the gain matrix and the tracking error and the sum of the input saturation function; the saturation function includes the control amount of the dynamic model of the fractional-order trajectory tracking system for the next iteration after the current one, and the input saturation amount of the control amount; the tracking error is the difference between the dynamic trajectory and the desired trajectory, and the control objective of the trajectory control model is to make the tracking error zero; The dynamic model of the fractional-order trajectory tracking system is: D α x k (s)=g(x k ,t)+A(x(t),t)sat(u k (t),u k *); Among them, D α x k (s) is the α-order derivative under Caputo’s definition, where α∈[0,1] is the order; A(x(t),t)∈R n×m ,g(x k ,t) is an uncertain function, differentiable everywhere, A(x(t),t) is the input perturbation matrix, x, t are variables; satisfies g(x1,t)-g(x2,t)|≤L|x1-x2|, L is the Lipschitz constant; sat(u k (t),u k *) is the saturation function; The expected trajectory is the expected trajectory in the expected trajectory model, and the expected trajectory model is: Among them, α∈[0,1] is the α-order derivative defined by Caputo; g(x d ,t) is an uncertain function, which is differentiable almost everywhere and satisfies the Lipschitz condition, u d (t) is the expected input of the system, x d (t) is the desired state of the system.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the trajectory control method of a mobile device based on anti-input saturation are implemented as described in any one of claims 1 to 3.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the steps of the trajectory control method of a mobile device based on anti-input saturation are implemented as described in any one of claims 1 to 3.

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