A mobile robot predefined time obstacle avoidance tracking control method and system

Abstract

The application discloses a kind of mobile robot predefined time obstacle avoidance tracking control method and system, method includes: the mobile robot control model with unknown nonlinear dynamics and external disturbance is constructed;Establish artificial potential field function containing minimum safety distance and obstacle avoidance detection range;Unknown nonlinear dynamics in the control model is approximated using fuzzy logic system, and system coordinate transformation is given, on this basis, establish Lyapunov function;Under the framework of backstepping recursion method, combined with dynamic surface control technology, construct predefined time filter;Design the adaptive law of mobile robot and predefined time obstacle avoidance controller.The present application is aimed at the problems such as unconstrained convergence time, difficult to balance obstacle avoidance and tracking of existing method, design predefined time filter and obstacle avoidance controller, with the improved artificial potential field function containing key parameters, dynamically adjust control parameters through adaptive law, realize the predefined time convergence of mobile robot system, collision-free accurate tracking.

Description

Technical Field

[0001] This invention belongs to the field of fuzzy adaptive control for mobile robots, and specifically relates to a predefined time obstacle avoidance tracking control method and system for mobile robots. Background Technology

[0002] In recent years, with the rapid development of industrial automation, intelligent logistics, and service robots, autonomous navigation and trajectory tracking control technologies for mobile robots have become a core support for promoting intelligent upgrades. Among them, the Mecanum wheeled omnidirectional mobile robot, with its flexible omnidirectional motion capabilities, can achieve complex movements such as translation and rotation in confined spaces and has been widely used in scenarios such as warehousing and handling, industrial assembly, and unmanned delivery. Its obstacle avoidance and tracking control performance directly determines operational efficiency and safety.

[0003] The core objective of predefined time-based obstacle avoidance tracking control for mobile robots is to enable the robot to accurately track a pre-set desired trajectory and avoid static or dynamic obstacles in real time within complex dynamic environments, while completing the control task within a pre-set fixed time to meet high-efficiency operational requirements. Currently, mainstream control methods in this field include PID control, model predictive control, and adaptive control. While these methods have achieved certain results in specific scenarios, they still face many challenges in practical applications.

[0004] First, most existing obstacle avoidance and tracking control methods do not strictly constrain the system convergence time. The control response speed depends on system parameter tuning and environmental complexity, making it difficult to guarantee that the robot can stably complete trajectory tracking and obstacle avoidance tasks within a preset fixed time. In scenarios with high time requirements, such as industrial assembly lines and emergency rescue, this uncertainty can seriously affect the continuity and reliability of the work process.

[0005] Second, the artificial potential field function used in some obstacle avoidance algorithms is not well designed and has insufficient adaptability to the minimum safe distance and obstacle avoidance detection range. It is prone to local minima traps or excessive obstacle avoidance leading to excessive trajectory deviation, making it difficult to balance obstacle avoidance safety and tracking accuracy. Summary of the Invention

[0006] To address the problems existing in the prior art, the purpose of this invention is to provide a predefined time obstacle avoidance and tracking control method and system for mobile robots. This method and system ensures that the controlled system can stably converge within a pre-set fixed time by constructing a predefined time filter and an adaptive controller. Simultaneously, by combining an artificial potential field function that includes the minimum safe distance and obstacle detection range, it enables the mobile robot to safely avoid obstacles and accurately track its trajectory in complex environments. Furthermore, this function is always continuously differentiable, thereby avoiding local minima.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] A predefined time-based obstacle avoidance tracking control method for a mobile robot includes the following steps:

[0009] Construct a control model for a mobile robot with unknown nonlinear dynamics and external disturbances;

[0010] Based on the mobile robot control model, an artificial potential field function including minimum safe distance and obstacle avoidance detection range is established;

[0011] The unknown nonlinear dynamics in the control model are approximated using a fuzzy logic system, and the system coordinate transformation is given. Based on this, a Lyapunov function is established.

[0012] Within the framework of the backstepping recursive method, a predefined time filter is constructed by combining dynamic surface control technology;

[0013] Based on the Lyapunov function and the predefined time filter, an adaptive law and a predefined time obstacle avoidance controller for the mobile robot are designed.

[0014] Furthermore, the mobile robot control model is constructed as follows:

[0015]

[0016] in, Represents the pose state of the mobile robot;

[0017] This represents the speed status of the mobile robot;

[0018] and These represent the mobile robot in the Earth coordinate system. shaft and Coordinate values ​​on the axis;

[0019] Represents the robot coordinate system Positive axis direction and Earth coordinate system The angle between the positive axis and the axis;

[0020] Represents system input;

[0021] These represent the inputs, or control torques, of the four wheels of the mobile robot.

[0022] Represents system output;

[0023] and Represents unknown nonlinear dynamics;

[0024] This represents a known control input gain matrix;

[0025] This represents the known nonlinear dynamics inherent in mobile robots themselves;

[0026] and This represents external interference;

[0027] Will , , and Abbreviated as , , and .

[0028] Furthermore, the artificial potential field function that includes the minimum safe distance and obstacle avoidance detection range is:

[0029]

[0030] This represents the collision-free distance error. Indicates the location of the obstacle;

[0031] and These represent the obstacle avoidance detection range and the minimum safe distance, respectively.

[0032] Taking the partial derivative of the artificial potential field function, we get:

[0033] .

[0034] Furthermore, the coordinate transformation is defined as follows:

[0035]

[0036] in, Represents tracking error. Represents the expected trajectory;

[0037] Represents virtual error. Represents the output of the filter;

[0038] Represents filtering error. Represents a virtual control law;

[0039] First construction of Lyapunov functions:

[0040]

[0041] in, It is an ideal adjustment scalar Its estimated value The estimation error;

[0042] Second construction of the Lyapunov function:

[0043]

[0044] in, It is an ideal adjustment scalar Its estimated value The estimation error.

[0045] Furthermore, the predefined time filter is constructed as follows:

[0046]

[0047] in, It is a design parameter;

[0048] and These are design parameters;

[0049] These are filter design parameters;

[0050] This is the predetermined convergence time;

[0051] It is a positive design parameter;

[0052] and These represent the initial values ​​of the predefined time filter and the virtual control law, respectively.

[0053] Furthermore, the adaptive law includes the first adaptive law and the second adaptive law;

[0054] The first adaptive law constructed is as follows:

[0055]

[0056] in, , Design parameters;

[0057] It is the output vector of the fuzzy logic system;

[0058] The second adaptive law is as follows:

[0059]

[0060] in, It is the output vector of the fuzzy logic system;

[0061] Based on the above, the virtual control law is obtained. and predefined time obstacle avoidance controller as follows:

[0062]

[0063] in, and These are positive design parameters. It is the first derivative of the reference signal;

[0064] Represents a set of obstacles;

[0065]

[0066] in, It is the control input gain matrix The false reversal;

[0067] These are positive design parameters.

[0068] Furthermore, the mobile robot is a Mecanum wheeled omnidirectional mobile robot.

[0069] The present invention also provides a predefined time obstacle avoidance tracking control system for mobile robots, for implementing the method, comprising:

[0070] The model construction module is used to construct a control model for a mobile robot with unknown nonlinear dynamics and external disturbances.

[0071] The potential field function establishment module is used to establish an artificial potential field function that includes the minimum safe distance and obstacle avoidance detection range;

[0072] The fuzzy approximation and coordinate transformation module is used to approximate unknown nonlinear dynamics using fuzzy logic systems and provide system coordinate transformations. Based on this, Lyapunov functions are established.

[0073] The filter construction module is used to construct predefined time filters within the framework of the backstepping recursion method, combined with dynamic surface control techniques.

[0074] The controller design module is used to design adaptive laws and predefined time-based obstacle avoidance controllers for mobile robots.

[0075] The present invention also provides a mobile robot comprising the aforementioned control system.

[0076] The mobile robot completes the tracking of the desired trajectory within a preset fixed time, and the distance between it and obstacles is always greater than the minimum safe distance during operation; the position state error and velocity state error of the mobile robot in the X direction, as well as the position state error and velocity state error in the Y direction, all converge to a stable state within the preset fixed time.

[0077] Beneficial effects: Compared with the prior art, the present invention has the following beneficial effects:

[0078] First, most existing obstacle avoidance and tracking control methods for mobile robots do not explicitly constrain the convergence time, and it is difficult to balance obstacle avoidance and tracking performance. This invention designs a predefined time filter and a predefined time obstacle avoidance controller. By reasonably selecting design parameters, it ensures stable convergence of the system within a preset fixed time. Simultaneously, it constructs an improved artificial potential field function that includes a minimum safe distance and obstacle detection range, effectively balancing obstacle avoidance safety and trajectory tracking accuracy, enabling collision-free and accurate tracking of the mobile robot in complex environments.

[0079] Secondly, the artificial potential field function used in some existing obstacle avoidance algorithms still has shortcomings in design. Their adaptability to the minimum safe distance and obstacle detection range is poor, easily leading to local minima traps or causing significant trajectory deviations due to excessive obstacle avoidance, making it difficult to balance obstacle avoidance safety and trajectory tracking accuracy. This invention designs a continuously differentiable improved artificial potential field function, ensuring that the function remains continuously differentiable after the mobile robot enters the obstacle detection range. This fundamentally avoids the local minima problem, effectively improving the obstacle avoidance safety of the mobile robot system while simultaneously guaranteeing trajectory tracking accuracy, achieving a dual optimization of obstacle avoidance safety and tracking accuracy. Attached Figure Description

[0080] Figure 1 This is a roadmap of the overall technology for predefined time-based obstacle avoidance and tracking control methods for mobile robots.

[0081] Figure 2 It is a map of the mobile robot's trajectory;

[0082] Figure 3 This is a graph showing the positional error in the X direction.

[0083] Figure 4 This is a graph showing the velocity state error in the X direction;

[0084] Figure 5 This is a curve showing the positional error in the Y direction.

[0085] Figure 6 This is a graph showing the velocity state error in the Y direction;

[0086] Figure 7 This is a graph showing the tracking error in the X direction;

[0087] Figure 8 This is a tracking error curve in the Y direction;

[0088] Figure 9 It is an input state curve graph. Detailed Implementation

[0089] The invention will now be further explained with reference to the accompanying drawings.

[0090] This invention proposes a predefined-time obstacle avoidance tracking control method for mobile robots within the framework of Lyapunov's stability law. Control is achieved through a predefined-time obstacle avoidance controller. The controller's development process includes constructing a mobile robot control model with unknown nonlinear dynamics and external disturbances, establishing an artificial potential field function, establishing a Lyapunov function, constructing a predefined-time filter, designing the mobile robot's adaptive law, and establishing the predefined-time obstacle avoidance controller. Under this control strategy, the system achieves predefined-time stability and ensures that the mobile robot accurately tracks the reference trajectory without collisions during operation.

[0091] First, a Mecanum wheeled omnidirectional mobile robot is selected as the controlled object. A dynamic model with unknown nonlinear dynamics and external disturbances is established. By analyzing this dynamic model, a hysteresis quantizer is constructed to quantize the continuous input signal into a discrete signal. An improved artificial potential field function is then constructed to achieve collision-free operation between the mobile robot and environmental obstacles. Within the framework of the backstepping recursive method, a fuzzy logic system is used to approximate the unknown nonlinear dynamics, thereby establishing a Lyapunov function. Combined with dynamic surface control technology, a predefined time filter is constructed. Based on the above work, the adaptive law of the mobile robot and a predefined time obstacle avoidance controller are obtained.

[0092] The overall technical roadmap of the mobile robot predefined time obstacle avoidance tracking control method involved in this invention is as follows: Figure 1 As shown. In some preferred embodiments, a mobile robot predefined time obstacle avoidance tracking control method of the present invention includes the following steps:

[0093] Step 1: Construct a control model for a mobile robot with unknown nonlinear dynamics and external disturbances.

[0094] The mobile robot control model considers the non-ideal states of the robot's actual operating scenario, namely, the existence of unknown nonlinear dynamics and external disturbances. The mobile robot control model is constructed as follows:

[0095]

[0096] in, Represents the pose state of the mobile robot;

[0097] This represents the speed status of the mobile robot;

[0098] and These represent the mobile robot in the Earth coordinate system. shaft and Coordinate values ​​on the axis;

[0099] Represents the robot coordinate system Positive axis direction and Earth coordinate system The angle between the positive axis and the axis;

[0100] Represents system input;

[0101] These represent the inputs, or control torques, of the four wheels of the mobile robot.

[0102] Represents system output;

[0103] and Represents unknown nonlinear dynamics;

[0104] This represents a known control input gain matrix;

[0105] This represents the known nonlinear dynamics inherent in mobile robots themselves;

[0106] and This represents external interference.

[0107] For ease of subsequent description, , , and Abbreviated as , , and .

[0108] Step 2: Based on the mobile robot control model, establish an artificial potential field function that includes the minimum safe distance and obstacle avoidance detection range.

[0109] The artificial potential field function remains continuously differentiable when the mobile robot enters the detection range:

[0110]

[0111] This represents the collision-free distance error. Indicates the location of the obstacle;

[0112] and These represent the obstacle avoidance detection range and the minimum safe distance, respectively.

[0113] Taking the partial derivative of the artificial potential function, we get:

[0114]

[0115] Step 3: Use a fuzzy logic system to approximate the unknown nonlinear dynamics in the control model and give the system coordinate transformation. Based on this, establish the Lyapunov function.

[0116] Define coordinate transformations, and for a second-order mobile robot model, only two Lyapunov functions need to be constructed.

[0117] The coordinate transformation is defined as follows:

[0118]

[0119] in, Represents tracking error. Represents the expected trajectory;

[0120] Represents virtual error. Represents the output of the filter;

[0121] Represents filtering error. This represents a virtual control law.

[0122] First construction of Lyapunov functions:

[0123]

[0124] in, It is an ideal adjustment scalar Its estimated value The estimation error.

[0125] Second construction of the Lyapunov function:

[0126]

[0127] in, It is an ideal adjustment scalar Its estimated value The estimation error.

[0128] Step 4: Within the framework of the backstepping recursion method, a predefined time filter is constructed by combining dynamic surface control technology.

[0129] The predefined time filters are as follows:

[0130]

[0131] in, It is a design parameter;

[0132] and These are design parameters;

[0133] These are filter design parameters;

[0134] This is the predetermined convergence time;

[0135] It is a positive design parameter;

[0136] and These represent the initial values ​​of the predefined time filter and the virtual control law, respectively.

[0137] Step 5: Based on the Lyapunov function and the predefined time filter, design the adaptive law of the mobile robot and the predefined time obstacle avoidance controller.

[0138] The first adaptive law constructed is as follows:

[0139]

[0140] in, , Design parameters;

[0141] It is the output vector of the fuzzy logic system.

[0142] The second adaptive law is as follows:

[0143]

[0144] in, It is the output vector of the fuzzy logic system.

[0145] Based on the above work, the virtual control law can be further obtained. and predefined time obstacle avoidance controller as follows:

[0146]

[0147] in, and These are positive design parameters. It is the first derivative of the reference signal;

[0148] Represents a set of obstacles.

[0149]

[0150] in, It is the control input gain matrix The false reversal;

[0151] These are positive design parameters.

[0152] Simulation results are as follows Figure 2-9 As shown. Figure 2 The mobile robot's trajectory was displayed; Figure 3 The effect of position and state tracking of the mobile robot in the X direction is shown; Figure 4 The robot's velocity state tracking effect in the X direction is shown; Figure 5 The robot's position tracking effect in the Y direction is shown; Figure 6 The robot's velocity state tracking effect in the Y direction is shown; Figure 7 The output tracking effect of the mobile robot in the X direction is shown; Figure 8 The output tracking effect of the mobile robot in the Y direction is shown; Figure 9 The input state curve of the mobile robot is displayed.

[0153] As can be seen from the simulation results above, the mobile robot can complete the tracking task within a preset fixed time and achieve collision-free operation between the mobile robot and environmental obstacles. The input state of the mobile robot stabilizes within the predefined time, and the tracking errors of the mobile robot's position and velocity states in the X and Y directions, as well as the overall output state, all stabilize within the predefined time. This achieves the expected predefined time obstacle avoidance tracking control effect, demonstrating the effectiveness of the predefined time obstacle avoidance controller designed in this invention.

[0154] Based on the above control method, the present invention also provides a predefined time obstacle avoidance and tracking control system for a mobile robot, comprising:

[0155] The model construction module is used to construct a control model for a mobile robot with unknown nonlinear dynamics and external disturbances.

[0156] The potential field function establishment module is used to establish an artificial potential field function that includes the minimum safe distance and obstacle avoidance detection range;

[0157] The fuzzy approximation and coordinate transformation module is used to approximate unknown nonlinear dynamics using fuzzy logic systems and provide system coordinate transformations. Based on this, Lyapunov functions are established.

[0158] The filter construction module is used to construct predefined time filters within the framework of the backstepping recursion method, combined with dynamic surface control techniques.

[0159] The controller design module is used to design adaptive laws and predefined time-based obstacle avoidance controllers for mobile robots.

[0160] This control system can be integrated into the controller of a mobile robot, enabling the mobile robot to complete the tracking of the desired trajectory within a preset fixed time, and ensuring that the distance between the mobile robot and obstacles is always greater than the minimum safe distance during operation; at the same time, the position state error and velocity state error of the mobile robot in the X direction, as well as the position state error and velocity state error in the Y direction, all converge to a stable state within the preset fixed time.

[0161] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A predefined time obstacle avoidance tracking control method for a mobile robot, characterized in that: Includes the following steps: Construct a control model for a mobile robot with unknown nonlinear dynamics and external disturbances; Based on the mobile robot control model, an artificial potential field function including minimum safe distance and obstacle avoidance detection range is established; The unknown nonlinear dynamics in the control model are approximated using a fuzzy logic system, and the system coordinate transformation is given. Based on this, a Lyapunov function is established. Within the framework of the backstepping recursive method, a predefined time filter is constructed by combining dynamic surface control technology; Based on the Lyapunov function and the predefined time filter, an adaptive law and a predefined time obstacle avoidance controller for the mobile robot are designed.

2. The method according to claim 1, characterized in that: The mobile robot control model is constructed as follows: in, Represents the pose state of the mobile robot; This represents the speed status of the mobile robot; and These represent the mobile robot in the Earth coordinate system. shaft and Coordinate values ​​on the axis; Represents the robot coordinate system Positive axis direction and Earth coordinate system The angle between the positive axis and the axis; Represents system input; These represent the inputs, or control torques, of the four wheels of the mobile robot. Represents system output; and Represents unknown nonlinear dynamics; This represents a known control input gain matrix; This represents the known nonlinear dynamics inherent in mobile robots themselves; and This represents external interference; Will , , and Abbreviated as , , and .

3. The method according to claim 2, characterized in that: The artificial potential field function, which includes the minimum safe distance and obstacle avoidance detection range, is: This represents the collision-free distance error. Indicates the location of the obstacle; and These represent the obstacle avoidance detection range and the minimum safe distance, respectively. Taking the partial derivative of the artificial potential field function, we get: 。 4. The method according to claim 3, characterized in that: The coordinate transformation is defined as follows: in, Represents tracking error. Represents the expected trajectory; Represents virtual error. Represents the output of the filter; Represents filtering error. Represents a virtual control law; First construction of Lyapunov functions: in, It is an ideal adjustment scalar Its estimated value The estimation error; Second construction of the Lyapunov function: in, It is an ideal adjustment scalar Its estimated value The estimation error.

5. The method according to claim 4, characterized in that: The predefined time filter is constructed as follows: in, It is a design parameter; and These are design parameters; These are filter design parameters; This is the predetermined convergence time; It is a positive design parameter; and These represent the initial values ​​of the predefined time filter and the virtual control law, respectively.

6. The method according to claim 5, characterized in that: The adaptive law includes the first adaptive law and the second adaptive law. The first adaptive law constructed is as follows: in, , Design parameters; It is the output vector of the fuzzy logic system; The second adaptive law is as follows: in, It is the output vector of the fuzzy logic system; Based on the above, the virtual control law is obtained. and predefined time obstacle avoidance controller as follows: in, and These are positive design parameters. It is the first derivative of the reference signal; Represents a set of obstacles; in, It is the control input gain matrix The false reversal; These are positive design parameters.

7. The method according to any one of claims 1-6, characterized in that: The mobile robot in question is a Mecanum wheeled omnidirectional mobile robot.

8. A predefined time obstacle avoidance tracking control system for a mobile robot, used to implement the method of claim 1, characterized in that: include: The model construction module is used to construct a control model for a mobile robot with unknown nonlinear dynamics and external disturbances. The potential field function establishment module is used to establish an artificial potential field function that includes the minimum safe distance and obstacle avoidance detection range; The fuzzy approximation and coordinate transformation module is used to approximate unknown nonlinear dynamics using fuzzy logic systems and provide system coordinate transformations. Based on this, Lyapunov functions are established. The filter construction module is used to construct predefined time filters within the framework of the backstepping recursion method, combined with dynamic surface control techniques. The controller design module is used to design adaptive laws and predefined time-based obstacle avoidance controllers for mobile robots.

9. A mobile robot, characterized in that: It includes the control system as described in claim 8.

10. The mobile robot according to claim 9, characterized in that: The mobile robot completes the tracking of the desired trajectory within a preset fixed time, and the distance between it and obstacles is always greater than the minimum safe distance during operation; the position state error and velocity state error of the mobile robot in the X direction, as well as the position state error and velocity state error in the Y direction, all converge to a stable state within the preset fixed time.

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