A finite time fractional order sliding mode control method and system for modular robots
By employing a finite-time fractional-order sliding mode control method, the problems of insufficient robustness and accuracy in trajectory tracking of modular quadruped robots are solved. The error is stably converged within a finite time, improving the robustness and engineering applicability of the control system. The sliding mode gain parameters are optimized to achieve globally optimal control performance.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- HEFEI UNIV OF TECH
- Filing Date
- 2026-04-20
- Publication Date
- 2026-07-24
AI Technical Summary
Modular quadruped robots exhibit weak robustness of sliding surfaces in trajectory tracking, insufficient trajectory tracking control accuracy, and slow control speed convergence. Existing sliding mode control technology cannot be compatible with unknown initial errors, and engineering deployment requires pre-calibration of the initial pose, limiting its applicability. Integer-order sliding surfaces are also less robust to model uncertainties and external disturbances.
A finite-time fractional sliding mode control method is adopted. By establishing a dynamic model of a single leg of a modular quadruped robot, a piecewise finite-time performance function is constructed. Combined with the fractional-time reaching law and an improved particle swarm optimization algorithm, the sliding mode gain parameter is optimized to achieve full-process error constraint and robustness improvement.
It achieves stable convergence of modular robot trajectory tracking error within a preset finite time, improves the engineering applicability and deployment efficiency of the control system, enhances robustness under uncertain model parameters and external disturbances, improves trajectory tracking accuracy and control smoothness, and avoids the subjectivity and inefficiency of manual trial and error.
Smart Images
Figure CN122449923A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of robot control technology, and more specifically to a finite-time fractional-order sliding mode control method and system for a modular robot. Background Technology
[0002] With the rapid development of robotics technology, modular quadruped robots, due to their superior terrain adaptability and mobility, have broad application prospects in unstructured scenarios such as industrial inspection, disaster relief, special operations, and intelligent warehousing. Compared with wheeled or tracked robots, modular quadruped robots, by coordinating the movement of multiple legs, can achieve stable walking, running, and even jumping in unstructured, rugged, and complex environments, becoming one of the important research directions in the field of robotics.
[0003] However, due to the strong nonlinearity, strong coupling, and uncertain model parameters inherent in the motion process, existing sliding mode control techniques still have many shortcomings: traditional preset performance functions cannot accommodate unknown initial errors, and initial poses need to be pre-calibrated for engineering deployment, limiting applicability; integer-order sliding modes are less robust to model uncertainties and external disturbances; conventional reaching law control lacks accuracy and easily leads to increased trajectory tracking errors. Therefore, research on finite-time fractional-order sliding mode control for modular robots is of significant research value. Summary of the Invention
[0004] The purpose of this invention is to provide a finite-time fractional-order sliding mode control method and system for modular robots, which solves the problems of weak sliding surface robustness, insufficient trajectory tracking control accuracy, and slow control speed convergence in the trajectory tracking of modular robots.
[0005] To achieve the above objectives, embodiments of the present invention provide a finite-time fractional-order sliding mode control method for a modular robot, the control method comprising: A dynamic model of a single leg of a modular quadruped robot is established, and the position tracking error and velocity error of the single leg joint are defined. Construct a piecewise finite-time performance function; The bounded tracking error constrained by the performance function is converted into an unbounded transformation error based on the transformation error method. Combining fractional-order reaching laws, a sliding mode control law with fractional-order reaching laws and specified performance in finite time is obtained based on Lyapunov stability theory; The sliding mode gain parameters of a fractional-order approach sliding mode control law with a specified performance in a finite-time period are optimized using an improved particle swarm optimization algorithm to obtain the optimal sliding mode gain parameters.
[0006] Optionally, a dynamic model of a single leg of a modular quadruped robot is established, and the position tracking error and velocity error of the single leg joint are defined, including: Construct a dynamic model based on formula (1). (1) The position tracking error of a single leg joint is defined according to formula (2). (2) According to formula (3), the velocity error of a single leg joint is defined. (3) in, For the control matrix, Let be the angular position vector of the joint. For time variables, Let be the angular acceleration of the joint. The inertia matrix, The matrix represents the Coriolis force and the centrifugal force. Let be the angular velocity of the joint. The gravity vector For joint position tracking error, This represents the desired angular position of the joint. For the speed error of the joint, The desired angular velocity of the joint.
[0007] Optionally, a piecewise finite-time performance function is constructed, including: The finite-time performance function is determined according to formula (4). (4) in, For finite-time performance functions, The performance function for the initial segment. The gain parameter of the performance function for the initial segment. This is the timeline for the initial stage. For time variables, for The convergence rate, The performance function for the finite-time convergence segment. It is a constant. For the time nodes of the finite-time convergence segment, As the initial boundary, To stabilize the boundary, For the performance function of the steady-state holding segment, This represents the position tracking error of the joint.
[0008] Optionally, the bounded tracking error constrained by the performance function is converted into an unbounded transformation error based on the transformation error method, including: The error transformation function is determined according to formula (5). (5) in, Let be the error transformation function, and .
[0009] Optionally, combining fractional-order reaching laws, a sliding mode control law with fractional-order reaching laws for specified performance in finite time is obtained based on Lyapunov stability theory, including: Construct fractional-order sliding surfaces according to formulas (6) to (9). (6) (7) (8) (9) in, For fractional-order sliding surfaces, The first derivative of a fractional sliding surface. The first derivative of the error transformation function. For the fractional derivative term of the error transformation function, For order, These are the coefficient terms of the error transformation function. Let be the first derivative of the coefficient term of the error transformation function. It is a symbolic function.
[0010] Optionally, combining fractional-order reaching laws, and based on Lyapunov stability theory, a finite-time fractional-order reaching sliding mode control law for specified performance is obtained, further comprising: The fractional-order reaching law is determined according to formula (10). (10) The fractional-order approach sliding mode control law for a given performance in finite time is obtained from formulas (11) to (13). (11) (12) (13) in, For the equivalent control matrix, It is a discontinuous control matrix. The inertia matrix, The gravity vector Let be the desired angular acceleration of the joint. These are the sliding mode gain parameters. This is the approach law index.
[0011] Optionally, the sliding mode gain parameters of the fractional-order reaching law sliding mode control law with a specified performance over a finite time are optimized using an improved particle swarm optimization algorithm to obtain the optimal sliding mode gain parameters, including: Initialize the particle swarm; Update the velocity and position of each particle; Calculate the fitness of each particle; The sliding mode gain parameter corresponding to the minimum fitness of each particle's history is selected as the optimal individual. The sliding mode gain parameter corresponding to the minimum fitness among all particles is selected as the global optimum. Determine whether the current iteration count has reached the preset iteration count; If the current iteration count reaches the preset iteration count, the global optimum is output as the optimal sliding mode gain parameter; If it is determined that the current iteration number has not reached the preset iteration number, the step is to update the velocity and position of each particle.
[0012] Optionally, the fitness of each particle is calculated, including: Construct the fitness function according to formula (14). (14) in, For the fitness function, The first weighting coefficient, For the second weighting coefficient, It is the third weighting coefficient, and , For convergence time.
[0013] Optionally, update the velocity and position of each particle, including: Update the inertia weights according to formula (15). (15) Update the particle velocity according to formula (16). (16) Update the particle's position according to formula (17). (17) in, For the updated inertia weights, This represents the maximum value of the inertia weight. This represents the maximum value of the inertia weight. The attenuation coefficient is... This represents the current iteration number. For the next iteration number, The maximum number of iterations, For the first The speed of each particle in the next iteration For the first The current iteration speed of each particle For the first The position of each particle in the next iteration. For the first The current position of each particle in the iteration. The first acceleration coefficient, The second acceleration coefficient, The first number is a random number. The second random number, For the first The best position in the history of each particle This represents the optimal position for all particles globally.
[0014] On the other hand, the present invention also provides a finite-time fractional-order sliding mode control system for a modular robot, the control system including a processor for executing the control method as described above.
[0015] Through the above technical solutions, this invention provides a finite-time fractional sliding mode control method and system for modular robots. A single-leg dynamic model is established using the Lagrange method. The constructed piecewise finite-time performance function eliminates the need for pre-calibrating the robot's initial pose, achieving full-process error constraints and ensuring stable convergence of tracking errors within a preset finite time, significantly improving the engineering applicability and deployment efficiency of the control system. The error transformation method transforms the performance-constrained tracking control problem into an unconstrained stabilization problem, reducing the difficulty of controller design and stability proof. The constructed fractional sliding surface introduces non-integer-order differential characteristics, effectively improving the system's robustness under uncertain model parameters, external disturbances, and unmodeled dynamic conditions. Furthermore, a fractional-order reaching law is used to dynamically adjust the system's approach speed, improving control smoothness and trajectory tracking accuracy while ensuring finite-time arrival at the sliding surface. Finally, an improved particle swarm optimization algorithm is introduced to achieve self-tuning of the sliding mode gain parameters, automatically optimizing based on a weighted optimum of tracking accuracy, control robustness, and convergence time, avoiding the subjectivity and inefficiency of manual trial and error, and achieving globally optimal control performance.
[0016] Other features and advantages of the embodiments of the present invention will be described in detail in the following detailed description section. Attached Figure Description
[0017] The accompanying drawings are provided to further illustrate embodiments of the present invention and form part of the specification. They are used together with the following detailed description to explain the embodiments of the present invention, but do not constitute a limitation thereof. In the drawings: Figure 1 This is a flowchart of a control method according to an embodiment of the present invention; Figure 2 This is a flowchart illustrating the construction of a dynamic model according to one embodiment of the present invention; Figure 3 This is a flowchart of obtaining a fractional-order approach sliding mode control law with a specified performance over a finite time, according to an embodiment of the present invention. Figure 4 This is a flowchart of optimizing sliding mode gain parameters according to one embodiment of the present invention; Figure 5 This is a flowchart illustrating the updating of particle velocity and position according to an embodiment of the present invention; Figure 6 This is a graph showing the tracking effect of a controller according to an embodiment of the present invention on trajectory errors; Figure 7 This is a schematic diagram of a modular quadruped robot according to one embodiment of the present invention. Detailed Implementation
[0018] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustration and explanation only and are not intended to limit the scope of the present invention.
[0019] It should be noted that the acquisition, transmission, storage, use, and processing of data in the technical solution of this application all comply with relevant laws and regulations. In the embodiments of this application, certain existing industry solutions such as software, components, and models may be mentioned. These should be considered exemplary, intended only to illustrate the feasibility of implementing the technical solution of this application, and do not imply that the applicant has already used or necessarily used such solutions.
[0020] Figure 1 This is a flowchart of a control method according to an embodiment of the present invention, in which the control method includes: In step S1, a dynamic model of a single leg of the modular quadruped robot is established, and the position tracking error and velocity error of the single leg joint are defined. In one example of the present invention, the modular quadruped robot is as follows: Figure 7 As shown.
[0021] In step S2, a piecewise finite-time performance function is constructed.
[0022] In step S3, the bounded tracking error constrained by the performance function is converted into an unbounded transformation error based on the transformation error method.
[0023] In step S4, the fractional-order reaching law is combined with the Lyapunov stability theory to obtain the finite-time specified performance fractional-order reaching sliding mode control law.
[0024] In step S5, the sliding mode gain parameters of the fractional-order approach sliding mode control law with a specified performance over a finite time are optimized according to the improved particle swarm optimization algorithm to obtain the optimal sliding mode gain parameters.
[0025] In steps S1 to S5, this invention employs a piecewise finite-time performance function, eliminating the need for pre-calibrating the robot's initial pose and achieving full-process error constraint. This ensures that the tracking error converges stably within a preset finite time, significantly improving the engineering applicability and deployment efficiency of the control system. The error transformation method transforms the performance-constrained tracking control problem into an unconstrained stabilization problem, reducing the difficulty of controller design and stability proof. The constructed fractional-order sliding surface introduces non-integer-order differential characteristics, effectively improving the system's robustness under uncertain model parameters and external disturbances. Furthermore, a fractional-order reaching law dynamically adjusts the system's approach speed, ensuring finite-time arrival at the sliding surface while improving control smoothness and trajectory tracking accuracy. Finally, an improved particle swarm optimization algorithm is introduced to achieve self-tuning of the sliding mode gain parameters. This automatically optimizes the system with a weighted optimum of tracking accuracy, chattering level, and convergence time, avoiding the subjectivity and inefficiency of manual trial and error, and achieving globally optimal control performance.
[0026] In this embodiment, the methods for establishing the dynamic model of a single leg of the modular quadruped robot can be various and known to those skilled in the art. In one example of the present invention, the Lagrange method is used to establish the dynamic model of the single leg. Specifically, the methods for establishing the dynamic model of a single leg of the modular quadruped robot can be... Figure 2 The method shown. Figure 2 The control method also includes: In step S11, a dynamic model is constructed according to formula (1). (1) In step S12, the position tracking error of a single leg joint is defined according to formula (2). (2) In step S13, the velocity error of a single leg joint is defined according to formula (3). (3) in, It is a 4×1 control matrix. Let be the angular position vector of the joint. For time variables, Let be the angular acceleration of the joint. It is a 4×4 inertia matrix. The matrix represents the 4×4 Coriolis force and centrifugal force. Let be the angular velocity of the joint. It is a 4×1 gravity vector. For joint position tracking error, This represents the desired angular position of the joint. For the speed error of the joint, The desired angular velocity of the joint. In a preferred embodiment of the invention, , , These are the desired angular positions of joints 1, 2, and 3, and the initial desired angles. .
[0027] Traditional preset performance functions cannot accommodate unknown initial errors, requiring pre-calibration of the initial pose for engineering deployment, which limits their practical applicability. To address this, this invention proposes constructing a piecewise finite-time performance function. By utilizing this function, arbitrary initial errors can be accommodated without prior knowledge of the initial position, and the convergence of the error within a specified finite time is guaranteed. In this embodiment, the method for constructing the piecewise finite-time performance function can be various as known to those skilled in the art. In a preferred example of this invention, specifically, constructing the piecewise finite-time performance function includes: The finite-time performance function is determined according to formula (4). (4) in, For finite-time performance functions, The performance function for the initial segment includes arbitrary initial tracking errors. The gain parameter of the performance function for the initial segment. This is the timeline for the initial stage. For time variables, for The convergence rate, The performance function is a finite-time convergence segment, ensuring that the tracking error is within a preset time. Convergence, It is a constant. For the time nodes of the finite-time convergence segment, As the initial boundary, To stabilize the boundary, Let be the performance function for the steady-state holding segment, and be the steady-state tracking error. This represents the position tracking error of the joint. All values are normal values preset by the user according to their needs, and they meet the continuity condition. , , The function is guaranteed to be monotonically decreasing. In one example of this invention, , , , , , , Furthermore, in this embodiment, the constrained tracking error is transformed into an unconstrained stabilization problem based on the transformation error method, simplifying the controller design. This invention transforms the original bounded error constraint... Convert to For stable control and ease of calculation, the formula for calculating the transformation error is as follows: (18) Transformation error is obtained from bounded error constraints satisfy By introducing an error transformation function to simplify the calculation, the error transformation formula is obtained after calculation as follows: The error transformation function is determined according to formula (5). (5) in, Let be the error transformation function, and .
[0028] Considering that integer-order sliding surfaces are relatively weak in robustness to model uncertainties and external disturbances, this invention enhances the system's robustness to disturbances and model uncertainties by constructing fractional-order sliding surfaces based on fractional derivative terms and error transformation functions. Specifically, as... Figure 3 As shown, it includes the following steps: In step S41, a fractional-order sliding surface is constructed according to formulas (6) to (9). (6) (7) (8) (9) in, For fractional-order sliding surfaces, The first derivative of a fractional sliding surface. The first derivative of the error transformation function. For the fractional derivative term of the error transformation function, For order, These are the coefficient terms of the error transformation function. Let be the first derivative of the coefficient term of the error transformation function. It is a symbolic function.
[0029] For controller design, the goal is to reduce the tracking error to zero. To achieve this goal and ensure the stability of the closed-loop system, the design can be based on Lyapunov stability theory, typically choosing a positive definite function related to the sliding surface as the Lyapunov function. For multi-input systems, the Lyapunov function can be defined as follows: ,in, It is a Lyapunov function. For time, Let be the sliding surface variable. According to Lyapunov's stability theorem, to ensure asymptotic stability of the system, the time derivative of this function must satisfy . ,in, In a preferred embodiment of the present invention, in step S42, the fractional-order reaching law is determined according to formula (10). (10) In step S43, the fractional-order approach sliding mode control law with specified performance over a finite time is obtained according to formulas (11) to (13). (11) (12) (13) in, This is the equivalent control matrix, used to counteract the inherent dynamic effects of the system and ensure stable sliding of the robot's single leg on the sliding surface. This is a discontinuous control matrix used to drive the system to rapidly approach the sliding surface and to suppress external disturbances and parameter uncertainties. The inertia matrix, The gravity vector Let be the desired angular acceleration of the joint. These are the sliding mode gain parameters. To approach the law exponent and satisfy This invention, used to suppress control chattering, employs a fractional-order reaching law that adjusts the reaching speed, balancing speed and smoothness. Traditional sliding mode control uses a sign function to construct a discontinuous control law. When the system moves near the sliding surface, it is prone to high-frequency switching of the control input due to disturbances, measurement noise, and unmodeled dynamics, thus affecting control robustness. This invention uses a fractional-order reaching law to dynamically adjust the system's reaching speed. When moving away from the sliding surface, it provides rapid reaching, ensuring finite-time convergence; when approaching the sliding surface, it automatically reduces the reaching speed, achieving smooth reaching, thus ensuring both finite-time convergence and the accuracy of trajectory tracking control.
[0030] In steps S41 to S43, the introduction of a fractional-order sliding surface significantly enhances the robustness to system model uncertainties and external disturbances, overcoming the limitation of traditional integer-order sliding surfaces in insufficient suppression of complex disturbances. Simultaneously, the tracking error convergence problem with complex boundary constraints is transformed into a stabilization problem for unconstrained transformation variables through an error transformation function, thus strictly guaranteeing that the system tracking error converges within a preset transient and steady-state performance range. Furthermore, the designed fractional-order reaching law adaptively adjusts the reaching speed according to the distance between the system state and the sliding surface. It provides strong convergence force to ensure speed when far from the sliding surface, and smooths the transition when approaching the sliding surface to significantly suppress control input chattering, achieving a balance between rapid dynamic response and smooth motion. Ultimately, the control law derived from Lyapunov's stability theory has an equivalent control part that precisely compensates for the nominal dynamics of the system, laying the foundation for high-precision tracking. Meanwhile, the discontinuous control part actively counteracts and compensates for various uncertainties, ensuring that the robot system can still achieve high-precision and robust trajectory tracking control within a finite time under actual parameter perturbations and external disturbances.
[0031] In existing technologies, sliding mode gain relies on manual trial and error tuning, making it difficult to achieve an optimal balance between tracking accuracy, convergence speed, and chatter suppression. Therefore, in this embodiment, to achieve automatic parameter optimization, improve trajectory tracking accuracy, reduce control convergence time, and enhance robustness, the sliding mode gain parameters are optimized using an improved particle swarm optimization algorithm, aiming for optimal overall trajectory tracking performance. Various methods known to those skilled in the art can be used to optimize the sliding mode gain parameters. In a preferred example of this invention, the method for optimizing the sliding mode gain parameters can be... Figure 4 The method shown. Figure 4 The control method also includes: In step S51, the particle swarm is initialized. Specifically, the number of particles in the initial particle swarm is 50.
[0032] In step S52, the velocity and position of each particle are updated.
[0033] In step S53, the fitness of each particle is calculated. This invention employs an improved particle swarm optimization algorithm to optimize the sliding mode gain parameters, aiming for optimal overall trajectory tracking performance, and constructs a weighted fitness function, specifically including: Construct the fitness function according to formula (14). (14) in, For the fitness function, note the difference between... distinguish, The first weighting coefficient, For the second weighting coefficient, It is the third weighting coefficient, and , To convergence time, specifically, , , .
[0034] In step S54, the sliding mode gain parameter corresponding to the minimum fitness of each particle in history is selected as the optimal individual.
[0035] In step S55, the sliding mode gain parameter corresponding to the minimum fitness among all particles is selected as the global optimum.
[0036] In step S56, it is determined whether the preset number of iterations has been reached. If the current number of iterations has reached the preset number of iterations, step S57 is executed; otherwise, step S52 is executed.
[0037] In step S57, the global optimum is output as the optimal sliding mode gain parameter.
[0038] In steps S51 to S57, the sliding mode gain parameter in the control law is used as a particle in the particle swarm optimization algorithm, and it is uniformly distributed within the constraint interval. Substituted into the control law, the fitness function value of each particle is calculated. The parameter corresponding to the historical minimum fitness function value of each particle is retained as the optimal individual. The parameter corresponding to the minimum fitness function value among all particles is selected as the global optimum. This iterative optimization is repeated until the maximum number of iterations is reached. The output global optimum particle is the optimized sliding mode gain parameter.
[0039] In this embodiment, the methods for updating particle velocity and position can be various, as known to those skilled in the art. In a preferred embodiment of the invention, the methods for updating particle velocity and position can be... Figure 5 The method shown in Figure 5 The control method also includes: In step S521, the inertia weights are updated according to formula (15). (15) In step S522, the particle velocity is updated according to formula (16). (16) In step S523, the particle position is updated according to formula (17). (17) in, For the updated inertia weights, This represents the maximum value of the inertia weight. This represents the maximum value of the inertia weight. The attenuation coefficient is... This represents the current iteration number. For the next iteration number, The maximum number of iterations, For the first The speed of each particle in the next iteration For the first The current iteration speed of each particle For the first The position of each particle in the next iteration. For the first The current position of each particle in the iteration. The first acceleration coefficient, The second acceleration coefficient, The first number is a random number. The second random number, For the first The best position in the history of each particle This represents the optimal position for all particles. In one example of this invention, , , Choose 0.8. Choose 100 times. .
[0040] Figure 6 This is a graph showing the tracking effect of a controller according to an embodiment of the present invention on trajectory errors. Figure 6 In the test, all three tracking error curves converged at t=2s, which verified the effectiveness of the designed controller. The convergence process was completed within 2 seconds, demonstrating the controller's good transient performance and response speed. After entering steady state, the tracking error curves became a flat straight line, with zero error, indicating that the controller has excellent robustness and good control accuracy.
[0041] On the other hand, the present invention also provides a finite-time fractional-order sliding mode control system for a modular robot, the control system including a processor for executing the control method as described above.
[0042] Through the above technical solutions, this invention provides a finite-time fractional sliding mode control method and system for modular robots. A single-leg dynamic model is established using the Lagrange method. The constructed piecewise finite-time performance function eliminates the need for pre-calibrating the robot's initial pose, achieving full-process error constraints and ensuring stable convergence of tracking errors within a preset finite time, significantly improving the engineering applicability and deployment efficiency of the control system. The error transformation method transforms the performance-constrained tracking control problem into an unconstrained stabilization problem, reducing the difficulty of controller design and stability proof. The constructed fractional sliding surface introduces non-integer-order differential characteristics, effectively improving the system's robustness under uncertain model parameters, external disturbances, and unmodeled dynamic conditions. Furthermore, a fractional-order reaching law is used to dynamically adjust the system's approach speed, improving control smoothness and trajectory tracking accuracy while ensuring finite-time arrival at the sliding surface. Finally, an improved particle swarm optimization algorithm is introduced to achieve self-tuning of the sliding mode gain parameters, automatically optimizing based on a weighted optimum of tracking accuracy, control robustness, and convergence time, avoiding the subjectivity and inefficiency of manual trial and error, and achieving globally optimal control performance.
[0043] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.
[0044] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.
[0045] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1The function specified in one or more boxes.
[0046] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.
[0047] In a typical configuration, a computing device includes one or more processors (CPU), input / output interfaces, network interfaces, and memory.
[0048] Memory may include non-persistent memory in computer-readable media, such as random access memory (RAM) and / or non-volatile memory, like read-only memory (ROM) or flash RAM. Memory is an example of computer-readable media.
[0049] Computer-readable media includes both permanent and non-permanent, removable and non-removable media that can store information using any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transient computer-readable media, such as modulated data signals and carrier waves.
[0050] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.
[0051] The above are merely embodiments of this application and are not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.
Claims
1. A finite-time fractional-order sliding mode control method for a modular robot, characterized in that, The control method includes: A dynamic model of a single leg of a modular quadruped robot is established, and the position tracking error and velocity error of the single leg joint are defined. Construct a piecewise finite-time performance function; The bounded tracking error constrained by the performance function is converted into an unbounded transformation error based on the transformation error method. Combining fractional-order reaching laws, a sliding mode control law with fractional-order reaching laws and specified performance in finite time is obtained based on Lyapunov stability theory; The sliding mode gain parameters of a fractional-order approach sliding mode control law with a specified performance in a finite-time period are optimized using an improved particle swarm optimization algorithm to obtain the optimal sliding mode gain parameters.
2. The control method according to claim 1, characterized in that, A dynamic model of a single leg of a modular quadruped robot is established, and the position tracking error and velocity error of the single leg joint are defined, including: Construct a dynamic model based on formula (1). ，（1） The position tracking error of a single leg joint is defined according to formula (2). ，（2） According to formula (3), the velocity error of a single leg joint is defined. ，（3） in, For the control matrix, Let be the angular position vector of the joint. For time variables, Let be the angular acceleration of the joint. The inertia matrix, The matrix represents the Coriolis force and the centrifugal force. Let be the angular velocity of the joint. The gravity vector For joint position tracking error, This represents the desired angular position of the joint. For the speed error of the joint, The desired angular velocity of the joint.
3. The control method according to claim 2, characterized in that, Constructing a piecewise finite-time performance function includes: The finite-time performance function is determined according to formula (4). ，（4） in, For finite-time performance functions, The performance function for the initial segment. The gain parameter of the performance function for the initial segment. This is the time point for the initial stage. For time variables, for The convergence rate, The performance function for the finite-time convergence segment. It is a constant. For the time nodes of the finite-time convergence segment, As the initial boundary, To stabilize the boundary, For the performance function of the steady-state holding segment, This represents the position tracking error of the joint.
4. The control method according to claim 3, characterized in that, The bounded tracking error constrained by the performance function is converted into an unbounded transformation error based on the transformation error method, including: The error transformation function is determined according to formula (5). ，（5） in, Let be the error transformation function, and .
5. The control method according to claim 4, characterized in that, Combining fractional-order reaching laws, and based on Lyapunov stability theory, a finite-time fractional-order reaching sliding mode control law for specified performance is obtained, including: Construct fractional-order sliding surfaces according to formulas (6) to (9). ，（6） ，（7） ，（8） ，（9） in, For fractional-order sliding surfaces, The first derivative of a fractional sliding surface. The first derivative of the error transformation function. For the fractional derivative term of the error transformation function, For order, These are the coefficient terms of the error transformation function. Let be the first derivative of the coefficient term of the error transformation function. It is a symbolic function.
6. The control method according to claim 5, characterized in that, Combining fractional-order reaching laws, and based on Lyapunov stability theory, a finite-time fractional-order reaching sliding mode control law for specified performance is obtained, which also includes: The fractional-order reaching law is determined according to formula (10). ，（10） The fractional-order approach sliding mode control law for a given performance in finite time is obtained from formulas (11) to (13). ，（11） ，（12） ，（13） in, For the equivalent control matrix, It is a discontinuous control matrix. The inertia matrix, The gravity vector Let be the desired angular acceleration of the joint. These are the sliding mode gain parameters. This is the convergence law index.
7. The control method according to claim 6, characterized in that, The sliding mode gain parameters of a fractional-order reaching law sliding mode control law with a specified performance in a finite-time period are optimized using an improved particle swarm optimization algorithm to obtain the optimal sliding mode gain parameters, including: Initialize the particle swarm; Update the velocity and position of each particle; Calculate the fitness of each particle; The sliding mode gain parameter corresponding to the minimum fitness of each particle's history is selected as the optimal individual. The sliding mode gain parameter corresponding to the minimum fitness among all particles is selected as the global optimum. Determine whether the current iteration count has reached the preset iteration count; If the current iteration count reaches the preset iteration count, the global optimum is output as the optimal sliding mode gain parameter; If it is determined that the current iteration number has not reached the preset iteration number, the step is to update the velocity and position of each particle.
8. The control method according to claim 7, characterized in that, Calculate the fitness of each particle, including: Construct the fitness function according to formula (14). ，（14） in, For the fitness function, The first weighting coefficient, For the second weighting coefficient, It is the third weighting coefficient, and , For convergence time.
9. The control method according to claim 8, characterized in that, Update the velocity and position of each particle, including: Update the inertia weights according to formula (15). ，（15） Update the particle velocity according to formula (16). ，（16） Update the particle's position according to formula (17). ，（17） in, For the updated inertia weights, This represents the maximum value of the inertia weight. This represents the maximum value of the inertia weight. The attenuation coefficient is... This represents the current iteration number. For the next iteration number, The maximum number of iterations, For the first The speed of each particle in the next iteration For the first The current iteration velocity of each particle For the first The position of each particle in the next iteration. For the first The current position of each particle in the iteration. The first acceleration coefficient, The second acceleration coefficient, The first number is a random number. The second random number, For the first The best position in the history of each particle This represents the optimal position for all particles globally.
10. A finite-time fractional-order sliding mode control system for a modular robot, characterized in that, The control system includes a processor for executing the control method as described in any one of claims 1 to 9.