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CN114952860A - Mobile robot repetitive motion control method and system based on discrete time neurodynamics - Google Patents

Mobile robot repetitive motion control method and system based on discrete time neurodynamics Download PDF

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CN114952860A
CN114952860A CN202210713454.8A CN202210713454A CN114952860A CN 114952860 A CN114952860 A CN 114952860A CN 202210713454 A CN202210713454 A CN 202210713454A CN 114952860 A CN114952860 A CN 114952860A
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mobile robot
repetitive motion
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CN114952860B (en
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邱斌斌
李晓东
郭津津
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Guangzhou Sizhi Lai Medical Technology Co ltd
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Sun Yat Sen University
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • B25J9/161—Hardware, e.g. neural networks, fuzzy logic, interfaces, processor
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J18/00—Arms
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1628—Programme controls characterised by the control loop
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1628—Programme controls characterised by the control loop
    • B25J9/163—Programme controls characterised by the control loop learning, adaptive, model based, rule based expert control
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
    • B25J9/1661—Programme controls characterised by programming, planning systems for manipulators characterised by task planning, object-oriented languages

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  • Mechanical Engineering (AREA)
  • Automation & Control Theory (AREA)
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Abstract

The invention relates to the field of robot control, and provides a repetitive motion control method and a repetitive motion control system for a mobile robot based on discrete time neurodynamics, wherein the method comprises the steps of constructing a position layer kinematic equation, a speed layer kinematic equation and a physical limit constraint of the mobile robot, and converting the physical limit constraint into a speed layer double-end inequality constraint; constructing a repetitive motion control scheme of the mobile robot based on a time-varying quadratic optimization problem; constructing a continuous time zero-ization neurodynamic model; and constructing a discrete time zero-ization neurodynamic model according to the five-step explicit linear multi-step rule and the continuous time zero-ization neurodynamic model, calculating a control variable of the mobile robot, and performing repeated motion control on the mobile robot. The invention can realize real-time repetitive motion control of the mobile robot containing physical limit constraint, and improves the motion real-time property, path tracking precision and physical limit constraint processing capacity of the mobile robot.

Description

基于离散时间神经动力学的移动机器人重复运动控制方法及 系统Method and system for repetitive motion control of mobile robot based on discrete-time neural dynamics

技术领域technical field

本发明涉及机器人控制领域，更具体地，涉及一种基于离散时间神经动力学的移动机器人重复运动控制方法及系统。The invention relates to the field of robot control, and more particularly, to a method and system for repetitive motion control of a mobile robot based on discrete-time neural dynamics.

背景技术Background technique

移动机器人主要由移动平台和固定在移动平台上的机械臂组成。移动机器人的重复运动控制是要求在完成闭合的路径跟踪后，移动平台和机械臂的最终状态均与初始状态保持一致。若移动平台和机械臂未恢复到初始状态，即出现非重复运动现象，则需要对移动机器人进行额外的配置调整或自运动过程，从而大大降低任务执行的效率。The mobile robot is mainly composed of a mobile platform and a robotic arm fixed on the mobile platform. The repetitive motion control of the mobile robot requires that the final state of the mobile platform and the manipulator be consistent with the initial state after completing the closed path tracking. If the mobile platform and the manipulator do not return to the initial state, that is, the phenomenon of non-repetitive motion occurs, additional configuration adjustments or self-motion processes need to be performed on the mobile robot, which greatly reduces the efficiency of task execution.

现有一种高性能冗余度机械臂重复运动规划方法与装置，包括设计二次型的重复运动性能指标，生成二次型优化冗余度解析方案；将步骤的二次型优化冗余度解析方案转化为二次规划的形式；将二次规划运用二次规划求解器进行求解并将求解结果传递给采用下位机控制器驱动冗余度机械臂运动。There is a high-performance redundant robotic arm repetitive motion planning method and device, including designing a quadratic repetitive motion performance index, generating a quadratic optimization redundancy analysis scheme; analyzing the quadratic optimization redundancy of the steps The scheme is transformed into the form of quadratic programming; the quadratic programming is solved by the quadratic programming solver and the solution results are passed to the lower computer controller to drive the motion of the redundant manipulator.

然而，上述方法将移动机器人的重复运动控制问题表述为时变二次型优化问题，并运用连续时间神经动力学方法或数值算法进行求解，存在计算精度较低和难以直接适用于离散时间系统等问题，而数值算法需要在每个计算时间点都进行反复的大量迭代计算以求出最优解，不能对移动机器人进行高效的实时可重复运动控制。However, the above methods formulate the repetitive motion control problem of mobile robots as a time-varying quadratic optimization problem, and use continuous-time neural dynamics methods or numerical algorithms to solve them, which have low computational accuracy and are difficult to directly apply to discrete-time systems, etc. However, the numerical algorithm needs to perform a large number of iterative calculations repeatedly at each calculation time point to obtain the optimal solution, which cannot perform efficient real-time repeatable motion control for mobile robots.

发明内容SUMMARY OF THE INVENTION

本发明为克服现有技术中不能对移动机器人进行高效的实时可重复运动控制的缺陷，提供一种基于离散时间神经动力学的移动机器人重复运动控制方法及系统。The present invention provides a method and system for repetitive motion control of a mobile robot based on discrete-time neural dynamics in order to overcome the defect in the prior art that high-efficiency real-time repeatable motion control cannot be performed on a mobile robot.

为解决上述技术问题，本发明的技术方案如下：For solving the above-mentioned technical problems, the technical scheme of the present invention is as follows:

第一个方面，本发明提出一种基于离散时间神经动力学的移动机器人重复运动控制方法，包括以下步骤：In a first aspect, the present invention proposes a discrete-time neural dynamics-based repetitive motion control method for a mobile robot, comprising the following steps:

S1：采集移动机器人的运动数据；S1: collect the motion data of the mobile robot;

S2：构建移动机器人的位置层运动学方程、速度层运动学方程和物理极限约束，并将所述物理极限约束转换为速度层双端不等式约束；S2: constructing the position layer kinematic equation, velocity layer kinematic equation and physical limit constraint of the mobile robot, and converting the physical limit constraint into a velocity layer double-ended inequality constraint;

S3：结合所述位置层运动学方程、速度层运动学方程和速度层双端不等式约束，构建基于时变二次型优化问题的移动机器人的重复运动控制方案；S3: Construct a repetitive motion control scheme for a mobile robot based on a time-varying quadratic optimization problem by combining the position layer kinematic equations, the velocity layer kinematic equations and the velocity layer double-end inequality constraints;

S4：基于零化神经动力学设计法则，将指数型惩罚策略引入所述基于时变二次型优化问题的移动机器人的重复运动控制方案，构建连续时间零化神经动力学模型；S4: Based on the design rule of zero neural dynamics, an exponential penalty strategy is introduced into the repetitive motion control scheme of the mobile robot based on the time-varying quadratic optimization problem, and a continuous time zero neural dynamic model is constructed;

S5：根据五步显式线性多步法则与所述连续时间零化神经动力学模型，构建离散时间零化神经动力学模型；S5: According to the five-step explicit linear multi-step rule and the continuous-time zero-neural dynamics model, construct a discrete-time zero-neural dynamics model;

S6：将所述移动机器人的运动数据输入所述离散时间零化神经动力学模型，计算出移动机器人的控制变量；S6: Input the motion data of the mobile robot into the discrete-time neutralized neural dynamics model, and calculate the control variables of the mobile robot;

S7：根据所述控制变量对移动机器人进行重复运动控制。S7: Perform repetitive motion control on the mobile robot according to the control variable.

第二个方面，本发明提出一种基于离散时间神经动力学的移动机器人重复运动控制系统，包括：In the second aspect, the present invention proposes a repetitive motion control system for a mobile robot based on discrete-time neural dynamics, including:

采集模块，用于采集移动机器人的运动数据；The acquisition module is used to collect the motion data of the mobile robot;

第一构建模块，用于构建移动机器人的位置层运动学方程、速度层运动学方程和物理极限约束，并将所述物理极限约束转换为速度层双端不等式约束；The first building module is used to construct the position layer kinematic equations, velocity layer kinematic equations and physical limit constraints of the mobile robot, and convert the physical limit constraints into velocity layer double-ended inequality constraints;

第二构建模块，用于结合所述位置层运动学方程、速度层运动学方程和速度层双端不等式约束，构建基于时变二次型优化问题的移动机器人的重复运动控制方案；The second building module is used for constructing the repetitive motion control scheme of the mobile robot based on the time-varying quadratic optimization problem by combining the kinematic equations of the position layer, the kinematic equations of the velocity layer and the double-ended inequality constraints of the velocity layer;

第三构建模块，用于基于零化神经动力学设计法则，将指数型惩罚策略引入所述基于时变二次型优化问题的移动机器人的重复运动控制方案，构建连续时间零化神经动力学模型；The third building block is used to introduce the exponential penalty strategy into the repetitive motion control scheme of the mobile robot based on the time-varying quadratic optimization problem based on the design rule of zero neural dynamics, and construct the continuous time zero neural dynamics model ;

第四构建模块，用于根据五步显式线性多步法则与所述连续时间零化神经动力学模型，构建离散时间零化神经动力学模型；a fourth building module for constructing a discrete-time zero-neural dynamics model according to the five-step explicit linear multi-step rule and the continuous-time zero-neural dynamics model;

计算模块，用于根据所述移动机器人的运动数据和所述离散时间零化神经动力学模型，计算出移动机器人的控制变量；a calculation module, used for calculating the control variables of the mobile robot according to the motion data of the mobile robot and the discrete-time zeroed neural dynamics model;

控制模块，用于根据所述控制变量对移动机器人进行重复运动控制。The control module is used for performing repetitive motion control on the mobile robot according to the control variable.

第三个方面，本发明提出一种电子设备，包括处理器以及存储器；所述存储器用于存储程序；所述处理器执行所述程序实现如基于离散时间神经动力学的移动机器人重复运动控制中任一方案的步骤。In a third aspect, the present invention provides an electronic device, including a processor and a memory; the memory is used to store a program; the processor executes the program to realize the repetitive motion control of a mobile robot based on discrete-time neural dynamics steps for either scenario.

第四个方面，本发明提出一种计算机可读存储介质，所述存储介质存储有程序，所述程序被处理器执行实现如基于离散时间神经动力学的移动机器人重复运动控制中任一方案的步骤。In a fourth aspect, the present invention provides a computer-readable storage medium, where a program is stored in the storage medium, and the program is executed by a processor to implement any one of the schemes in the repetitive motion control of a mobile robot based on discrete-time neural dynamics step.

与现有技术相比，本发明技术方案的有益效果是：本发明通过构建移动机器人的位置层运动学方程、速度层运动学方程和速度层双端不等式约束，设计出基于时变二次型优化问题的移动机器人的重复运动控制方案，并在所述移动机器人的重复运动控制方案的基础上引入指数型惩罚策略和五步显式线性多步法则，构建出离散时间零化神经动力学模型，能够在每个计算时间间隔中，仅需基于当前和先前的已知数据信息并通过一次更新计算，就能准确预测出下一时间点的求解结果，从而实现对含物理极限约束的移动机器人高精度实时重复运动控制，有效消除了非重复运动现象，有力提升了移动机器人的运动实时性、路径跟踪精度以及物理极限约束处理能力。Compared with the prior art, the beneficial effects of the technical solution of the present invention are: the present invention designs a time-varying quadratic type based on the constraints of the position layer kinematic equation, velocity layer kinematic equation and velocity layer double-end inequality constraints of the mobile robot. On the basis of the repetitive motion control scheme of the mobile robot, an exponential penalty strategy and a five-step explicit linear multi-step rule are introduced on the basis of the repetitive motion control scheme of the mobile robot, and a discrete-time zero neural dynamics model is constructed , which can accurately predict the solution result at the next time point based on the current and previous known data information and through one update calculation in each calculation time interval, so as to realize the mobile robot with physical limit constraints. High-precision real-time repetitive motion control effectively eliminates the phenomenon of non-repetitive motion, and effectively improves the real-time motion, path tracking accuracy and physical limit constraint processing capabilities of mobile robots.

附图说明Description of drawings

图1为基于离散时间神经动力学的移动机器人重复运动控制方法流程图。Fig. 1 is a flow chart of the repetitive motion control method of a mobile robot based on discrete-time neural dynamics.

图2为本发明的移动机器人的简化模型图。FIG. 2 is a simplified model diagram of the mobile robot of the present invention.

图3为本发明的移动平台的运动学模型图。FIG. 3 is a kinematic model diagram of the mobile platform of the present invention.

图4为本发明的移动机器人的运动轨迹和末端执行器的实际轨迹与期望路径图。FIG. 4 is a diagram of the motion trajectory of the mobile robot and the actual trajectory and expected path of the end effector of the present invention.

图5为本发明的移动平台与机械臂之间的连接点和移动平台的航向角图。FIG. 5 is a view of the connection point between the mobile platform and the mechanical arm and the heading angle of the mobile platform according to the present invention.

图6为本发明的移动机器人的组合角度向量的元素轨迹图。FIG. 6 is an element trajectory diagram of a combined angle vector of the mobile robot of the present invention.

图7为本发明的移动机器人的组合速度向量的元素轨迹图。FIG. 7 is an element trajectory diagram of the combined velocity vector of the mobile robot of the present invention.

图8为本发明的移动机器人的末端执行器跟踪误差向量的元素轨迹图。FIG. 8 is an element trajectory diagram of the tracking error vector of the end effector of the mobile robot of the present invention.

图9为基于离散时间神经动力学的移动机器人重复运动控制系统架构图。FIG. 9 is an architecture diagram of a repetitive motion control system for a mobile robot based on discrete-time neural dynamics.

具体实施方式Detailed ways

附图仅用于示例性说明，不能理解为对本专利的限制；The accompanying drawings are for illustrative purposes only, and should not be construed as limitations on this patent;

下面结合附图和实施例对本发明的技术方案做进一步的说明。The technical solutions of the present invention will be further described below with reference to the accompanying drawings and embodiments.

实施例1Example 1

请参阅图1，本实施例提出一种基于离散时间神经动力学的移动机器人重复运动控制方法，包括以下步骤：Referring to FIG. 1 , this embodiment proposes a method for controlling repetitive motion of a mobile robot based on discrete-time neural dynamics, including the following steps:

S1：采集移动机器人的运动数据。S1: Collect motion data of the mobile robot.

S2：构建移动机器人的位置层运动学方程、速度层运动学方程和物理极限约束，并将所述物理极限约束转换为速度层双端不等式约束。S2: Construct position-level kinematic equations, velocity-level kinematics equations, and physical limit constraints of the mobile robot, and convert the physical limit constraints into velocity-level double-ended inequality constraints.

S3：结合所述位置层运动学方程、速度层运动学方程和速度层双端不等式约束，构建基于时变二次型优化问题的移动机器人的重复运动控制方案。S3: Construct a repetitive motion control scheme for a mobile robot based on a time-varying quadratic optimization problem by combining the position layer kinematic equations, the velocity layer kinematic equations, and the velocity layer double-ended inequality constraints.

本实施例中，通过将移动机器人的组合角度向量和组合速度向量的物理极限约束统一转换为基于组合速度向量的表达式，即速度层双端不等式约束，构建出决策变量为组合速度向量的移动机器人的重复运动控制方案，使得所述重复运动控制方案重新表述为一个在速度层上解析的标准的时变二次型优化问题。In this embodiment, by uniformly converting the physical limit constraints of the combined angle vector and the combined velocity vector of the mobile robot into an expression based on the combined velocity vector, that is, the double-ended inequality constraint of the velocity layer, the decision variable is constructed as the movement of the combined velocity vector. The repetitive motion control scheme of the robot, such that the repetitive motion control scheme is reformulated as a standard time-varying quadratic optimization problem parsed in the velocity layer.

S4：基于零化神经动力学设计法则，将指数型惩罚策略引入所述基于时变二次型优化问题的移动机器人的重复运动控制方案，构建连续时间零化神经动力学模型。S4: Based on the design rule of zeroed neural dynamics, an exponential penalty strategy is introduced into the repetitive motion control scheme of the mobile robot based on the time-varying quadratic optimization problem, and a continuous-time zeroed neural dynamic model is constructed.

S5：根据五步显式线性多步法则与所述连续时间零化神经动力学模型，构建离散时间零化神经动力学模型。S5: According to the five-step explicit linear multi-step rule and the continuous-time zero-neural dynamics model, construct a discrete-time zero-neural dynamics model.

S6：将所述移动机器人的运动数据输入所述离散时间零化神经动力学模型，计算出移动机器人的控制变量。S6: Input the motion data of the mobile robot into the discrete-time neutralized neural dynamics model, and calculate the control variables of the mobile robot.

S7：根据所述控制变量对移动机器人进行重复运动控制。S7: Perform repetitive motion control on the mobile robot according to the control variable.

通过构建移动机器人的位置层运动学方程、速度层运动学方程和速度层双端不等式约束，设计出基于时变二次型优化问题的移动机器人的重复运动控制方案，并在所述移动机器人的重复运动控制方案的基础上引入指数型惩罚策略和五步显式线性多步法则，构建出离散时间零化神经动力学模型，能够在每个计算时间间隔中，仅需基于当前和先前的已知数据信息并通过一次更新计算，就能准确预测出下一时间点的求解结果，从而实现对含物理极限约束的移动机器人高精度实时重复运动控制，有效消除了非重复运动现象，有力提升了移动机器人的运动实时性、路径跟踪精度以及物理极限约束处理能力。By constructing the kinematic equations of the position layer, the kinematic equations of the velocity layer and the double-end inequality constraints of the velocity layer, a repetitive motion control scheme of the mobile robot based on the time-varying quadratic optimization problem is designed, and the mobile robot's repetitive motion control scheme is designed. On the basis of the repetitive motion control scheme, an exponential penalty strategy and a five-step explicit linear multi-step rule are introduced to construct a discrete-time zero-neutral neural dynamics model, which can only be based on the current and previous By knowing the data information and updating the calculation once, the solution result at the next time point can be accurately predicted, so as to realize the high-precision real-time repetitive motion control of the mobile robot with physical limit constraints, effectively eliminate the phenomenon of non-repetitive motion, and effectively improve the The real-time motion, path tracking accuracy and physical limit constraint processing capability of mobile robots.

实施例2Example 2

请参阅图2-图8，本实施例提出一种基于离散时间神经动力学的移动机器人重复运动控制方法，包括以下步骤：Please refer to FIG. 2-FIG. 8. This embodiment proposes a method for controlling repetitive motion of a mobile robot based on discrete-time neural dynamics, including the following steps:

S1：采集移动机器人的运动数据；S1: collect the motion data of the mobile robot;

本实施例中，所述移动机器人的运动数据包括移动机器人的组合角度向量、末端执行器的实际位置向量、移动平台左驱动轮和右驱动轮的旋转角度、固定在移动平台上六关节冗余度机械臂的关节角度向量、移动平台的航向角、移动机器人的组合速度向量、末端执行器的期望路径。In this embodiment, the motion data of the mobile robot includes the combined angle vector of the mobile robot, the actual position vector of the end effector, the rotation angle of the left driving wheel and the right driving wheel of the mobile platform, and the redundant six joints fixed on the mobile platform. The joint angle vector of the robot arm, the heading angle of the mobile platform, the combined velocity vector of the mobile robot, and the desired path of the end effector.

S2：构建移动机器人的位置层运动学方程、速度层运动学方程和物理极限约束，并将所述物理极限约束转换为速度层双端不等式约束：S2: Construct position layer kinematic equations, velocity layer kinematic equations and physical limit constraints of the mobile robot, and convert the physical limit constraints into velocity layer double-ended inequality constraints:

S2.1：确定移动机器人运动的离散时间点，并在所述离散时间点构建位置层运动学方程。S2.1: Determine the discrete time points of the motion of the mobile robot, and construct the kinematic equation of the position layer at the discrete time points.

本实施例中，在离散时间点

Figure BDA0003708833300000051
中，构建位置层运动学方程，其表达式如下所示：In this embodiment, at discrete time points
Figure BDA0003708833300000051
, construct the kinematic equation of the position layer, and its expression is as follows:

Φ(Θk+1)＝ractual,k+1 Φ(Θ k+1 )=r actual,k+1

Figure BDA0003708833300000052
Figure BDA0003708833300000052

其中，k为更新索引，

Figure BDA0003708833300000053
为时间步长，tfinal为整个计算时间区间的最终时间点，
Figure BDA0003708833300000054
为非线性映射函数阵列，
Figure BDA0003708833300000055
为实数集合，Θk+1为移动机器人的组合角度向量，ractual,k+1为末端执行器的实际位置向量，
Figure BDA0003708833300000056
为移动平台左驱动轮和右驱动轮的旋转角度集，θk+1为固定在移动平台上六关节冗余度机械臂的关节角度向量。Among them, k is the update index,
Figure BDA0003708833300000053
is the time step, t final is the final time point of the entire calculation time interval,
Figure BDA0003708833300000054
is an array of nonlinear mapping functions,
Figure BDA0003708833300000055
is a set of real numbers, Θ k+1 is the combined angle vector of the mobile robot, r actual,k+1 is the actual position vector of the end effector,
Figure BDA0003708833300000056
is the rotation angle set of the left driving wheel and the right driving wheel of the mobile platform, and θ k+1 is the joint angle vector of the six-joint redundant manipulator fixed on the mobile platform.

离散时间点

Figure BDA0003708833300000057
由k和
Figure BDA0003708833300000058
值确定，泛指下一离散时间点，而tk泛指当前离散时间点。在离散时间点tk+1进行表达可以更好地说明待求解的方案和问题是针对下一离散时间点的。discrete time points
Figure BDA0003708833300000057
by k and
Figure BDA0003708833300000058
The value is determined, generally refers to the next discrete time point, and t k generally refers to the current discrete time point. Expressing at a discrete time point t k+1 can better illustrate that the solutions and problems to be solved are for the next discrete time point.

S2.2：根据所述位置层运动学方程，构建速度层运动学方程。S2.2: According to the kinematic equation of the position layer, construct the kinematic equation of the velocity layer.

本实施例中，为了监测和控制末端执行器跟踪期望路径的过程，定义末端执行器的定位误差向量为∈k+1＝ractual,k+1-rdesired,k+1，其中rdesired,k+1为末端执行器的期望路径。In this embodiment, in order to monitor and control the process of the end effector tracking the desired path, the positioning error vector of the end effector is defined as ∈ k+1 =r actual,k+1 -r desired,k+1 , where r desired, k+1 is the desired path of the end effector.

通过引入上述的末端执行器定位误差作为误差反馈，所述速度层运动学方程的表达式如下所示：By introducing the above-mentioned end effector positioning error as error feedback, the expression of the velocity layer kinematic equation is as follows:

Figure BDA0003708833300000059
Figure BDA0003708833300000059

Figure BDA00037088333000000510
Figure BDA00037088333000000510

其中，φk+1为移动平台的航向角，

Figure BDA00037088333000000511
为移动机器人的组合速度向量，
Figure BDA00037088333000000512
为移动平台左驱动轮和右驱动轮的旋转速度集，
Figure BDA00037088333000000513
为固定在移动平台上六关节冗余度机械臂的关节速度向量，J(φk+1,θk+1)为与雅可比相关的矩阵；ζk+1为含末端执行器位置误差反馈的向量，
Figure BDA00037088333000000514
为末端执行器的期望路径的时间导数，rdesired,k+1为末端执行器的期望路径，λ1为可设定的参数。Among them, φ k+1 is the heading angle of the mobile platform,
Figure BDA00037088333000000511
is the combined velocity vector of the mobile robot,
Figure BDA00037088333000000512
is the rotation speed set of the left and right drive wheels of the mobile platform,
Figure BDA00037088333000000513
is the joint velocity vector of the six-joint redundant manipulator fixed on the mobile platform, J(φ k+1 , θ k+1 ) is the Jacobian-related matrix; ζ k+1 is the position error feedback including the end effector a vector of ,
Figure BDA00037088333000000514
is the time derivative of the desired path of the end effector, r desired,k+1 is the desired path of the end effector, and λ 1 is a parameter that can be set.

S2.3：通过离散时变双端不等式组，构建物理极限约束。S2.3: Construct physical limit constraints through discrete time-varying two-ended inequalities.

本实施例中，所述移动机器人的物理极限约束的表达式如下所示：In this embodiment, the expression of the physical limit constraint of the mobile robot is as follows:

Figure BDA0003708833300000061
Figure BDA0003708833300000061

其中，Θ-表示移动机器人的组合角度向量的下限，Θ+表示移动机器人的组合角度向量的上限，

Figure BDA0003708833300000062
表示移动机器人的组合速度向量的下限，
Figure BDA0003708833300000063
表示移动机器人的组合速度向量的上限。where Θ - represents the lower bound of the combined angle vector of the mobile robot, Θ + represents the upper bound of the combined angle vector of the mobile robot,
Figure BDA0003708833300000062
represents the lower bound of the combined velocity vector of the mobile robot,
Figure BDA0003708833300000063
Represents the upper bound of the combined velocity vector of the mobile robot.

S2.4：基于指数型极限转换策略，将所述物理极限约束转换为速度层双端不等式约束，其表达式如下所示：S2.4: Based on the exponential limit conversion strategy, the physical limit constraint is converted into a velocity layer double-ended inequality constraint, and its expression is as follows:

Figure BDA0003708833300000064
Figure BDA0003708833300000064

其中，αk+1表示双端不等式约束的下极限，βk+1表示双端不等式约束的上极限，αk+1的第i个元素αi,k+1(i＝1,2,…,n)，以及βk+1的第i个元素βi,k+1(i＝1,2,…,n)，分别有如下定义：Among them, α k+1 represents the lower limit of the double-ended inequality constraint, β k+1 represents the upper limit of the double-ended inequality constraint, and the i-th element of α k + 1 α i,k+1 (i=1,2, …,n), and the i-th element β i,k+1 (i=1,2,…,n) of β k +1, respectively, have the following definitions:

Figure BDA0003708833300000065
Figure BDA0003708833300000065

其中，exp(·)表示指数函数；σ1>0为可设定的参数，用于调节减速幅度；参数σ2∈(0,1)为可设定的参数，用于调节需要减速的临界区域范围，即

Figure BDA0003708833300000066
和
Figure BDA0003708833300000067
Among them, exp( ) represents an exponential function; σ 1 >0 is a parameter that can be set to adjust the deceleration amplitude; parameter σ 2 ∈(0,1) is a parameter that can be set to adjust the critical value that needs to be decelerated area, i.e.
Figure BDA0003708833300000066
and
Figure BDA0003708833300000067

S3：结合所述位置层运动学方程、速度层运动学方程和速度层双端不等式约束，构建基于时变二次型优化问题的移动机器人的重复运动控制方案：S3: Combine the kinematic equations of the position layer, the kinematic equations of the velocity layer and the double-end inequality constraints of the velocity layer to construct a repetitive motion control scheme of the mobile robot based on the time-varying quadratic optimization problem:

S3.1：结合位置层运动学方程、速度层运动学方程和速度层双端不等式约束，设计移动机器人的重复运动控制方案，其表达式如下所示：S3.1: Combine the kinematic equations of the position layer, the kinematic equations of the velocity layer and the double-end inequality constraints of the velocity layer to design the repetitive motion control scheme of the mobile robot, and its expression is as follows:

Figure BDA0003708833300000068
Figure BDA0003708833300000068

Figure BDA0003708833300000069
Figure BDA0003708833300000069

Figure BDA00037088333000000610
Figure BDA00037088333000000610

其中，Dk+1表示重复运动性能指标的系数矩阵，dk+1表示重复运动性能指标的系数向量，Dk+1和dk+1的表达式分别如下所示：Among them, D k+1 represents the coefficient matrix of the repetitive motion performance index, d k+1 represents the coefficient vector of the repetitive motion performance indicator, and the expressions of D k+1 and d k+1 are respectively as follows:

Figure BDA00037088333000000611
Figure BDA00037088333000000611

Figure BDA0003708833300000071
Figure BDA0003708833300000071

Figure BDA0003708833300000072
Figure BDA0003708833300000072

其中，Ck+1表示与移动平台航向角相关的辅助矩阵，λ2、λ3和λ4均为正的设计参数；pconnection,k+1＝[xconnection,k+1；yconnectioh,k+1]为移动平台与机械臂之间的连接点，xconnection,k+1表示所述连接点在X轴的坐标，yconnection,k+1表示所述连接点在Y轴的坐标；pconnection(0)表示移动平台与机械臂之间的连接点的初始状态，φ(0)为移动平台的航向角的初始状态，θ(0)表示机械臂的关节角度向量的初始状态，a为左驱动轮和右驱动轮到两轮轴中点的距离；b为两轮轴中点到连接点pconnection,k+1的距离，γ为左驱动轮和右驱动轮的半径；0表示零矩阵，I表示单位矩阵。Wherein, C k+1 represents the auxiliary matrix related to the heading angle of the mobile platform, and λ 2 , λ 3 and λ 4 are all positive design parameters; p connection,k+1 =[x connection,k+1 ; y connectioh, k+1 ] is the connection point between the mobile platform and the mechanical arm, x connection, k+1 represents the coordinate of the connection point on the X axis, y connection, k+1 represents the coordinate of the connection point on the Y axis; p connection (0) represents the initial state of the connection point between the mobile platform and the manipulator, φ(0) is the initial state of the heading angle of the mobile platform, θ(0) represents the initial state of the joint angle vector of the manipulator, a is the distance from the left driving wheel and the right driving wheel to the midpoint of the two axles; b is the distance from the midpoint of the two axles to the connection point p connection,k+1 , γ is the radius of the left driving wheel and the right driving wheel; 0 represents the zero matrix , I represents the identity matrix.

S3.2：将所述重复运动控制方案转换为一个时变二次型优化问题，得到基于时变二次型优化问题的重复运动控制方案，其表达式如下所示：S3.2: Convert the repetitive motion control scheme into a time-varying quadratic optimization problem, and obtain a repetitive motion control scheme based on the time-varying quadratic optimization problem, and its expression is as follows:

Figure BDA0003708833300000073
Figure BDA0003708833300000073

s.t.Gk+1xk+1＝gk+1 stG k+1 x k+1 =g k+1

Hk+1xk+1≤hk+1 H k+1 x k+1 ≤h k+1

其中，T表示向量或矩阵的转置运算符，

Figure BDA0003708833300000074
为待求解的决策变量向量，
Figure BDA0003708833300000075
为目标函数中的正定对称系数矩阵，
Figure BDA0003708833300000076
为目标函数中的系数向量，
Figure BDA0003708833300000077
为等式约束中的行满秩系数矩阵，
Figure BDA0003708833300000078
为等式约束中的系数向量，
Figure BDA0003708833300000079
为不等式约束中的系数矩阵，
Figure BDA00037088333000000710
Figure BDA00037088333000000711
为不等式约束中的系数向量。where T represents the transpose operator of a vector or matrix,
Figure BDA0003708833300000074
is the decision variable vector to be solved,
Figure BDA0003708833300000075
is the positive definite symmetric coefficient matrix in the objective function,
Figure BDA0003708833300000076
is the coefficient vector in the objective function,
Figure BDA0003708833300000077
is the row full rank coefficient matrix in the equality constraint,
Figure BDA0003708833300000078
is the coefficient vector in the equality constraint,
Figure BDA0003708833300000079
is the coefficient matrix in the inequality constraint,
Figure BDA00037088333000000710
Figure BDA00037088333000000711
is a vector of coefficients in inequality constraints.

S4：基于零化神经动力学设计法则，将指数型惩罚策略引入所述基于时变二次型优化问题的移动机器人的重复运动控制方案，构建连续时间零化神经动力学模型：S4: Based on the design rule of zero neural dynamics, the exponential penalty strategy is introduced into the repetitive motion control scheme of the mobile robot based on the time-varying quadratic optimization problem, and the continuous time zero neural dynamics model is constructed:

S4.1：将指数型惩罚策略引入基于时变二次型优化问题的重复运动控制方案，消除所述重复运动控制方案中的不等式约束，得到仅带等式约束的重复运动控制方案，其表达式如下所示：S4.1: The exponential penalty strategy is introduced into the repetitive motion control scheme based on the time-varying quadratic optimization problem, the inequality constraints in the repetitive motion control scheme are eliminated, and the repetitive motion control scheme with only equality constraints is obtained. The expression The formula is as follows:

Figure BDA0003708833300000081
Figure BDA0003708833300000081

s.t.Gk+1xk+1＝gk+1 stG k+1 x k+1 =g k+1

其中，

Figure BDA0003708833300000082
为指数型惩罚函数，其表达式如下所示：in,
Figure BDA0003708833300000082
is an exponential penalty function whose expression is as follows:

Figure BDA0003708833300000083
Figure BDA0003708833300000083

其中，σi(xk+1,tk+1)＝-Hi,k+1xk+1+hi,k+1表示惩罚函数中的第i个辅助变量，Hi,k+1表示由矩阵Hk+1的第i行元素所构成的行向量，hi,k+1表示向量hk+1的第i个元素，μ和ν表示正的设计参数。Among them, σ i (x k+1, t k+1 )=-H i,k+1 x k+1 +h i,k+1 represents the ith auxiliary variable in the penalty function, H i,k+ 1 represents the row vector formed by the i-th row element of the matrix H k+1 , hi ,k+1 represents the i-th element of the vector h k+1 , and μ and ν represent positive design parameters.

S4.2：根据拉格朗日乘子法，将所述仅带等式约束的重复运动控制方案转换为一个时变方程组问题，其表达式如下所示：S4.2: According to the Lagrange multiplier method, the repetitive motion control scheme with only equality constraints is transformed into a time-varying equation system problem, and its expression is as follows:

Uk+1yk+1+ω(xk+1,tk+1)＝0U k+1 y k+1 +ω(x k+1 ,t k+1 )=0

其中，Uk+1、yk+1和ω(xk+1,tk+1)的表达式分别如下所示：Among them, the expressions of U k+1 , y k+1 and ω(x k+1 , t k+1 ) are respectively as follows:

Figure BDA0003708833300000084
Figure BDA0003708833300000084

Figure BDA0003708833300000085
Figure BDA0003708833300000085

Figure BDA0003708833300000086
Figure BDA0003708833300000086

其中，

Figure BDA0003708833300000087
为拉格朗日乘子向量。in,
Figure BDA0003708833300000087
is the Lagrange multiplier vector.

S4.3：将所述时变方程组问题进行连续化操作，得到连续时间时变方程组问题，其表达式如下所示：S4.3: Perform continuous operation on the time-varying equations problem to obtain the continuous-time time-varying equations problem, and its expression is as follows:

U(t)y(t)+ω(x(t),t)＝0U(t)y(t)+ω(x(t),t)=0

S4.4：将所述连续时间时变方程组问题的误差函数定义为ε(t)＝U(t)y(t)+ω(x(t),t)，并结合零化神经动力学设计法则

Figure BDA0003708833300000088
Figure BDA0003708833300000089
得到连续时间零化神经动力学模型，其表达式如下所示：S4.4: Define the error function of the continuous-time time-varying system of equations as ε(t)=U(t)y(t)+ω(x(t),t), and combine the zeroed neural dynamics design rules
Figure BDA0003708833300000088
Figure BDA0003708833300000089
The continuous-time zeroed neural dynamics model is obtained, and its expression is as follows:

Figure BDA00037088333000000810
Figure BDA00037088333000000810

其中，η为正的设计参数，用于调节收敛速率；

Figure BDA00037088333000000811
为由单调递增的奇激励函数所构成的阵列；M(x(t),t)表示系数矩阵，P(x(t),t)表示时间导数矩阵，u(x(t),t)表示时间导数向量，且M(x(t),t)、P(x(t),t)和u(x(t),t)的表达式分别如下所示：Among them, η is a positive design parameter used to adjust the convergence rate;
Figure BDA00037088333000000811
is an array composed of monotonically increasing odd excitation functions; M(x(t), t) represents the coefficient matrix, P(x(t), t) represents the time derivative matrix, and u(x(t), t) represents the time derivative vector, and the expressions for M(x(t),t), P(x(t),t) and u(x(t),t) are as follows:

Figure BDA0003708833300000091
Figure BDA0003708833300000091

Figure BDA0003708833300000092
Figure BDA0003708833300000092

Figure BDA0003708833300000093
Figure BDA0003708833300000093

S5：根据五步显式线性多步法则与所述连续时间零化神经动力学模型，构建离散时间零化神经动力学模型，并根据所述离散时间零化神经动力学模型计算移动机器人的控制变量。S5: According to the five-step explicit linear multi-step rule and the continuous-time zero-neural dynamics model, construct a discrete-time zero-neural-dynamic model, and calculate the control of the mobile robot according to the discrete-time zero-neural-dynamic model variable.

本实施例中，所述五步显式线性多步法则源于线性多步法，可以用于微分方程形式动力学系统的离散时间求解。基于五步显式线性多步法则的模型仅需使用当前和先前的五个离散时间点的结果及导数值，通过显式的线性组合形式，就能预测性地计算出下一离散时间点的解，而不需要利用到下一离散时间点的信息。五步显式线性多步法则涉及六个相邻的离散时间点，也即包含了五个递进步骤，所以称之为五步。而且由于五步显式线性多步法则不需要利用到下一离散时间点的信息，所以称之为显式。In this embodiment, the five-step explicit linear multi-step method is derived from the linear multi-step method, and can be used for discrete-time solution of a differential equation formal dynamic system. The model based on the five-step explicit linear multi-step rule only needs to use the results and derivative values of the current and previous five discrete time points, through an explicit linear combination form, can predictably calculate the next discrete time point. solution without using information up to the next discrete point in time. The five-step explicit linear multi-step rule involves six adjacent discrete time points, that is, contains five progressive steps, so it is called five steps. And because the five-step explicit linear multi-step rule does not need to use the information to the next discrete time point, it is called explicit.

本实施例中，五步显式线性多步法则的表达式如下所示：In this embodiment, the expression of the five-step explicit linear multi-step rule is as follows:

Figure BDA0003708833300000094
Figure BDA0003708833300000094

结合五步显式线性多步法则与所述连续时间零化神经动力学模型，得到离散时间零化神经动力学模型，其表达式如下所示：Combining the five-step explicit linear multi-step rule with the continuous-time zeroed neural dynamics model, the discrete-time zeroed neural dynamics model is obtained, and its expression is as follows:

Figure BDA0003708833300000095
Figure BDA0003708833300000095

其中，

Figure BDA0003708833300000096
为计算赋值运算符；
Figure BDA0003708833300000097
Figure BDA0003708833300000098
Figure BDA0003708833300000099
为离散时间零化神经动力学模型的截断误差，表示离散时间零化神经动力学模型具有六阶的计算精度。in,
Figure BDA0003708833300000096
assignment operator for computation;
Figure BDA0003708833300000097
Figure BDA0003708833300000098
Figure BDA0003708833300000099
is the truncation error of the discrete-time nulled neural dynamics model, indicating that the discrete-time nulled neural dynamics model has a sixth-order computational accuracy.

S6：将所述移动机器人的运动数据输入所述离散时间零化神经动力学模型，计算出移动机器人的控制变量。S6: Input the motion data of the mobile robot into the discrete-time neutralized neural dynamics model, and calculate the control variables of the mobile robot.

S7：根据所述控制变量对移动机器人进行重复运动控制。S7: Perform repetitive motion control on the mobile robot according to the control variable.

本实施例中，采用下位机控制器根据所述控制变量，驱动移动机器人执行重复运动控制任务。In this embodiment, the lower computer controller is used to drive the mobile robot to perform repetitive motion control tasks according to the control variables.

在具体实施过程中，为了保证上述离散时间神经动力学模型的收敛速率，选取幂-S形函数作为激励函数。In the specific implementation process, in order to ensure the convergence rate of the above discrete-time neural dynamics model, a power-S-shaped function is selected as the excitation function.

在进行数值实验时，移动机器人的末端执行器被期望跟踪一个复杂的利萨茹图形路径，其表达式如下所示：During numerical experiments, the end effector of a mobile robot is expected to trace a complex Lissajous graph path, which is expressed as follows:

Figure BDA0003708833300000101
Figure BDA0003708833300000101

其中，δ1、δ2和δ3为决定期望路径位置的三个常数。Among them, δ 1 , δ 2 and δ 3 are three constants that determine the desired path position.

设置时间步长

Figure BDA0003708833300000102
单次重复运动持续时间tfinal＝10s，左右驱动轮到两轮轴中点的距离a＝0.32m，两轮轴中点到移动平台与机械臂之间的连接点的距离b＝0.1m，左右驱动轮的半径γ＝0.1025m，其它参数设置为η＝25，μ＝0.004，ν＝300，σ1＝9，σ2＝0.1，λ1＝10，λ2＝λ3＝λ4＝30。set time step
Figure BDA0003708833300000102
The duration of a single repetitive motion is t final = 10s, the distance from the left and right driving wheels to the midpoint of the two axles a=0.32m, and the distance from the midpoint of the two axles to the connection point between the mobile platform and the robotic arm b=0.1m, the left and right drive The radius of the wheel is γ=0.1025 m, other parameters are set to η=25, μ=0.004, ν=300, σ 1 =9, σ 2 =0.1, λ 1 =10, λ 2 =λ 3 =λ 4 =30.

此外，移动平台与机械臂之间的连接点的初始位置pconnection(0)＝[xconnection(0)；yconnection(0)]＝[0；0]m，移动平台的初始航向角φ(0)＝0.1rad，移动机器人的组合角度向量Θ(0)＝[0,0,π/12,π/3,π/3,π/3,π/3,π/3]Trad。移动机器人的物理极限约束分别设置如下：In addition, the initial position of the connection point between the mobile platform and the manipulator p connection (0)=[x connection (0); y connection (0)]=[0; 0]m, the initial heading angle φ of the mobile platform ( 0)=0.1rad, the combined angle vector Θ(0)=[0,0,π/12,π/3,π/3,π/3,π/3,π/3] T rad of the mobile robot. The physical limit constraints of the mobile robot are respectively set as follows:

Θ+＝[∞,∞,0.524,2.356,1.088,6.283,6.283,6.283]TradΘ + = [∞,∞,0.524,2.356,1.088,6.283,6.283,6.283] T rad

Θ-＝-[∞,∞,0.524,0.175,6.283,6.283,6.283,6.283]TradΘ - =-[∞,∞,0.524,0.175,6.283,6.283,6.283,6.283] T rad

Figure BDA0003708833300000103
Figure BDA0003708833300000103

最后，通过利用该离散时间零化神经动力学模型计算得到控制变量，从而实现对含物理极限约束的移动机器人的高精度实时重复运动控制。Finally, the control variables are calculated by using the discrete-time zero neural dynamics model, so as to realize the high-precision real-time repetitive motion control of the mobile robot with physical limit constraints.

如图4所示，其为本发明的移动机器人的运动轨迹及末端执行器的实际轨迹与期望路径，从图4中可以看到末端执行器的实际轨迹与期望的利萨茹图形路径相吻合，而且移动机器人在完成路径跟踪任务后其末态与初态相重合。图5为本发明的移动平台与机械臂之间的连接点和移动平台的航向角图，图6为本发明的移动机器人的组合角度向量的元素轨迹图，从图5和图6可以看到，三个实现重复运动的重要变量，即移动平台与机械臂之间的连接点pconnection,k+1，移动平台的航向角φk+1以及移动机器人的组合角度向量Θk+1，最终都返回到它们的初态，从而保证在完成末端执行器闭合路径跟踪任务后，可以实现移动机器人协调重复运动控制的目的。此外，图7为本发明的移动机器人的组合速度向量的元素轨迹图，图8为本发明的移动机器人的末端执行器跟踪误差向量的元素轨迹图，从图7和图8可以看到，移动机器人的组合速度向量

Figure BDA0003708833300000111
的所有元素轨迹在任务执行结束后均收敛到零，而且末端执行器定位误差向量∈k+1＝ractual,k+1-rdesired,k+1的X、Y、Z轴分量均小于7×10-6m，显然末端执行器的跟踪精度足够高。另外，从图6和图7可以看到，移动机器人的组合角度向量和组合速度向量的所有元素都限制在给定的物理约束上下极限内。特别地，移动机器人的机械臂第三个关节角度θ3,k+1的时变轨迹多次到达物理极限的上界，但从未越过上界。显然，当第三个关节的角度θ3,k+1即将到达物理极限的上界时，基于指数型极限转换策略所得到的速度层双端不等式约束成功被激活，进而使得第三个关节的速度
Figure BDA0003708833300000112
进行减速以实现对物理极限的躲避。值得指出的是，离散时间零化神经动力学模型每次更新的平均计算时间约为9.3×10-4s，远小于所采用的时间步长
Figure BDA0003708833300000113
从而可以满足移动机器人严格实时运动控制的要求。总之，这些结果很好地证实了对含物理极限约束移动机器人的高精度实时重复运动控制。As shown in Figure 4, it is the motion trajectory of the mobile robot of the present invention and the actual trajectory and the desired path of the end effector. It can be seen from Figure 4 that the actual trajectory of the end effector is consistent with the expected Lissajous graphic path , and the final state of the mobile robot coincides with the initial state after completing the path tracking task. Fig. 5 is the connection point between the mobile platform and the mechanical arm of the present invention and the heading angle diagram of the mobile platform, Fig. 6 is the element trajectory diagram of the combined angle vector of the mobile robot of the present invention, as can be seen from Fig. 5 and Fig. 6 , three important variables to realize repetitive motion, namely the connection point p connection,k+1 between the mobile platform and the manipulator, the heading angle φ k+1 of the mobile platform and the combined angle vector Θ k+1 of the mobile robot, and finally All return to their initial state, thus ensuring that the purpose of coordinated repetitive motion control of the mobile robot can be achieved after the end-effector closed path tracking task is completed. In addition, FIG. 7 is the element trajectory diagram of the combined velocity vector of the mobile robot of the present invention, and FIG. 8 is the element trajectory diagram of the end effector tracking error vector of the mobile robot of the present invention. As can be seen from FIG. 7 and FIG. Combined velocity vector of the robot
Figure BDA0003708833300000111
All element trajectories of , converge to zero after the execution of the task, and the end effector positioning error vector ∈ k+1 =r actual,k+1 -r desired, the X, Y, Z axis components of k+1 are all less than 7 ×10 -6 m, obviously the tracking accuracy of the end effector is high enough. In addition, it can be seen from Figures 6 and 7 that all elements of the combined angle vector and combined velocity vector of the mobile robot are constrained within the upper and lower limits of the given physical constraints. In particular, the time-varying trajectory of the third joint angle θ3 ,k+1 of the robotic arm of the mobile robot reaches the upper bound of the physical limit many times, but never crosses the upper bound. Obviously, when the angle θ 3,k+1 of the third joint is about to reach the upper bound of the physical limit, the double-ended inequality constraint of the velocity layer obtained based on the exponential limit transformation strategy is successfully activated, which makes the third joint’s speed
Figure BDA0003708833300000112
Slow down to avoid physical limits. It is worth pointing out that the average computation time of each update of the discrete-time zero-neutral neural dynamics model is about 9.3 × 10 s, which is much smaller than the adopted time step
Figure BDA0003708833300000113
Therefore, it can meet the requirements of strict real-time motion control of mobile robots. Taken together, these results provide a good demonstration of high-accuracy real-time repetitive motion control of mobile robots with physical limit constraints.

实施例3Example 3

请参阅图9，本实施例提出一种基于离散时间神经动力学的移动机器人重复运动控制系统，包括：Referring to FIG. 9 , this embodiment proposes a repetitive motion control system for a mobile robot based on discrete-time neural dynamics, including:

采集模块，用于采集移动机器人的运动数据。The acquisition module is used to collect the motion data of the mobile robot.

第一构建模块，用于构建移动机器人的位置层运动学方程、速度层运动学方程和物理极限约束，并将所述物理极限约束转换为速度层双端不等式约束。The first building module is used to construct the position layer kinematic equation, the velocity layer kinematic equation and the physical limit constraint of the mobile robot, and convert the physical limit constraint into the velocity layer double-ended inequality constraint.

本实施例中，根据更新索引和时间步长确定离散时间点，并在所述离散时间点构建位置层运动学方程。In this embodiment, discrete time points are determined according to the update index and the time step, and the kinematic equation of the position layer is constructed at the discrete time points.

本实施例中，根据所述位置层运动学方程，构建速度层运动学方程。In this embodiment, the kinematic equation of the velocity layer is constructed according to the kinematic equation of the position layer.

本实施例中，通过离散时变双端不等式组，构建物理极限约束。In this embodiment, physical limit constraints are constructed by discrete time-varying two-ended inequality groups.

本实施例中，基于指数型极限转换策略，将所述物理极限约束转换为速度层双端不等式约束。In this embodiment, based on an exponential limit conversion strategy, the physical limit constraint is converted into a velocity layer double-ended inequality constraint.

第二构建模块，用于结合所述位置层运动学方程、速度层运动学方程和速度层双端不等式约束，构建基于时变二次型优化问题的移动机器人的重复运动控制方案。The second building module is used for constructing a repetitive motion control scheme of the mobile robot based on the time-varying quadratic optimization problem by combining the position layer kinematic equations, the velocity layer kinematic equations and the velocity layer double-ended inequality constraints.

本实施例中，结合位置层运动学方程、速度层运动学方程和速度层双端不等式约束，设计移动机器人的重复运动控制方案。In this embodiment, the repetitive motion control scheme of the mobile robot is designed by combining the kinematic equations of the position layer, the kinematic equations of the velocity layer, and the double-ended inequality constraints of the velocity layer.

本实施例中，将所述重复运动控制方案转换为一个时变二次型优化问题，得到基于时变二次型优化问题的重复运动控制方案。In this embodiment, the repetitive motion control scheme is converted into a time-varying quadratic optimization problem, and a repetitive motion control scheme based on the time-varying quadratic optimization problem is obtained.

第三构建模块，用于基于零化神经动力学设计法则，将指数型惩罚策略引入所述基于时变二次型优化问题的移动机器人的重复运动控制方案，构建连续时间零化神经动力学模型。The third building block is used to introduce the exponential penalty strategy into the repetitive motion control scheme of the mobile robot based on the time-varying quadratic optimization problem based on the design rule of zero neural dynamics, and construct the continuous time zero neural dynamics model .

本实施例中，将指数型惩罚策略引入基于时变二次型优化问题的重复运动控制方案，消除所述重复运动控制方案中的不等式约束，得到仅带等式约束的重复运动控制方案。In this embodiment, an exponential penalty strategy is introduced into the repetitive motion control scheme based on the time-varying quadratic optimization problem, the inequality constraints in the repetitive motion control scheme are eliminated, and a repetitive motion control scheme with only equality constraints is obtained.

根据拉格朗日乘子法，将所述仅带等式约束的重复运动控制方案转换为一个时变方程组问题。将所述时变方程组问题进行连续化操作，得到连续时间时变方程组问题，并给出连续时间时变方程组问题的误差函数，结合零化神经动力学设计法则，得到连续时间零化神经动力学模型。According to the Lagrangian multiplier method, the repetitive motion control scheme with only equality constraints is transformed into a time-varying system of equations problem. The continuous operation of the time-varying equations problem is carried out to obtain the continuous-time time-varying equations problem, and the error function of the continuous-time time-varying equations problem is given. Combined with the design rule of nulling neural dynamics, the continuous-time zeroing is obtained. Neurodynamic Models.

第四构建模块，用于根据五步显式线性多步法则与所述连续时间零化神经动力学模型，构建离散时间零化神经动力学模型，并根据所述离散时间零化神经动力学模型计算移动机器人的控制变量。a fourth building block for constructing a discrete-time nulled neural dynamics model according to the five-step explicit linear multi-step rule and the continuous-time nulled neural dynamics model, and based on the discrete-time nulled neural dynamics model Calculate the control variables for the mobile robot.

计算模块，用于根据所述移动机器人的运动数据和所述离散时间零化神经动力学模型，计算出移动机器人的控制变量。The calculation module is configured to calculate the control variables of the mobile robot according to the motion data of the mobile robot and the discrete-time zero-neural dynamics model.

控制模块，用于根据所述控制变量对移动机器人进行重复运动控制。The control module is used for performing repetitive motion control on the mobile robot according to the control variable.

本实施例中，采用下位机控制器根据所述控制变量，驱动移动机器人执行重复运动控制任务。In this embodiment, the lower computer controller is used to drive the mobile robot to perform repetitive motion control tasks according to the control variables.

通过构建移动机器人的位置层运动学方程、速度层运动学方程和速度层双端不等式约束，设计出基于时变二次型优化问题的移动机器人的重复运动控制方案，并在所述移动机器人的重复运动控制方案的基础上引入指数型惩罚策略和五步显式线性多步法则，构建出离散时间零化神经动力学模型，能够在每个计算时间间隔中，仅需基于当前和先前的已知数据信息并通过一次更新计算，就能准确预测出下一时间点的求解结果，从而实现对含物理极限约束的移动机器人高精度实时重复运动控制，有效消除了非重复运动现象，有力提升了移动机器人的运动实时性、路径跟踪精度以及物理极限约束处理能力。By constructing the kinematic equations of the position layer, the kinematic equations of the velocity layer and the double-ended inequality constraints of the velocity layer of the mobile robot, a repetitive motion control scheme of the mobile robot based on the time-varying quadratic optimization problem is designed. On the basis of the repetitive motion control scheme, an exponential penalty strategy and a five-step explicit linear multi-step rule are introduced to construct a discrete-time zero-neutral neural dynamics model, which can only be based on the current and previous By knowing the data information and updating the calculation once, the solution result at the next time point can be accurately predicted, so as to realize the high-precision real-time repetitive motion control of the mobile robot with physical limit constraints, effectively eliminate the phenomenon of non-repetitive motion, and effectively improve the The real-time motion, path tracking accuracy and physical limit constraint processing capability of mobile robots.

附图中描述位置关系的用语仅用于示例性说明，不能理解为对本专利的限制；The terms describing the positional relationship in the accompanying drawings are only used for exemplary illustration, and should not be construed as a limitation on this patent;

显然，本发明的上述实施例仅仅是为清楚地说明本发明所做的举例，而并非是对本发明的实施方式的限定。对于所属领域的普通技术人员来说，在上述说明的基础上还可以做出其它不同形式的变化或变动。这里无需也无法对所有的实施方式予以穷举。凡在本发明的精神和原则之内所作的任何修改、等同替换和改进等，均应包含在本发明权利要求的保护范围之内。Obviously, the above-mentioned embodiments of the present invention are only examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. For those of ordinary skill in the art, changes or modifications in other different forms can also be made on the basis of the above description. There is no need and cannot be exhaustive of all implementations here. Any modifications, equivalent replacements and improvements made within the spirit and principle of the present invention shall be included within the protection scope of the claims of the present invention.

Claims (10)

1.基于离散时间神经动力学的移动机器人重复运动控制方法，其特征在于，包括：1. a mobile robot repetitive motion control method based on discrete-time neural dynamics, is characterized in that, comprises: S1：采集移动机器人的运动数据；S1: collect the motion data of the mobile robot; S2：构建移动机器人的位置层运动学方程、速度层运动学方程和物理极限约束，并将所述物理极限约束转换为速度层双端不等式约束；S2: constructing the position layer kinematic equation, velocity layer kinematic equation and physical limit constraint of the mobile robot, and converting the physical limit constraint into a velocity layer double-ended inequality constraint; S3：结合所述位置层运动学方程、速度层运动学方程和速度层双端不等式约束，构建基于时变二次型优化问题的移动机器人的重复运动控制方案；S3: Construct a repetitive motion control scheme for a mobile robot based on a time-varying quadratic optimization problem by combining the position layer kinematic equations, the velocity layer kinematic equations and the velocity layer double-end inequality constraints; S4：基于零化神经动力学设计法则，将指数型惩罚策略引入所述基于时变二次型优化问题的移动机器人的重复运动控制方案，构建连续时间零化神经动力学模型；S4: Based on the design rule of zero neural dynamics, an exponential penalty strategy is introduced into the repetitive motion control scheme of the mobile robot based on the time-varying quadratic optimization problem, and a continuous time zero neural dynamic model is constructed; S5：根据五步显式线性多步法则与所述连续时间零化神经动力学模型，构建离散时间零化神经动力学模型；S5: According to the five-step explicit linear multi-step rule and the continuous-time zero-neural dynamics model, construct a discrete-time zero-neural dynamics model; S6：将所述移动机器人的运动数据输入所述离散时间零化神经动力学模型，计算出移动机器人的控制变量；S6: Input the motion data of the mobile robot into the discrete-time neutralized neural dynamics model, and calculate the control variables of the mobile robot; S7：根据所述控制变量对移动机器人进行重复运动控制。S7: Perform repetitive motion control on the mobile robot according to the control variable. 2.根据权利要求1所述的基于离散时间神经动力学的移动机器人重复运动控制方法，其特征在于，S2的具体步骤包括：2. the mobile robot repetitive motion control method based on discrete-time neural dynamics according to claim 1, is characterized in that, the concrete steps of S2 comprise: S2.1：确定移动机器人运动的离散时间点，并在所述离散时间点构建位置层运动学方程；S2.1: Determine the discrete time points of the motion of the mobile robot, and construct the kinematic equation of the position layer at the discrete time points; S2.2：根据所述位置层运动学方程，构建速度层运动学方程；S2.2: According to the kinematic equation of the position layer, construct the kinematic equation of the velocity layer; S2.3：通过离散时变双端不等式组，构建物理极限约束；S2.3: Construct physical limit constraints through discrete time-varying double-ended inequalities; S2.4：基于指数型极限转换策略，将所述物理极限约束转换为速度层双端不等式约束。S2.4: Based on an exponential limit transformation strategy, transform the physical limit constraint into a velocity layer double-ended inequality constraint. 3.根据权利要求2所述的基于离散时间神经动力学的移动机器人重复运动控制方法，其特征在于，3. the mobile robot repetitive motion control method based on discrete-time neural dynamics according to claim 2, is characterized in that, 在离散时间点
Figure FDA0003708833290000011
中，构建位置层运动学方程，其表达式如下所示：at discrete points in time
Figure FDA0003708833290000011
, construct the kinematic equation of the position layer, and its expression is as follows: Φ(Θk+1)＝ractual,k+1 Φ(Θ k+1 )=r actual,k+1
Figure FDA0003708833290000021
Figure FDA0003708833290000021
 其中，k为更新索引，
Figure FDA0003708833290000022
为时间步长，tfinal为整个计算时间区间的最终时间点，Φ(·):
Figure FDA0003708833290000023
为非线性映射函数阵列，
Figure FDA0003708833290000024
为实数集合，Θk+1为移动机器人的组合角度向量，ractual,k+1为末端执行器的实际位置向量，
Figure FDA0003708833290000025
为移动平台左驱动轮和右驱动轮的旋转角度集，θk+1为固定在移动平台上六关节冗余度机械臂的关节角度向量；Among them, k is the update index,
Figure FDA0003708833290000022
is the time step, t final is the final time point of the entire calculation time interval, Φ( ):
Figure FDA0003708833290000023
is an array of nonlinear mapping functions,
Figure FDA0003708833290000024
is a set of real numbers, Θ k+1 is the combined angle vector of the mobile robot, r actual,k+1 is the actual position vector of the end effector,
Figure FDA0003708833290000025
is the rotation angle set of the left driving wheel and the right driving wheel of the mobile platform, θ k+1 is the joint angle vector of the six-joint redundant manipulator fixed on the mobile platform; 所述速度层运动学方程的表达式如下所示：The expression of the velocity layer kinematic equation is as follows:
Figure FDA0003708833290000026
Figure FDA0003708833290000026
Figure FDA0003708833290000027
Figure FDA0003708833290000027
 其中，φk+1为移动平台的航向角，
Figure FDA0003708833290000028
为移动机器人的组合速度向量，
Figure FDA0003708833290000029
为移动平台左驱动轮和右驱动轮的旋转速度集，
Figure FDA00037088332900000210
为固定在移动平台上六关节冗余度机械臂的关节速度向量，J(φk+1,θk+1)为与雅可比相关的矩阵；ζk+1为含末端执行器位置误差反馈的向量，
Figure FDA00037088332900000211
为末端执行器的期望路径的时间导数，rdesired,k+1为末端执行器的期望路径，λ1为可设定的参数；Among them, φ k+1 is the heading angle of the mobile platform,
Figure FDA0003708833290000028
is the combined velocity vector of the mobile robot,
Figure FDA0003708833290000029
is the rotation speed set of the left and right drive wheels of the mobile platform,
Figure FDA00037088332900000210
is the joint velocity vector of the six-joint redundant manipulator fixed on the mobile platform, J(φ k+1 , θ k+1 ) is the Jacobian-related matrix; ζ k+1 is the position error feedback including the end effector a vector of ,
Figure FDA00037088332900000211
is the time derivative of the desired path of the end effector, r desired,k+1 is the desired path of the end effector, and λ 1 is a parameter that can be set; 所述物理极限约束的表达式如下所示：The expression for the physical limit constraint is as follows:
Figure FDA00037088332900000212
Figure FDA00037088332900000212
 其中，Θ-表示移动机器人的组合角度向量的下限，Θ+表示移动机器人的组合角度向量的上限，
Figure FDA00037088332900000213
表示移动机器人的组合速度向量的下限，
Figure FDA00037088332900000214
表示移动机器人的组合速度向量的上限；where Θ - represents the lower bound of the combined angle vector of the mobile robot, Θ + represents the upper bound of the combined angle vector of the mobile robot,
Figure FDA00037088332900000213
represents the lower bound of the combined velocity vector of the mobile robot,
Figure FDA00037088332900000214
represents the upper limit of the combined velocity vector of the mobile robot; 基于指数型极限转换策略，将所述物理极限约束转换为速度层双端不等式约束，其表达式如下所示：Based on the exponential limit transformation strategy, the physical limit constraint is transformed into a velocity layer double-ended inequality constraint, and its expression is as follows:
Figure FDA00037088332900000215
Figure FDA00037088332900000215
 其中，αk+1表示双端不等式约束的下极限，βk+1表示双端不等式约束的上极限，αk+1的第i个元素αi,j+1(i＝1,2,…,n)，以及βk+1的第i个元素βi,k+1(i＝1,2,…,n)，分别有如下定义：Among them, α k+1 represents the lower limit of the double-ended inequality constraint, β k+1 represents the upper limit of the double-ended inequality constraint, and the i-th element of α k+1 α i,j+1 (i=1,2, …,n), and the i-th element β i,k+1 (i=1,2,…,n) of β k +1, respectively, have the following definitions:
Figure FDA00037088332900000216
Figure FDA00037088332900000216
 其中，exp(·)表示指数函数；σ1＞0为可设定的参数，用于调节减速幅度；参数σ2∈(0,1)为可设定的参数，用于调节需要减速的临界区域范围，即
Figure FDA00037088332900000217
和
Figure FDA00037088332900000218
Among them, exp( ) represents an exponential function; σ 1 > 0 is a settable parameter for adjusting the deceleration amplitude; parameter σ 2 ∈(0,1) is a settable parameter for adjusting the critical value of deceleration area, i.e.
Figure FDA00037088332900000217
and
Figure FDA00037088332900000218
 4.根据权利要求3所述的基于离散时间神经动力学的移动机器人重复运动控制方法，其特征在于，S3的具体步骤包括：4. the mobile robot repetitive motion control method based on discrete-time neural dynamics according to claim 3, is characterized in that, the concrete steps of S3 comprise: S3.1：结合位置层运动学方程、速度层运动学方程和速度层双端不等式约束，设计移动机器人的重复运动控制方案，其表达式如下所示：S3.1: Combine the kinematic equations of the position layer, the kinematic equations of the velocity layer and the double-end inequality constraints of the velocity layer to design the repetitive motion control scheme of the mobile robot, and its expression is as follows:
Figure FDA0003708833290000031
Figure FDA0003708833290000031
Figure FDA0003708833290000032
Figure FDA0003708833290000032
Figure FDA0003708833290000033
Figure FDA0003708833290000033
 其中，Dk+1表示重复运动性能指标的系数矩阵，dk+1表示重复运动性能指标的系数向量，Dk+1和dk+1的表达式分别如下所示：Among them, D k+1 represents the coefficient matrix of the repetitive motion performance index, d k+1 represents the coefficient vector of the repetitive motion performance indicator, and the expressions of D k+1 and d k+1 are respectively as follows:
Figure FDA0003708833290000034
Figure FDA0003708833290000034
Figure FDA0003708833290000035
Figure FDA0003708833290000035
Figure FDA0003708833290000036
Figure FDA0003708833290000036
 其中，Ck+1表示与移动平台航向角相关的辅助矩阵，λ2、λ3和λ4均为正的设计参数；pconnection,k+1＝[xconnection,k+1；yconnection,k+1]为移动平台与机械臂之间的连接点，xconnection,k+1表示所述连接点在X轴的坐标，yconnection,k+1表示所述连接点在Y轴的坐标；pconnection(0)表示移动平台与机械臂之间的连接点的初始状态，φ(0)为移动平台的航向角的初始状态，θ(0)表示机械臂的关节角度向量的初始状态，a为左驱动轮和右驱动轮到两轮轴中点的距离；b为两轮轴中点到连接点pconnection,k+1的距离，γ为左驱动轮和右驱动轮的半径；O表示零矩阵，I表示单位矩阵；Among them, C k+1 represents the auxiliary matrix related to the heading angle of the mobile platform, and λ 2 , λ 3 and λ 4 are all positive design parameters; p connection,k+1 =[x connection,k+1 ; y connection, k+1 ] is the connection point between the mobile platform and the mechanical arm, x connection, k+1 represents the coordinate of the connection point on the X axis, y connection, k+1 represents the coordinate of the connection point on the Y axis; p connection (0) represents the initial state of the connection point between the mobile platform and the manipulator, φ(0) is the initial state of the heading angle of the mobile platform, θ(0) represents the initial state of the joint angle vector of the manipulator, a is the distance from the left driving wheel and the right driving wheel to the midpoint of the two axles; b is the distance from the midpoint of the two axles to the connection point p connection,k+1 , γ is the radius of the left driving wheel and the right driving wheel; O represents the zero matrix , I represents the identity matrix; S3.2：将所述重复运动控制方案转换为一个时变二次型优化问题，得到基于时变二次型优化问题的重复运动控制方案，其表达式如下所示：S3.2: Convert the repetitive motion control scheme into a time-varying quadratic optimization problem, and obtain a repetitive motion control scheme based on the time-varying quadratic optimization problem, and its expression is as follows:
Figure FDA0003708833290000037
Figure FDA0003708833290000037
 s.t.Gk+1xk+1＝gk+1 stG k+1 x k+1 =g k+1 Hk+1xk+1≤hk+1 H k+1 x k+1 ≤h k+1 其中，T表示向量或矩阵的转置运算符，
Figure FDA0003708833290000038
为待求解的决策变量向量，
Figure FDA0003708833290000041
为目标函数中的正定对称系数矩阵，
Figure FDA0003708833290000042
为目标函数中的系数向量，
Figure FDA0003708833290000043
为等式约束中的行满秩系数矩阵，
Figure FDA0003708833290000044
为等式约束中的系数向量，
Figure FDA0003708833290000045
为不等式约束中的系数矩阵，
Figure FDA0003708833290000046
Figure FDA0003708833290000047
为不等式约束中的系数向量。where T represents the transpose operator of a vector or matrix,
Figure FDA0003708833290000038
is the decision variable vector to be solved,
Figure FDA0003708833290000041
is the positive definite symmetric coefficient matrix in the objective function,
Figure FDA0003708833290000042
is the coefficient vector in the objective function,
Figure FDA0003708833290000043
is the row full rank coefficient matrix in the equality constraint,
Figure FDA0003708833290000044
is the coefficient vector in the equality constraint,
Figure FDA0003708833290000045
is the coefficient matrix in the inequality constraint,
Figure FDA0003708833290000046
Figure FDA0003708833290000047
is a vector of coefficients in inequality constraints. 5.根据权利要求4所述的基于离散时间神经动力学的移动机器人重复运动控制方法，其特征在于，S4的具体步骤包括：5. the mobile robot repetitive motion control method based on discrete-time neural dynamics according to claim 4, is characterized in that, the concrete steps of S4 comprise: S4.1：将指数型惩罚策略引入基于时变二次型优化问题的重复运动控制方案，消除所述重复运动控制方案中的不等式约束，得到仅带等式约束的重复运动控制方案，其表达式如下所示：S4.1: The exponential penalty strategy is introduced into the repetitive motion control scheme based on the time-varying quadratic optimization problem, the inequality constraints in the repetitive motion control scheme are eliminated, and the repetitive motion control scheme with only equality constraints is obtained. The expression The formula is as follows:
Figure FDA0003708833290000048
Figure FDA0003708833290000048
 s.t.Gk+1xk+1＝gk+1 stG k+1 x k+1 =g k+1 其中，
Figure FDA0003708833290000049
为指数型惩罚函数，其表达式如下所示：in,
Figure FDA0003708833290000049
is an exponential penalty function whose expression is as follows:
Figure FDA00037088332900000410
Figure FDA00037088332900000410
 其中，σi(xk+1,tk+1)＝-Hi,k+1xk+1+hi,k+1表示惩罚函数中的第i个辅助变量，Hi,k+1表示由矩阵Hk+1的第i行元素所构成的行向量，hi,k+1表示向量hk+1的第i个元素，μ和ν表示正的设计参数；Among them, σ i (x k+1 ,t k+1 )=-H i,k+1 x k+1 +h i,k+1 represents the ith auxiliary variable in the penalty function, H i,k+ 1 represents the row vector formed by the i-th row element of the matrix H k+1 , h i,k+1 represents the i-th element of the vector h k+1 , μ and ν represent positive design parameters; S4.2：根据拉格朗日乘子法，将所述仅带等式约束的重复运动控制方案转换为一个时变方程组问题，其表达式如下所示：S4.2: According to the Lagrange multiplier method, the repetitive motion control scheme with only equality constraints is transformed into a time-varying equation system problem, and its expression is as follows: Uk+1yk+1+ω(xk+1,tk+1)＝0U k+1 y k+1 +ω(x k+1 ,t k+1 )=0 其中，Uk+1、yk+1和ω(xk+1,tk+1)的表达式分别如下所示：Among them, the expressions of U k+1 , y k+1 and ω(x k+1 , t k+1 ) are respectively as follows:
Figure FDA00037088332900000411
Figure FDA00037088332900000411
Figure FDA00037088332900000412
Figure FDA00037088332900000412
Figure FDA00037088332900000413
Figure FDA00037088332900000413
 其中，
Figure FDA00037088332900000414
为拉格朗日乘子向量；in,
Figure FDA00037088332900000414
is the Lagrange multiplier vector; S4.3：将所述时变方程组问题进行连续化操作，得到连续时间时变方程组问题，其表达式如下所示：S4.3: Perform continuous operation on the time-varying equations problem to obtain the continuous-time time-varying equations problem, and its expression is as follows: U(t)y(t)+ω(x(t),t)＝0U(t)y(t)+ω(x(t),t)=0 S4.4：将所述连续时间时变方程组问题的误差函数定义为ε(t)＝U(t)y(t)+ω(x(t),t)，并结合零化神经动力学设计法则
Figure FDA0003708833290000051
Figure FDA0003708833290000052
得到连续时间零化神经动力学模型，其表达式如下所示：S4.4: Define the error function of the continuous-time time-varying system of equations as ε(t)=U(t)y(t)+ω(x(t),t), and combine the zeroed neural dynamics design rules
Figure FDA0003708833290000051
Figure FDA0003708833290000052
The continuous-time zeroed neural dynamics model is obtained, and its expression is as follows:
Figure FDA0003708833290000053
Figure FDA0003708833290000053
 其中，η为正的设计参数，用于调节收敛速率；Ψ(·):
Figure FDA0003708833290000054
为由单调递增的奇激励函数所构成的阵列；M(x(t),t)表示系数矩阵，P(x(t),t)表示时间导数矩阵，u(x(t),t)表示时间导数向量，且M(x(t),t)、P(x(t),t)和u(x(t),t)的表达式分别如下所示：Among them, η is a positive design parameter used to adjust the convergence rate; Ψ( ):
Figure FDA0003708833290000054
is an array composed of monotonically increasing odd excitation functions; M(x(t), t) represents the coefficient matrix, P(x(t), t) represents the time derivative matrix, and u(x(t), t) represents the time derivative vector, and the expressions for M(x(t),t), P(x(t),t) and u(x(t),t) are respectively as follows:
Figure FDA0003708833290000055
Figure FDA0003708833290000055
Figure FDA0003708833290000056
Figure FDA0003708833290000056
Figure FDA0003708833290000057
Figure FDA0003708833290000057
 6.根据权利要求5所述的基于离散时间神经动力学的移动机器人重复运动控制方法，其特征在于，S5中，根据五步显式线性多步法则与所述连续时间零化神经动力学模型，构建离散时间零化神经动力学模型，其表达式如下所示：6. The method for controlling repetitive motion of a mobile robot based on discrete-time neural dynamics according to claim 5, characterized in that, in S5, according to five-step explicit linear multi-step rule and the continuous-time zero neural dynamics model , construct a discrete-time zero-neutral neural dynamics model whose expression is as follows:
Figure FDA0003708833290000058
Figure FDA0003708833290000058
 其中，
Figure FDA0003708833290000059
为计算赋值运算符；
Figure FDA00037088332900000510
Figure FDA00037088332900000511
Figure FDA00037088332900000512
为离散时间零化神经动力学模型的截断误差，表示离散时间零化神经动力学模型具有六阶的计算精度。in,
Figure FDA0003708833290000059
assignment operator for computation;
Figure FDA00037088332900000510
Figure FDA00037088332900000511
Figure FDA00037088332900000512
is the truncation error of the discrete-time nulled neural dynamics model, indicating that the discrete-time nulled neural dynamics model has a sixth-order computational accuracy. 7.根据权利要求1～6任一项所述的基于离散时间神经动力学的移动机器人重复运动控制方法，其特征在于，S7中，采用下位机控制器根据所述控制变量，驱动移动机器人执行重复运动控制任务。7. The method for controlling repetitive motion of a mobile robot based on discrete-time neural dynamics according to any one of claims 1 to 6, wherein in S7, a lower computer controller is used to drive the mobile robot to execute according to the control variable. Repeat the motion control task. 8.基于离散时间神经动力学的移动机器人重复运动控制系统，应用于权利要求1～7任一项所述的基于离散时间神经动力学的移动机器人重复运动控制方法，其特征在于，包括：8. A mobile robot repetitive motion control system based on discrete-time neural dynamics, applied to the discrete-time neural dynamics-based repetitive motion control method for a mobile robot according to any one of claims 1 to 7, characterized in that, comprising: 采集模块，用于采集移动机器人的运动数据；The acquisition module is used to collect the motion data of the mobile robot; 第一构建模块，用于构建移动机器人的位置层运动学方程、速度层运动学方程和物理极限约束，并将所述物理极限约束转换为速度层双端不等式约束；The first building module is used to construct the position layer kinematic equations, velocity layer kinematic equations and physical limit constraints of the mobile robot, and convert the physical limit constraints into velocity layer double-ended inequality constraints; 第二构建模块，用于结合所述位置层运动学方程、速度层运动学方程和速度层双端不等式约束，构建基于时变二次型优化问题的移动机器人的重复运动控制方案；The second building module is used for constructing the repetitive motion control scheme of the mobile robot based on the time-varying quadratic optimization problem by combining the kinematic equations of the position layer, the kinematic equations of the velocity layer and the double-ended inequality constraints of the velocity layer; 第三构建模块，用于基于零化神经动力学设计法则，将指数型惩罚策略引入所述基于时变二次型优化问题的移动机器人的重复运动控制方案，构建连续时间零化神经动力学模型；The third building block is used to introduce the exponential penalty strategy into the repetitive motion control scheme of the mobile robot based on the time-varying quadratic optimization problem based on the design rule of zero neural dynamics, and construct the continuous time zero neural dynamics model ; 第四构建模块，用于根据五步显式线性多步法则与所述连续时间零化神经动力学模型，构建离散时间零化神经动力学模型；a fourth building module for constructing a discrete-time zero-neural dynamics model according to the five-step explicit linear multi-step rule and the continuous-time zero-neural dynamics model; 计算模块，用于根据所述移动机器人的运动数据和所述离散时间零化神经动力学模型，计算出移动机器人的控制变量；a calculation module, used for calculating the control variables of the mobile robot according to the motion data of the mobile robot and the discrete-time zeroed neural dynamics model; 控制模块，用于根据所述控制变量对移动机器人进行重复运动控制。The control module is used to control the repetitive motion of the mobile robot according to the control variable. 9.一种电子设备，其特征在于，包括处理器以及存储器；所述存储器用于存储程序；所述处理器执行所述程序实现如权利要求1～7中任一项所述的基于离散时间神经动力学的移动机器人重复运动控制方法。9 . An electronic device, characterized in that it comprises a processor and a memory; the memory is used to store a program; the processor executes the program to implement the discrete-time-based method according to any one of claims 1 to 7 A neurodynamic approach to repetitive motion control of mobile robots. 10.一种计算机可读存储介质，其特征在于，所述存储介质存储有程序，所述程序被处理器执行实现如权利要求1～7中任一项所述的基于离散时间神经动力学的移动机器人重复运动控制方法。10. A computer-readable storage medium, characterized in that the storage medium stores a program, and the program is executed by a processor to realize the discrete-time neural dynamics-based algorithm according to any one of claims 1 to 7. 11 . A mobile robot repetitive motion control method.
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