+

CN113021334B - Robot control method with optimal energy - Google Patents

Robot control method with optimal energy Download PDF

Info

Publication number
CN113021334B
CN113021334B CN201911371228.0A CN201911371228A CN113021334B CN 113021334 B CN113021334 B CN 113021334B CN 201911371228 A CN201911371228 A CN 201911371228A CN 113021334 B CN113021334 B CN 113021334B
Authority
CN
China
Prior art keywords
robot
state
current
control torque
acceleration
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201911371228.0A
Other languages
Chinese (zh)
Other versions
CN113021334A (en
Inventor
徐智浩
唐观荣
吴鸿敏
周雪峰
李帅
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Guangdong Institute of Intelligent Manufacturing
Original Assignee
Guangdong Institute of Intelligent Manufacturing
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Guangdong Institute of Intelligent Manufacturing filed Critical Guangdong Institute of Intelligent Manufacturing
Priority to CN201911371228.0A priority Critical patent/CN113021334B/en
Publication of CN113021334A publication Critical patent/CN113021334A/en
Application granted granted Critical
Publication of CN113021334B publication Critical patent/CN113021334B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • 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
    • B25J9/1633—Programme controls characterised by the control loop compliant, force, torque control, e.g. combined with position 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
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • B25J9/1605—Simulation of manipulator lay-out, design, modelling of manipulator

Landscapes

  • Engineering & Computer Science (AREA)
  • Robotics (AREA)
  • Mechanical Engineering (AREA)
  • Automation & Control Theory (AREA)
  • Feedback Control In General (AREA)
  • Manipulator (AREA)

Abstract

本发明公开了一种能量最优的机器人控制方法，所述方法包括：初始化机器人的状态变量以及机器人的控制力矩；通过机器人传感器读取到当前机器人状态；通过计算得出当前时刻的雅克比矩阵和参考加速度；将所述当前机器人状态的不等式约束在加速度层统一进行描述，并确定上界和下界；对待优化函数进行凸优化处理，并得到最终的约束优化模型；采用动态神经网络对所述当前机器人状态以及控制力矩进行更新，得到更新后的机器人状态以及控制力矩；基于所述更新后的机器人状态以及控制力矩，判断机器人的工作时间是否大于预设时间；若否，执行所述控制力矩，并返回至所述通过机器人传感器读取到当前机器人状态。在本发明实施中，该方法能量最优，且效率高。

Figure 201911371228

The invention discloses a robot control method with optimal energy. The method includes: initializing the state variables of the robot and the control torque of the robot; reading the current robot state through the robot sensor; obtaining the Jacobian matrix at the current moment through calculation and reference acceleration; describe the inequality constraints of the current robot state uniformly in the acceleration layer, and determine the upper and lower bounds; perform convex optimization processing on the function to be optimized, and obtain the final constraint optimization model; use dynamic neural network to describe the The current robot state and control torque are updated to obtain the updated robot state and control torque; based on the updated robot state and control torque, determine whether the working time of the robot is greater than the preset time; if not, execute the control torque , and return to the current robot state read through the robot sensor. In the implementation of the present invention, the energy of the method is optimal and the efficiency is high.

Figure 201911371228

Description

一种能量最优的机器人控制方法An energy-optimized robot control method

技术领域technical field

本发明涉及机器人控制的技术领域，尤其涉及一种能量最优的机器人控制方法。The invention relates to the technical field of robot control, in particular to an energy-optimized robot control method.

背景技术Background technique

机器人已经广泛应用于工业生产、航空航天、农业等领域，为实现智能制造发挥重要作用；在低碳环保、节能减排的重大需求下，在完成机器人高性能控制的同时，降低机器人的能量消耗，具有重大意义。目前，针对机器人的能量优化研究，主要集中在轨迹规划阶段，虽然能够实现能量的优化，但是这种方案是离线完成的，这制约了机器人的工作效率；其中，一种面向冗余机械臂液压驱动系统的能量优化方案，考虑了机器人的部分不等式约束，但是没有考虑机械臂的关节力矩限制，同时该方法直接对机器人的雅克比矩阵进行求逆运算，带来计算过缓、成本过高的问题。Robots have been widely used in industrial production, aerospace, agriculture and other fields, and play an important role in realizing intelligent manufacturing; under the major demands of low-carbon environmental protection, energy conservation and emission reduction, while completing the high-performance control of robots, the energy consumption of robots is reduced ,has great significance. At present, the energy optimization research for robots mainly focuses on the trajectory planning stage. Although energy optimization can be achieved, this solution is done off-line, which restricts the work efficiency of the robot. The energy optimization scheme of the drive system considers the partial inequality constraints of the robot, but does not consider the joint torque constraints of the manipulator. At the same time, this method directly inverts the Jacobian matrix of the robot, resulting in slow calculation and high cost. question.

发明内容SUMMARY OF THE INVENTION

本发明的目的在于克服现有技术的不足，本发明提供了一种能量最优的机器人控制方法，通过设计控制量，在使机器人实现对末端轨迹的跟踪，同时必须是机器人的各状态不超过限制。The purpose of the present invention is to overcome the deficiencies of the prior art. The present invention provides a robot control method with optimal energy. By designing the control amount, the robot can track the end trajectory, and at the same time, the states of the robot must not exceed limit.

为了解决上述技术问题，本发明实施例提供了一种能量最优的机器人控制方法，所述方法包括：In order to solve the above technical problems, an embodiment of the present invention provides an energy-optimized robot control method, which includes:

初始化机器人的状态变量以及机器人的控制力矩；Initialize the state variables of the robot and the control torque of the robot;

在所述初始化之后，通过机器人传感器读取到当前机器人状态；After the initialization, the current robot state is read through the robot sensor;

根据所述当前机器人状态，通过计算得出当前时刻的雅克比矩阵和参考加速度；According to the current robot state, the Jacobian matrix and the reference acceleration at the current moment are obtained by calculation;

基于所述当前时刻的雅克比矩阵和参考加速度，将所述当前机器人状态的不等式约束在加速度层统一进行描述，并确定上界和下界；Based on the Jacobian matrix at the current moment and the reference acceleration, the inequality constraints of the current robot state are uniformly described in the acceleration layer, and the upper bound and the lower bound are determined;

基于所述描述和所述上界和下界，对待优化函数进行凸优化处理，并得到最终的约束优化模型；Based on the description and the upper and lower bounds, a convex optimization process is performed on the function to be optimized, and a final constrained optimization model is obtained;

基于所述最终的约束优化模型，采用动态神经网络对所述当前机器人状态以及控制力矩进行更新，得到更新后的机器人状态以及控制力矩；Based on the final constraint optimization model, a dynamic neural network is used to update the current robot state and control torque to obtain the updated robot state and control torque;

基于所述更新后的机器人状态以及控制力矩，判断机器人的工作时间是否大于预设时间；Based on the updated state of the robot and the control torque, determine whether the working time of the robot is greater than the preset time;

若否，执行所述控制力矩，并返回至所述通过机器人传感器读取到当前机器人状态。If not, execute the control torque, and return to the current robot state read through the robot sensor.

可选的，所述在所述初始化之后，通过机器人传感器读取到当前机器人状态中，所述当前机器人状态包括：机器人的关节角度、角速度和角加速度。Optionally, after the initialization, the current robot state is read through a robot sensor, and the current robot state includes: the joint angle, angular velocity and angular acceleration of the robot.

可选的，所述雅克比矩阵的具体计算公式如下：Optionally, the specific calculation formula of the Jacobian matrix is as follows:

Figure BDA0002337077810000021
Figure BDA0002337077810000021

进一步的，得到所述参考加速度的具体计算公式如下：Further, the specific calculation formula for obtaining the reference acceleration is as follows:

Figure BDA0002337077810000022
Figure BDA0002337077810000022

其中，J(θ)为机器人的雅克比矩阵；

Figure BDA0002337077810000023
为机器人的角速度；
Figure BDA0002337077810000024
为机器人末端执行器的期望速度；k为控制参数，为正值；e为机器人运动控制误差；
Figure BDA0002337077810000025
为机器人的角加速度；
Figure BDA0002337077810000026
为机器人的参考加速度；
Figure BDA0002337077810000027
为机器人末端执行器的期望加速度。Among them, J(θ) is the Jacobian matrix of the robot;
Figure BDA0002337077810000023
is the angular velocity of the robot;
Figure BDA0002337077810000024
is the expected speed of the robot end effector; k is the control parameter, which is a positive value; e is the robot motion control error;
Figure BDA0002337077810000025
is the angular acceleration of the robot;
Figure BDA0002337077810000026
is the reference acceleration of the robot;
Figure BDA0002337077810000027
is the desired acceleration of the robot end effector.

可选的，所述基于所述当前时刻的雅克比矩阵和参考加速度，将所述当前机器人状态的不等式约束在加速度层统一进行描述，并确定上界和下界包括：Optionally, based on the Jacobian matrix at the current moment and the reference acceleration, the inequality constraints of the current robot state are uniformly described in the acceleration layer, and the upper and lower bounds are determined including:

基于所述当前时刻的雅克比矩阵和参考加速度，利用动力学模型，将机器人的力矩约束进行改写，得到改写后的模型；Based on the Jacobian matrix and the reference acceleration at the current moment, the dynamic model is used to rewrite the torque constraint of the robot to obtain the rewritten model;

基于所述改写后的模型，将所述当前机器人状态的不等式约束在加速度层统一进行描述；Based on the rewritten model, the inequality constraints of the current robot state are uniformly described in the acceleration layer;

根据所述当前机器人状态的不等式约束在加速度层的描述，确定所述当前机器人状态的上界和下界。According to the description of the inequality constraint of the current robot state in the acceleration layer, the upper bound and the lower bound of the current robot state are determined.

可选的，所述改写后的模型的具体公式如下：Optionally, the specific formula of the rewritten model is as follows:

Figure BDA0002337077810000031
Figure BDA0002337077810000031

进一步的，将所述当前机器人状态的不等式约束在加速度层统一进行描述的具体公式如下：Further, the specific formula for uniformly describing the inequality of the current robot state in the acceleration layer is as follows:

Figure BDA0002337077810000032
Figure BDA0002337077810000032

进一步的，确定所述上界和下界分别为：Further, it is determined that the upper and lower bounds are respectively:

Figure BDA0002337077810000033
Figure BDA0002337077810000033

Figure BDA0002337077810000034
Figure BDA0002337077810000034

其中，θ、

Figure BDA0002337077810000035
分别为机器人的关节角度、角速度与角加速度；τ为机器人的关节控制力矩；M(θ)、
Figure BDA0002337077810000036
G(θ)分别为机器人的惯量矩阵、离心力与哥矢力矩阵以及重力矩；θ-、θ+、
Figure BDA0002337077810000037
τ-、τ+分别为θ、
Figure BDA0002337077810000038
τ的下界与上界；kp、kv为控制参数，均为正值。Among them, θ,
Figure BDA0002337077810000035
are the joint angle, angular velocity and angular acceleration of the robot respectively; τ is the joint control torque of the robot; M(θ),
Figure BDA0002337077810000036
G(θ) are the inertia matrix, the centrifugal force and the vector force matrix and the gravitational moment of the robot respectively; θ - , θ + ,
Figure BDA0002337077810000037
τ - and τ + are θ,
Figure BDA0002337077810000038
The lower and upper bounds of τ; k p and k v are control parameters, which are all positive values.

可选的，所述对待优化函数进行凸优化处理的具体计算公式如下：Optionally, the specific calculation formula for performing convex optimization processing on the function to be optimized is as follows:

Figure BDA0002337077810000039
Figure BDA0002337077810000039

Figure BDA00023370778100000310
Figure BDA00023370778100000310

进一步的，得到最终的约束优化模型，具体公式如下：Further, the final constrained optimization model is obtained, and the specific formula is as follows:

Figure BDA00023370778100000311
Figure BDA00023370778100000311

其中，in,

Figure BDA00023370778100000312
Figure BDA00023370778100000312

Figure BDA00023370778100000313
Figure BDA00023370778100000313

Figure BDA00023370778100000314
Figure BDA00023370778100000314

其中，θ、

Figure BDA00023370778100000316
分别为机器人的关节角度、角速度与角加速度；τ为机器人的关节控制力矩；
Figure BDA00023370778100000318
为机器人的参考加速度；M(θ)、
Figure BDA00023370778100000317
G(θ)分别为机器人的惯量矩阵、离心力与哥矢力矩阵以及重力矩；J(θ)为机器人的雅克比矩阵；c1、c2分别为控制参数，均为正值；T为转置的运算。Among them, θ,
Figure BDA00023370778100000316
are the joint angle, angular velocity and angular acceleration of the robot respectively; τ is the joint control torque of the robot;
Figure BDA00023370778100000318
is the reference acceleration of the robot; M(θ),
Figure BDA00023370778100000317
G(θ) is the inertia matrix, centrifugal force and vector force matrix and gravitational moment of the robot respectively; J(θ) is the Jacobian matrix of the robot; c 1 and c 2 are the control parameters, which are positive values; T is the rotation set operation.

可选的，基于所述最终的约束优化模型，对机器人的控制算法重新构建模型；其中，所述重新构建模型的具体公式如下：Optionally, based on the final constraint optimization model, a model is reconstructed for the control algorithm of the robot; wherein, the specific formula of the reconstructed model is as follows:

Figure BDA0002337077810000041
Figure BDA0002337077810000041

Figure BDA0002337077810000042
Figure BDA0002337077810000042

Figure BDA0002337077810000043
Figure BDA0002337077810000043

可选的，所述基于所述最终的约束优化模型，采用动态神经网络对所述当前机器人状态以及控制力矩进行更新，得到更新后的机器人状态以及控制力矩包括：Optionally, based on the final constraint optimization model, a dynamic neural network is used to update the current robot state and control torque, and obtaining the updated robot state and control torque includes:

基于所述最终的约束优化模型，采用动态神经网络，并通过计算得出机器人加速度的信息；Based on the final constraint optimization model, a dynamic neural network is used, and the information of the robot acceleration is obtained by calculation;

根据所述加速度的信息，以及结合机器人的关节控制力矩与机器人运动之间的关系，通过计算得出所述当前机器人状态以及控制力矩；According to the information of the acceleration and the relationship between the joint control torque of the robot and the motion of the robot, the current robot state and the control torque are obtained by calculation;

基于通过计算得出所述当前机器人状态以及控制力矩，得到更新后的机器人状态以及控制力矩。Based on the current robot state and control torque obtained through calculation, the updated robot state and control torque are obtained.

可选的，所述动态神经网络的具体计算公式如下：Optionally, the specific calculation formula of the dynamic neural network is as follows:

Figure BDA0002337077810000044
Figure BDA0002337077810000044

进一步的，得到所述控制力矩的具体计算公式如下：Further, the specific calculation formula for obtaining the control torque is as follows:

Figure BDA0002337077810000045
Figure BDA0002337077810000045

其中，∈为一个预设的控制增益，且为正值；PΩ()为一个投影算子，将

Figure BDA0002337077810000046
投影到集合Ω＝[η-，η+]中；Δt为一个控制周期的时间间隔；t为时间。Among them, ∈ is a preset control gain, and is a positive value; P Ω () is a projection operator, the
Figure BDA0002337077810000046
Projected into the set Ω=[η - , η + ]; Δt is the time interval of one control cycle; t is the time.

可选的，所述基于所述更新后的机器人状态以及控制力矩，判断机器人的工作时间是否大于预设时间包括：Optionally, judging whether the working time of the robot is greater than the preset time based on the updated robot state and control torque includes:

基于所述更新后的机器人状态以及控制力矩，将机器人的工作时间与预设时间进行判断，判断前者是否大于后者；Based on the updated robot state and control torque, judge the working time of the robot and the preset time, and judge whether the former is greater than the latter;

若是，停止执行；If so, stop execution;

若否，执行所述控制力矩，并返回至所述通过机器人传感器读取到当前机器人状态。If not, execute the control torque, and return to the current robot state read through the robot sensor.

在本发明实施中，一种能量最优的机器人控制方法适用于具有冗余自由度的机器人系统；所述方法能够在实现实时运动控制的同时，保证机器人关节角度、角速度、角加速度以及输出力矩的有界性；同时，所述方法无需对机器人雅克比矩阵进行求逆运算，能够提升控制器的实时性，有效地提高效率，且能够降低机器人完成所需任务的输出功率。In the implementation of the present invention, an energy-optimized robot control method is suitable for a robot system with redundant degrees of freedom; the method can ensure the joint angle, angular velocity, angular acceleration and output torque of the robot while realizing real-time motion control At the same time, the method does not need to invert the Jacobian matrix of the robot, can improve the real-time performance of the controller, effectively improve the efficiency, and can reduce the output power of the robot to complete the required tasks.

附图说明Description of drawings

为了更清楚地说明本发明实施例或现有技术中的技术方案，下面将对实施例或现有技术描述中所需要使用的附图作简单地介绍，显而易见的，下面描述中的附图仅仅是本发明的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动的前提下，还可以根据这些附图获得其它的附图。In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the accompanying drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only These are some embodiments of the present invention, and for those of ordinary skill in the art, other drawings can also be obtained from these drawings without creative effort.

图1是本发明实施例中的能量最优的机器人控制方法的流程示意图。FIG. 1 is a schematic flowchart of an energy-optimized robot control method in an embodiment of the present invention.

具体实施方式Detailed ways

下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有作出创造性劳动前提下所获得的所有其它实施例，都属于本发明保护的范围。The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

实施例Example

请参阅图1，图1是本发明实施中能量最优的机器人控制方法的流程示意图。Please refer to FIG. 1 . FIG. 1 is a schematic flowchart of an energy-optimized robot control method in the implementation of the present invention.

如图1所示，一种能量最优的机器人控制方法，所述方法包括：As shown in Figure 1, an energy-optimized robot control method includes:

S11：初始化机器人的状态变量以及机器人的控制力矩；S11: Initialize the state variables of the robot and the control torque of the robot;

具体的，当t＝0时刻时，将机器人的状态变量以及机器人的控制力矩进行初始化，保证不受其他因素的干扰。Specifically, when t=0, the state variables of the robot and the control torque of the robot are initialized to ensure that they are not disturbed by other factors.

S12：在所述初始化之后，通过机器人传感器读取到当前机器人状态；S12: After the initialization, read the current robot state through the robot sensor;

在本发明具体实施过程中，所述在所述初始化之后，通过机器人传感器读取到当前机器人状态中，所述当前机器人状态包括：机器人的关节角度、角速度和角加速度。In the specific implementation process of the present invention, after the initialization, the current robot state is read through the robot sensor, and the current robot state includes: the joint angle, angular velocity and angular acceleration of the robot.

S13：根据所述当前机器人状态，通过计算得出当前时刻的雅克比矩阵和参考加速度；S13: According to the current robot state, the Jacobian matrix and the reference acceleration at the current moment are obtained by calculation;

具体的，用xd来描述机器人末端执行器完成给定任务需要跟踪的期望轨迹，则机器人的第一个基本控制目标可以描述为设计控制量，使末端执行器对其期望值的误差e＝xd-x→0；根据实际的跟踪误差e，构建在速度层面的控制策略J(θ)，其中J(θ)为机器人的雅克比矩阵，再进一步的拓展到加速度层面上；其中，Specifically, x d is used to describe the expected trajectory that the robot end effector needs to track to complete a given task, then the first basic control objective of the robot can be described as a design control quantity, so that the error of the end effector to its expected value e=x d -x→0; according to the actual tracking error e, the control strategy J(θ) is constructed at the speed level, where J(θ) is the Jacobian matrix of the robot, and further extended to the acceleration level; among them,

所述雅克比矩阵的具体计算公式如下：The specific calculation formula of the Jacobian matrix is as follows:

Figure BDA0002337077810000061
Figure BDA0002337077810000061

进一步的，得到所述参考加速度的具体计算公式如下：Further, the specific calculation formula for obtaining the reference acceleration is as follows:

Figure BDA0002337077810000062
Figure BDA0002337077810000062

其中，J(θ)为机器人的雅克比矩阵；

Figure BDA0002337077810000063
为机器人的角速度；
Figure BDA0002337077810000064
为机器人末端执行器的期望速度；k为控制参数，为正值；e为机器人运动控制误差；
Figure BDA0002337077810000065
为机器人的角加速度；
Figure BDA0002337077810000066
为机器人的参考加速度；
Figure BDA0002337077810000067
为机器人末端执行器的期望加速度。Among them, J(θ) is the Jacobian matrix of the robot;
Figure BDA0002337077810000063
is the angular velocity of the robot;
Figure BDA0002337077810000064
is the expected speed of the robot end effector; k is the control parameter, which is a positive value; e is the robot motion control error;
Figure BDA0002337077810000065
is the angular acceleration of the robot;
Figure BDA0002337077810000066
is the reference acceleration of the robot;
Figure BDA0002337077810000067
is the desired acceleration of the robot end effector.

S14：基于所述当前时刻的雅克比矩阵和参考加速度，将所述当前机器人状态的不等式约束在加速度层统一进行描述，并确定上界和下界；S14: Based on the Jacobian matrix at the current moment and the reference acceleration, the inequality constraints of the current robot state are uniformly described in the acceleration layer, and the upper bound and the lower bound are determined;

在本发明具体实施过程中，所述基于所述当前时刻的雅克比矩阵和参考加速度，将所述当前机器人状态的不等式约束在加速度层统一进行描述，并确定上界和下界包括：基于所述当前时刻的雅克比矩阵和参考加速度，利用动力学模型，将机器人的力矩约束进行改写，得到改写后的模型；基于所述改写后的模型，将所述当前机器人状态的不等式约束在加速度层统一进行描述；根据所述当前机器人状态的不等式约束在加速度层的描述，确定所述当前机器人状态的上界和下界。In the specific implementation process of the present invention, based on the Jacobian matrix at the current moment and the reference acceleration, the inequality constraints of the current robot state are described in a unified manner in the acceleration layer, and the determination of the upper bound and the lower bound includes: based on the The Jacobian matrix and the reference acceleration at the current moment are used to rewrite the torque constraints of the robot by using the dynamic model to obtain a rewritten model; based on the rewritten model, the inequality constraints of the current robot state are unified in the acceleration layer. Describe; according to the description of the current robot state inequality constraint in the acceleration layer, determine the upper and lower bounds of the current robot state.

具体的，所述改写后的模型的具体公式如下：Specifically, the specific formula of the rewritten model is as follows:

Figure BDA0002337077810000068
Figure BDA0002337077810000068

进一步的，将所述当前机器人状态的不等式约束在加速度层统一进行描述的具体公式如下：Further, the specific formula for uniformly describing the inequality of the current robot state in the acceleration layer is as follows:

Figure BDA0002337077810000069
Figure BDA0002337077810000069

进一步的，确定所述上界和下界分别为：Further, it is determined that the upper and lower bounds are respectively:

Figure BDA0002337077810000071
Figure BDA0002337077810000071

Figure BDA0002337077810000072
Figure BDA0002337077810000072

其中，θ、

Figure BDA0002337077810000073
分别为机器人的关节角度、角速度与角加速度；τ为机器人的关节控制力矩；M(θ)、
Figure BDA0002337077810000074
G(θ)分别为机器人的惯量矩阵、离心力与哥矢力矩阵以及重力矩；θ-、θ+、
Figure BDA0002337077810000075
τ-、τ+分别为θ、
Figure BDA0002337077810000076
τ的下界与上界；kp、kv为控制参数，均为正值。Among them, θ,
Figure BDA0002337077810000073
are the joint angle, angular velocity and angular acceleration of the robot respectively; τ is the joint control torque of the robot; M(θ),
Figure BDA0002337077810000074
G(θ) are the inertia matrix, the centrifugal force and the vector force matrix and the gravitational moment of the robot respectively; θ - , θ + ,
Figure BDA0002337077810000075
τ - and τ + are θ,
Figure BDA0002337077810000076
The lower and upper bounds of τ; k p and k v are control parameters, which are all positive values.

S15：基于所述描述和所述上界和下界，对待优化函数进行凸优化处理，并得到最终的约束优化模型；S15: Based on the description and the upper and lower bounds, perform convex optimization processing on the function to be optimized, and obtain a final constrained optimization model;

具体的，所述对待优化函数进行凸优化处理的具体计算公式如下：Specifically, the specific calculation formula for performing convex optimization processing on the function to be optimized is as follows:

Figure BDA0002337077810000077
Figure BDA0002337077810000077

Figure BDA0002337077810000078
Figure BDA0002337077810000078

进一步的，得到最终的约束优化模型，具体公式如下：Further, the final constrained optimization model is obtained, and the specific formula is as follows:

Figure BDA0002337077810000079
Figure BDA0002337077810000079

其中，in,

Figure BDA00023370778100000710
Figure BDA00023370778100000710

Figure BDA00023370778100000711
Figure BDA00023370778100000711

Figure BDA00023370778100000712
Figure BDA00023370778100000712

其中，θ、

Figure BDA00023370778100000714
分别为机器人的关节角度、角速度与角加速度；τ为机器人的关节控制力矩；
Figure BDA00023370778100000715
为机器人的参考加速度；M(θ)、
Figure BDA00023370778100000716
G(θ)分别为机器人的惯量矩阵、离心力与哥矢力矩阵以及重力矩；J(θ)为机器人的雅克比矩阵；c1、c2分别为控制参数，均为正值；T为转置的运算。Among them, θ,
Figure BDA00023370778100000714
are the joint angle, angular velocity and angular acceleration of the robot respectively; τ is the joint control torque of the robot;
Figure BDA00023370778100000715
is the reference acceleration of the robot; M(θ),
Figure BDA00023370778100000716
G(θ) is the inertia matrix, centrifugal force and vector force matrix and gravitational moment of the robot respectively; J(θ) is the Jacobian matrix of the robot; c 1 and c 2 are the control parameters, which are positive values; T is the rotation set operation.

进一步的，基于所述最终的约束优化模型，对机器人的控制算法重新构建模型；其中，所述重新构建模型的具体公式如下：Further, based on the final constraint optimization model, a model is reconstructed for the control algorithm of the robot; wherein, the specific formula of the reconstructed model is as follows:

Figure BDA00023370778100000717
Figure BDA00023370778100000717

Figure BDA00023370778100000718
Figure BDA00023370778100000718

Figure BDA0002337077810000081
Figure BDA0002337077810000081

S16：基于所述最终的约束优化模型，采用动态神经网络对所述当前机器人状态以及控制力矩进行更新，得到更新后的机器人状态以及控制力矩；S16: Based on the final constraint optimization model, use a dynamic neural network to update the current robot state and control torque to obtain the updated robot state and control torque;

在本发明具体实施过程中，所述基于所述最终的约束优化模型，采用动态神经网络对所述当前机器人状态以及控制力矩进行更新，得到更新后的机器人状态以及控制力矩包括：基于所述最终的约束优化模型，采用动态神经网络，并通过计算得出机器人加速度的信息；根据所述加速度的信息，以及结合机器人的关节控制力矩与机器人运动之间的关系，通过计算得出所述当前机器人状态以及控制力矩；基于通过计算得出所述当前机器人状态以及控制力矩，得到更新后的机器人状态以及控制力矩。In the specific implementation process of the present invention, based on the final constraint optimization model, using a dynamic neural network to update the current robot state and control torque to obtain the updated robot state and control torque includes: The constraint optimization model is based on the dynamic neural network, and the information of the robot's acceleration is obtained by calculation; according to the information of the acceleration, and the relationship between the joint control torque of the robot and the motion of the robot, the current robot is obtained by calculation. state and control torque; based on the current robot state and control torque obtained through calculation, the updated robot state and control torque are obtained.

具体的，所述动态神经网络的具体计算公式如下：Specifically, the specific calculation formula of the dynamic neural network is as follows:

Figure BDA0002337077810000082
Figure BDA0002337077810000082

进一步的，得到所述控制力矩的具体计算公式如下：Further, the specific calculation formula for obtaining the control torque is as follows:

Figure BDA0002337077810000083
Figure BDA0002337077810000083

其中，∈为一个预设的控制增益，且为正值；PΩ()为一个投影算子，将

Figure BDA0002337077810000084
投影到集合Ω＝[η-，η+]中；Δt为一个控制周期的时间间隔；t为时间。Among them, ∈ is a preset control gain, and is a positive value; P Ω () is a projection operator, the
Figure BDA0002337077810000084
Projected into the set Ω=[η - , η + ]; Δt is the time interval of one control cycle; t is the time.

S17：基于所述更新后的机器人状态以及控制力矩，判断机器人的工作时间是否大于预设时间；S17: Based on the updated robot state and control torque, determine whether the working time of the robot is greater than a preset time;

S18：若否，执行所述控制力矩，并返回至所述通过机器人传感器读取到当前机器人状态；S18: If no, execute the control torque, and return to the current robot state read through the robot sensor;

S19：若是，停止执行。S19: If yes, stop the execution.

在本发明具体实施过程中，基于所述更新后的机器人状态以及控制力矩，将机器人的工作时间与预设时间进行判断，判断前者是否大于后者；若是，停止执行；若否，执行所述控制力矩，并返回至所述通过机器人传感器读取到当前机器人状态，重复S12-S17的步骤。In the specific implementation process of the present invention, based on the updated robot state and control torque, the working time of the robot and the preset time are judged to determine whether the former is greater than the latter; if so, stop the execution; if not, execute the described Control the torque, and return to the current robot state read through the robot sensor, and repeat steps S12-S17.

在本发明实施中，一种能量最优的机器人控制方法适用于具有冗余自由度的机器人系统；所述方法能够在实现实时运动控制的同时，保证机器人关节角度、角速度、角加速度以及输出力矩的有界性；同时，所述方法无需对机器人雅克比矩阵进行求逆运算，能够提升控制器的实时性，有效地提高效率，且能够降低机器人完成所需任务的输出功率。In the implementation of the present invention, an energy-optimized robot control method is suitable for a robot system with redundant degrees of freedom; the method can ensure the joint angle, angular velocity, angular acceleration and output torque of the robot while realizing real-time motion control At the same time, the method does not need to invert the Jacobian matrix of the robot, can improve the real-time performance of the controller, effectively improve the efficiency, and can reduce the output power of the robot to complete the required tasks.

本领域普通技术人员可以理解上述实施例的各种方法中的全部或部分步骤是可以通过程序来指令相关的硬件来完成，该程序可以存储于一计算机可读存储介质中，存储介质可以包括：只读存储器(ROM，Read Only Memory)、随机存取存储器(RAM，RandomAccess Memory)、磁盘或光盘等。Those of ordinary skill in the art can understand that all or part of the steps in the various methods of the above embodiments can be completed by instructing relevant hardware through a program, and the program can be stored in a computer-readable storage medium, and the storage medium can include: Read Only Memory (ROM, Read Only Memory), Random Access Memory (RAM, Random Access Memory), magnetic disk or optical disk, etc.

另外，以上对本发明实施例所提供的一种能量最优的机器人控制方法进行了详细介绍，本文中应采用了具体个例对本发明的原理及实施方式进行了阐述，以上实施例的说明只是用于帮助理解本发明的方法及其核心思想；同时，对于本领域的一般技术人员，依据本发明的思想，在具体实施方式及应用范围上均会有改变之处，综上所述，本说明书内容不应理解为对本发明的限制。In addition, a robot control method with optimal energy provided by the embodiments of the present invention has been introduced in detail above. In this paper, specific examples should be used to illustrate the principles and implementations of the present invention. The descriptions of the above embodiments are only used for In order to help understand the method of the present invention and its core idea; at the same time, for those skilled in the art, according to the idea of the present invention, there will be changes in the specific implementation and application scope. In summary, this specification The content should not be construed as limiting the present invention.

Claims (3)

1.一种能量最优的机器人控制方法，其特征在于，所述方法包括：1. an energy-optimized robot control method, wherein the method comprises: 初始化机器人的状态变量以及机器人的控制力矩；Initialize the state variables of the robot and the control torque of the robot; 在所述初始化之后，通过机器人传感器读取到当前机器人状态；After the initialization, the current robot state is read through the robot sensor; 根据所述当前机器人状态，通过计算得出当前时刻的雅克比矩阵和参考加速度；According to the current robot state, the Jacobian matrix and the reference acceleration at the current moment are obtained by calculation; 基于所述当前时刻的雅克比矩阵和参考加速度，将所述当前机器人状态的不等式约束在加速度层统一进行描述，并确定上界和下界；Based on the Jacobian matrix at the current moment and the reference acceleration, the inequality constraints of the current robot state are uniformly described in the acceleration layer, and the upper bound and the lower bound are determined; 基于所述描述和所述上界和下界，对待优化函数进行凸优化处理，并得到最终的约束优化模型；Based on the description and the upper and lower bounds, a convex optimization process is performed on the function to be optimized, and a final constrained optimization model is obtained; 基于所述最终的约束优化模型，采用动态神经网络对所述当前机器人状态以及控制力矩进行更新，得到更新后的机器人状态以及控制力矩；Based on the final constraint optimization model, a dynamic neural network is used to update the current robot state and control torque to obtain the updated robot state and control torque; 基于所述更新后的机器人状态以及控制力矩，判断机器人的工作时间是否大于预设时间；Based on the updated state of the robot and the control torque, determine whether the working time of the robot is greater than the preset time; 若否，执行所述控制力矩，并返回至所述通过机器人传感器读取到当前机器人状态；If not, execute the control torque, and return to the current robot state read through the robot sensor; 所述在所述初始化之后，通过机器人传感器读取到当前机器人状态中，所述当前机器人状态包括：机器人的关节角度、角速度和角加速度；After the initialization, the current robot state is read through the robot sensor, and the current robot state includes: the joint angle, angular velocity and angular acceleration of the robot; 所述基于所述当前时刻的雅克比矩阵和参考加速度，将所述当前机器人状态的不等式约束在加速度层统一进行描述，并确定上界和下界包括：Based on the Jacobian matrix at the current moment and the reference acceleration, the inequality constraints of the current robot state are uniformly described in the acceleration layer, and the upper and lower bounds are determined including: 基于所述当前时刻的雅克比矩阵和参考加速度，利用动力学模型，将机器人的力矩约束进行改写，得到改写后的模型；Based on the Jacobian matrix and the reference acceleration at the current moment, the dynamic model is used to rewrite the torque constraint of the robot to obtain the rewritten model; 基于所述改写后的模型，将所述当前机器人状态的不等式约束在加速度层统一进行描述；Based on the rewritten model, the inequality constraints of the current robot state are uniformly described in the acceleration layer; 根据所述当前机器人状态的不等式约束在加速度层的描述，确定所述当前机器人状态的上界和下界；According to the description of the inequality constraint of the current robot state in the acceleration layer, determine the upper bound and the lower bound of the current robot state; 所述改写后的模型的具体公式如下：The specific formula of the rewritten model is as follows:
Figure FDA0003671776430000011
Figure FDA0003671776430000011
Figure FDA0003671776430000021
Figure FDA0003671776430000021
 进一步的，将所述当前机器人状态的不等式约束在加速度层统一进行描述的具体公式如下：Further, the specific formula for uniformly describing the inequality of the current robot state in the acceleration layer is as follows:
Figure FDA0003671776430000022
Figure FDA0003671776430000022
 进一步的，确定所述上界和下界分别为：Further, it is determined that the upper and lower bounds are respectively:
Figure FDA0003671776430000023
Figure FDA0003671776430000023
Figure FDA0003671776430000024
Figure FDA0003671776430000024
 其中，θ、
Figure FDA0003671776430000025
分别为机器人的关节角度、角速度与角加速度；τ为机器人的关节控制力矩；M(θ)、
Figure FDA0003671776430000026
G(θ)分别为机器人的惯量矩阵、离心力与哥矢力矩阵以及重力矩；θ-、θ+、
Figure FDA0003671776430000027
τ-、τ+分别为θ、
Figure FDA0003671776430000028
τ的下界与上界；kp、kv为控制参数，均为正值；Among them, θ,
Figure FDA0003671776430000025
are the joint angle, angular velocity and angular acceleration of the robot respectively; τ is the joint control torque of the robot; M(θ),
Figure FDA0003671776430000026
G(θ) are the inertia matrix, the centrifugal force and the vector force matrix and the gravitational moment of the robot respectively; θ - , θ + ,
Figure FDA0003671776430000027
τ - and τ + are θ,
Figure FDA0003671776430000028
The lower and upper bounds of τ; k p and k v are control parameters, which are all positive values; 所述对待优化函数进行凸优化处理的具体计算公式如下：The specific calculation formula for the convex optimization processing of the function to be optimized is as follows:
Figure FDA0003671776430000029
Figure FDA0003671776430000029
Figure FDA00036717764300000210
Figure FDA00036717764300000210
 进一步的，得到最终的约束优化模型，具体公式如下：Further, the final constrained optimization model is obtained, and the specific formula is as follows:
Figure FDA00036717764300000211
Figure FDA00036717764300000211
 其中，in,
Figure FDA00036717764300000212
Figure FDA00036717764300000212
Figure FDA00036717764300000213
Figure FDA00036717764300000213
Figure FDA00036717764300000214
Figure FDA00036717764300000214
 其中，θ、
Figure FDA00036717764300000215
分别为机器人的关节角度、角速度与角加速度；τ为机器人的关节控制力矩；
Figure FDA00036717764300000216
为机器人的参考加速度；M(θ)、
Figure FDA00036717764300000217
G(θ)分别为机器人的惯量矩阵、离心力与哥矢力矩阵以及重力矩；J(θ)为机器人的雅克比矩阵；c1、c2分别为控制参数，均为正值；T为转置的运算；Among them, θ,
Figure FDA00036717764300000215
are the joint angle, angular velocity and angular acceleration of the robot respectively; τ is the joint control torque of the robot;
Figure FDA00036717764300000216
is the reference acceleration of the robot; M(θ),
Figure FDA00036717764300000217
G(θ) is the inertia matrix, centrifugal force and vector force matrix and gravitational moment of the robot respectively; J(θ) is the Jacobian matrix of the robot; c 1 and c 2 are the control parameters, which are positive values; T is the rotation set operation; 基于所述最终的约束优化模型，对机器人的控制算法重新构建模型；其中，所述重新构建模型的具体公式如下：Based on the final constraint optimization model, reconstruct the model for the control algorithm of the robot; wherein, the specific formula of the reconstructed model is as follows:
Figure FDA0003671776430000031
Figure FDA0003671776430000031
Figure FDA0003671776430000032
Figure FDA0003671776430000032
Figure FDA0003671776430000033
Figure FDA0003671776430000033
 所述基于所述最终的约束优化模型，采用动态神经网络对所述当前机器人状态以及控制力矩进行更新，得到更新后的机器人状态以及控制力矩包括：Based on the final constraint optimization model, a dynamic neural network is used to update the current robot state and control torque, and obtaining the updated robot state and control torque includes: 基于所述最终的约束优化模型，采用动态神经网络，并通过计算得出机器人加速度的信息；Based on the final constraint optimization model, a dynamic neural network is used, and the information of the robot acceleration is obtained by calculation; 根据所述加速度的信息，以及结合机器人的关节控制力矩与机器人运动之间的关系，通过计算得出所述当前机器人状态以及控制力矩；According to the information of the acceleration and the relationship between the joint control torque of the robot and the motion of the robot, the current robot state and the control torque are obtained by calculation; 基于通过计算得出所述当前机器人状态以及控制力矩，得到更新后的机器人状态以及控制力矩；Based on the current robot state and control torque obtained by calculation, the updated robot state and control torque are obtained; 所述动态神经网络的具体计算公式如下：The specific calculation formula of the dynamic neural network is as follows:
Figure FDA0003671776430000034
Figure FDA0003671776430000034
 进一步的，得到所述控制力矩的具体计算公式如下：Further, the specific calculation formula for obtaining the control torque is as follows:
Figure FDA0003671776430000035
Figure FDA0003671776430000035
 其中，∈为一个预设的控制增益，且为正值；PΩ()为一个投影算子，将
Figure FDA0003671776430000036
投影到集合Ω＝[η-，η+]中；Δt为一个控制周期的时间间隔；t为时间。Among them, ∈ is a preset control gain, and is a positive value; P Ω () is a projection operator, the
Figure FDA0003671776430000036
Projected into the set Ω=[η - , η + ]; Δt is the time interval of one control cycle; t is the time. 2.根据权利要求1所述的一种能量最优的机器人控制方法，其特征在于，所述雅克比矩阵的具体计算公式如下：2. the optimal robot control method of a kind of energy according to claim 1, is characterized in that, the concrete calculation formula of described Jacobian matrix is as follows:
Figure FDA0003671776430000037
Figure FDA0003671776430000037
 进一步的，得到所述参考加速度的具体计算公式如下：Further, the specific calculation formula for obtaining the reference acceleration is as follows:
Figure FDA0003671776430000038
Figure FDA0003671776430000038
 其中，J(θ)为机器人的雅克比矩阵；
Figure FDA0003671776430000039
为机器人的角速度；
Figure FDA00036717764300000310
为机器人末端执行器的期望速度；k为控制参数，为正值；e为机器人运动控制误差；
Figure FDA00036717764300000311
为机器人的角加速度；
Figure FDA00036717764300000312
为机器人的参考加速度；
Figure FDA00036717764300000313
为机器人末端执行器的期望加速度。Among them, J(θ) is the Jacobian matrix of the robot;
Figure FDA0003671776430000039
is the angular velocity of the robot;
Figure FDA00036717764300000310
is the expected speed of the robot end effector; k is the control parameter, which is a positive value; e is the robot motion control error;
Figure FDA00036717764300000311
is the angular acceleration of the robot;
Figure FDA00036717764300000312
is the reference acceleration of the robot;
Figure FDA00036717764300000313
is the desired acceleration of the robot end effector. 3.根据权利要求1所述的一种能量最优的机器人控制方法，其特征在于，所述基于所述更新后的机器人状态以及控制力矩，判断机器人的工作时间是否大于预设时间包括：3. A kind of robot control method with optimal energy according to claim 1, is characterized in that, described based on described updated robot state and control torque, judging whether the working time of robot is greater than preset time comprises: 基于所述更新后的机器人状态以及控制力矩，将机器人的工作时间与预设时间进行判断，判断前者是否大于后者；Based on the updated robot state and control torque, judge the working time of the robot and the preset time, and judge whether the former is greater than the latter; 若是，停止执行；If so, stop execution; 若否，执行所述控制力矩，并返回至所述通过机器人传感器读取到当前机器人状态。If not, execute the control torque, and return to the current robot state read through the robot sensor.
CN201911371228.0A 2019-12-25 2019-12-25 Robot control method with optimal energy Active CN113021334B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201911371228.0A CN113021334B (en) 2019-12-25 2019-12-25 Robot control method with optimal energy

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201911371228.0A CN113021334B (en) 2019-12-25 2019-12-25 Robot control method with optimal energy

Publications (2)

Publication Number Publication Date
CN113021334A CN113021334A (en) 2021-06-25
CN113021334B true CN113021334B (en) 2022-09-30

Family

ID=76458852

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201911371228.0A Active CN113021334B (en) 2019-12-25 2019-12-25 Robot control method with optimal energy

Country Status (1)

Country Link
CN (1) CN113021334B (en)

Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110209048A (en) * 2019-05-20 2019-09-06 华南理工大学 Robot time optimal trajectory planning method, equipment based on kinetic model

Family Cites Families (10)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP3326472B2 (en) * 1999-11-10 2002-09-24 独立行政法人 航空宇宙技術研究所 Articulated robot
WO2011042049A1 (en) * 2009-10-06 2011-04-14 Abb Technology Ab A method for reducing the energy consumption of an industrial robot and an industrial robot system
EP2485875B1 (en) * 2009-10-06 2013-04-24 ABB Technology AG A method for reducing the energy consumption of an industrial robot and an industrial robot system
US9649765B2 (en) * 2013-03-11 2017-05-16 Siemens Aktiengesellschaft Reducing energy consumption of industrial robots by using new methods for motion path programming
DE102013013847A1 (en) * 2013-08-20 2015-02-26 Kuka Roboter Gmbh Energy-optimized configuration of a manipulator
CN105388755B (en) * 2015-05-12 2018-08-24 北京理工大学 A kind of anthropomorphic robot is led leg the efficiency optimal control method taken a step
CN107199569B (en) * 2017-06-22 2020-01-21 华中科技大学 Joint robot trajectory planning method based on joint energy balanced distribution
CN108393886B (en) * 2018-01-25 2020-03-17 北京理工大学 Distributed multi-mobile manipulator cooperative carrying method capable of optimizing energy and operation degree
CN108621157A (en) * 2018-04-27 2018-10-09 上海师范大学 Mechanical arm energetic optimum trajectory planning control method and device based on model constraint
CN109986554A (en) * 2019-01-21 2019-07-09 中国船舶重工集团公司第七一六研究所 A kind of geometry method for optimally controlling of industrial robot path planning

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110209048A (en) * 2019-05-20 2019-09-06 华南理工大学 Robot time optimal trajectory planning method, equipment based on kinetic model

Also Published As

Publication number Publication date
CN113021334A (en) 2021-06-25

Similar Documents

Publication Publication Date Title
CN113681543B (en) A zero-force control method of manipulator based on model prediction
CN108621157A (en) Mechanical arm energetic optimum trajectory planning control method and device based on model constraint
CN105772917B (en) A kind of three joint spot welding robot's Trajectory Tracking Control methods
CN111037560B (en) A collaborative robot compliance force control method and system
CN111923039B (en) A Reinforcement Learning-Based Path Planning Method for Redundant Manipulators
CN114800489A (en) Mechanical arm compliance control method based on combination of definite learning and composite learning, storage medium and robot
CN105159096A (en) Redundancy space manipulator joint torque optimization method based on particle swarm algorithm
CN114952868A (en) 7-DOF SRS-type robotic arm control method and device, and piano-playing robot
CN112894821B (en) Method, device and equipment for dragging and teaching control of collaborative robot based on current method
CN107943053A (en) A kind of paths planning method of mobile robot
CN112222703B (en) Energy consumption optimal trajectory planning method for welding robot
CN115139301B (en) Mechanical arm motion planning method based on topological structure self-adaptive neural network
CN112936286B (en) Self-adaptive consistency tracking control method and system for multi-flexible mechanical arm system
CN108227490A (en) A kind of model-free adaption sliding-mode control of New-type mixed-coupled formula automobile electrophoretic coating conveyor structure
CN115922746B (en) Industrial robot shaft hole assembly system and active compliance control method
CN117182929A (en) Flexible control method and device for on-orbit assembly of double-arm robot
CN115946131A (en) A motion control simulation calculation method and device for a flexible joint manipulator
CN117075620B (en) Multi-task navigation scheduling method and system for multi-inspection robot
CN109062039A (en) A kind of adaptive robust control method of Three Degree Of Freedom Delta parallel robot
CN117945271A (en) Seven-degree-of-freedom tower crane self-adaptive sliding mode control method and system
CN115179280A (en) Reward shaping method based on magnetic field in mechanical arm control for reinforcement learning
CN118605135A (en) A robot posture control method for nut feeding kit
CN113021334B (en) Robot control method with optimal energy
CN108890630A (en) A kind of robot teaching system and method
CN119057781A (en) A trajectory planning method, device and medium based on DC-driven robotic arm

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant
点击 这是indexloc提供的php浏览器服务，不要输入任何密码和下载