CN116141341A - Method for realizing pointing action of five-degree-of-freedom mechanical arm meeting Cartesian space constraint - Google Patents

Method for realizing pointing action of five-degree-of-freedom mechanical arm meeting Cartesian space constraint Download PDF

Info

Publication number
CN116141341A
CN116141341A CN202310432715.3A CN202310432715A CN116141341A CN 116141341 A CN116141341 A CN 116141341A CN 202310432715 A CN202310432715 A CN 202310432715A CN 116141341 A CN116141341 A CN 116141341A
Authority
CN
China
Prior art keywords
joint
coordinate system
target point
pointed
optimization
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.)
Granted
Application number
CN202310432715.3A
Other languages
Chinese (zh)
Other versions
CN116141341B (en
Inventor
黄秋兰
郑博升
宛敏红
宋伟
谢安桓
朱世强
顾建军
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.)
Zhejiang Lab
Original Assignee
Zhejiang Lab
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 Zhejiang Lab filed Critical Zhejiang Lab
Priority to CN202310432715.3A priority Critical patent/CN116141341B/en
Publication of CN116141341A publication Critical patent/CN116141341A/en
Application granted granted Critical
Publication of CN116141341B publication Critical patent/CN116141341B/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
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • 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
    • B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T10/00—Road transport of goods or passengers
    • Y02T10/10—Internal combustion engine [ICE] based vehicles
    • Y02T10/40—Engine management systems

Landscapes

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

Abstract

The invention discloses a method for realizing pointing action of a five-degree-of-freedom mechanical arm, which meets the constraint of Cartesian space, and comprises the following steps: acquiring the length of each joint rod of the mechanical arm, a target point to be pointed and a track sequence of the target point to be pointed; taking the collineation of the outward coordinate axis of the wrist coordinate system and the target point to be pointed as a main optimization target, and constructing a nonlinear optimization equation set; taking a target point track sequence to be pointed as input, and carrying out optimization solution on a nonlinear optimization equation set by using a sequence least square method; if the variation of the joint variable obtained by the optimization solution and the joint variable of the previous frame exceeds the allowable range, selecting the joint variable of the previous frame to be assigned to the joint variable sequence; otherwise, adding the joint variable obtained by the optimization solution into a joint variable sequence, and performing angle interpolation on the joint variable sequence; and transmitting the joint angle sequence data subjected to angle interpolation to a robot controller so as to drive the 5R mechanical arm to point to the target point track by using a servo control method.

Description

满足笛卡尔空间约束的五自由度机械臂指向动作实现方法A method for realizing pointing motion of a five-DOF manipulator satisfying Cartesian space constraints

技术领域Technical Field

本发明属于导览机器人机械臂动作生成技术领域，尤其涉及满足笛卡尔空间约束的五自由度机械臂指向动作实现方法。The present invention belongs to the technical field of manipulator action generation of a guide robot, and in particular to a method for realizing pointing actions of a five-degree-of-freedom manipulator satisfying Cartesian space constraints.

背景技术Background Art

机器人的动作指向广泛应用于服务行业中，例如在景区、博物馆等场景中，机器人可以做导游为顾客提供景点讲解、带领游览、问答拍照等多重功能；在政务大厅、企业前台、交通枢纽等场景中，机器人可以作为业务咨询及办理的客服人员，为顾客提供、迎宾接待、窗口引导、产品咨询、业务办理等服务。指向动作是一种具备引导性的动作，本身能够由目标点轨迹生成动作，在离线动作间加以穿插在线指向，提高离线动作通用性、稳定性，也能为机械臂的抓取预先提供一个准备性的动作。The robot's motion pointing is widely used in the service industry. For example, in scenic spots and museums, robots can act as tour guides to provide customers with multiple functions such as scenic spot explanations, tour guides, Q&A and photo taking. In government halls, corporate front desks, transportation hubs and other scenes, robots can act as customer service personnel for business consultation and processing, providing customers with services such as welcoming reception, window guidance, product consultation, and business processing. Pointing motion is a guiding motion that can generate motion from the target point trajectory. Online pointing can be interspersed between offline motions to improve the versatility and stability of offline motions, and can also provide a preparatory motion for the robot arm to grasp.

在实现本发明的过程中，发明人发现现有技术中至少存在如下问题：In the process of implementing the present invention, the inventors found that there are at least the following problems in the prior art:

目前，在机器人的动作指向的实际应用中，一般需要预先定义一系列离线动作以满足机器人的使用需求，当导引环境发生变化，离线动作往往需要重新配置或重新示教。同时，离线动作的配置又需要满足环境、杆件、机器人本体的笛卡尔空间约束，需要人为进行调试生成离线动作关节轨迹。同时，机器人的指向动作往往需要指向超出机械臂操作空间的远点，此时不适用于使用逆运动学方法。At present, in the actual application of robot motion pointing, it is generally necessary to predefine a series of offline motions to meet the robot's usage requirements. When the guidance environment changes, the offline motions often need to be reconfigured or re-taught. At the same time, the configuration of offline motions needs to meet the Cartesian space constraints of the environment, rods, and robot body, and manual debugging is required to generate offline motion joint trajectories. At the same time, the robot's pointing motion often needs to point to a far point beyond the robot's operating space, which is not suitable for the use of inverse kinematics methods.

发明内容Summary of the invention

本申请实施例的目的是提供一种满足笛卡尔空间约束的五自由度机械臂指向动作实现方法，以解决当导引环境发生变化后，机器人中存在离线动作需要人为调试的不足。The purpose of the embodiments of the present application is to provide a method for realizing pointing motion of a five-degree-of-freedom robotic arm that satisfies Cartesian space constraints, so as to solve the problem that when the guidance environment changes, there are offline actions in the robot that require manual debugging.

根据本申请实施例的第一方面，提供一种满足笛卡尔空间约束的五自由度机械臂指向动作实现方法，包括：According to a first aspect of an embodiment of the present application, a method for realizing a pointing action of a five-degree-of-freedom manipulator satisfying Cartesian space constraints is provided, comprising:

获取机械臂的各个关节杆长、待指向目标点、待指向目标点轨迹序列；Obtain the length of each joint rod of the robot arm, the target point to be pointed to, and the trajectory sequence of the target point to be pointed to;

以世界坐标系、当前5R机械臂关节坐标系间关系以及各个关节间杆长为参数，以所述待指向目标点作为变量，以腕部坐标系向外坐标轴与待指向目标点共线为主要优化目标，将针对机器人本体的笛卡尔空间约束、针对环境的笛卡尔空间约束、各个关节的角度约束转换为非线性优化方程组的限制条件，构建非线性优化方程组；Taking the relationship between the world coordinate system, the current 5R robot arm joint coordinate system and the rod length between each joint as parameters, taking the target point to be pointed to as a variable, taking the outward coordinate axis of the wrist coordinate system and the target point to be pointed to be collinear as the main optimization goal, converting the Cartesian space constraints for the robot body, the Cartesian space constraints for the environment, and the angle constraints of each joint into the restriction conditions of the nonlinear optimization equation group, and constructing the nonlinear optimization equation group;

以所述待指向目标点轨迹序列作为输入，使用序列最小二乘法对所述非线性优化方程组进行优化求解；Taking the trajectory sequence of the target point to be pointed to as input, the nonlinear optimization equation group is optimized and solved using the sequential least squares method;

若优化求解得到的关节变量和上一帧的关节变量的变化量超出可允许范围，则选用上一帧的关节变量赋到关节变量序列中；若优化求解得到的关节变量和上一帧的关节变量的变化量在所述可允许范围内，则对将优化求解得到的关节变量加入关节变量序列中，并对所述关节变量序列进行角度插补；If the variation of the joint variables obtained by the optimization solution and the joint variables of the previous frame exceeds the allowable range, the joint variables of the previous frame are selected and assigned to the joint variable sequence; if the variation of the joint variables obtained by the optimization solution and the joint variables of the previous frame is within the allowable range, the joint variables obtained by the optimization solution are added to the joint variable sequence, and the angle interpolation of the joint variable sequence is performed;

将进行角度插补后的关节角度序列数据传输到机器人工控机上，以使用伺服控制的方法驱动5R机械臂指向目标点轨迹。The joint angle sequence data after angle interpolation is transmitted to the robot industrial computer, so as to drive the 5R robot arm to point to the target point trajectory using the servo control method.

进一步地，根据5R机械臂的世界坐标系、各关节坐标系、关节间杆长建立5R机械臂的正向运动学模型，根据所述正向运动学模型得到所述世界坐标系、当前5R机械臂关节坐标系间关系。Furthermore, a forward kinematics model of the 5R robotic arm is established according to the world coordinate system, the coordinate systems of each joint, and the rod length between the joints of the 5R robotic arm, and the relationship between the world coordinate system and the current 5R robotic arm joint coordinate system is obtained according to the forward kinematics model.

进一步地，所述主要优化目标具体为：最小化所指向目标点与腕部坐标系原点组成的矢量与肘部杆件矢量于世界坐标系下的偏移量、所指向目标点于肘部杆件矢量方向上的投影量、所指向目标点与腕部坐标系原点组成的矢量与腕部坐标系x,y轴的内积。Furthermore, the main optimization objectives are specifically: minimizing the offset of the vector composed of the target point pointed to and the origin of the wrist coordinate system and the elbow rod vector in the world coordinate system, the projection of the target point pointed to in the direction of the elbow rod vector, and the inner product of the vector composed of the target point pointed to and the origin of the wrist coordinate system and the x, y axes of the wrist coordinate system.

进一步地，在构建非线性优化方程组前，引入关节变量与前次求解结果之间偏差的L2范数作为次优化目标。Furthermore, before constructing the nonlinear optimization equation group, the L2 norm of the deviation between the joint variables and the previous solution results is introduced as the sub-optimization objective.

进一步地，所构建的非线性优化方程组为：Furthermore, the constructed nonlinear optimization equations are:

Figure SMS_1
，
Figure SMS_1
,

其中

Figure SMS_5
分别为肩部的三个关节角、肘部的关节角和腕部的关节角，
Figure SMS_13
为
Figure SMS_20
对应的权重系数，
Figure SMS_4
为待指向目标点相对于世界坐标系原点在Z轴方向上的偏移，
Figure SMS_14
、
Figure SMS_22
同理；
Figure SMS_29
表示腕部坐标系相对于世界坐标系的变换矩阵，
Figure SMS_7
表示腕部X轴在世界坐标系下的表示，
Figure SMS_10
表示腕部Y轴在世界坐标系下的表示，
Figure SMS_18
表示腕部Z轴在世界坐标系下的表示，
Figure SMS_26
表示腕部坐标系相对世界坐标系的原点偏移，
Figure SMS_6
、
Figure SMS_15
、
Figure SMS_24
为腕部坐标系原点相对于世界坐标系原点的位置，
Figure SMS_31
表示待指向目标点相对于相对世界坐标系的原点偏移，
Figure SMS_8
、
Figure SMS_16
、
Figure SMS_23
、
Figure SMS_30
、
Figure SMS_2
、
Figure SMS_12
、
Figure SMS_21
同理；
Figure SMS_28
为第j个关节的第i次优化结果，
Figure SMS_3
为第j个关节针对待指向目标点的第i-1次优化结果，
Figure SMS_11
为针对环境的笛卡尔空间约束，
Figure SMS_19
为针对机器人本体的笛卡尔空间约束，
Figure SMS_27
、
Figure SMS_9
分别为
Figure SMS_17
和
Figure SMS_25
对应的权重系数。in
Figure SMS_5
They are the three joint angles of the shoulder, the joint angle of the elbow and the joint angle of the wrist.
Figure SMS_13
for
Figure SMS_20
The corresponding weight coefficient is,
Figure SMS_4
is the offset of the target point to be pointed to relative to the origin of the world coordinate system in the Z-axis direction,
Figure SMS_14
,
Figure SMS_22
Similarly;
Figure SMS_29
Represents the transformation matrix of the wrist coordinate system relative to the world coordinate system,
Figure SMS_7
Indicates the wrist X-axis in the world coordinate system.
Figure SMS_10
Indicates the wrist Y-axis in the world coordinate system.
Figure SMS_18
Indicates the wrist Z axis in the world coordinate system.
Figure SMS_26
Indicates the origin offset of the wrist coordinate system relative to the world coordinate system.
Figure SMS_6
,
Figure SMS_15
,
Figure SMS_24
is the position of the wrist coordinate system origin relative to the world coordinate system origin,
Figure SMS_31
Indicates the offset of the target point to be pointed to relative to the origin of the relative world coordinate system.
Figure SMS_8
,
Figure SMS_16
,
Figure SMS_23
,
Figure SMS_30
,
Figure SMS_2
,
Figure SMS_12
,
Figure SMS_21
Similarly;
Figure SMS_28
is the i-th optimization result of the j-th joint,
Figure SMS_3
is the i-1th optimization result of the jth joint for the target point to be pointed to,
Figure SMS_11
is the Cartesian space constraint for the environment,
Figure SMS_19
is the Cartesian space constraint for the robot body,
Figure SMS_27
,
Figure SMS_9
They are
Figure SMS_17
and
Figure SMS_25
The corresponding weight coefficient.

进一步地，利用修正Akima分段三次Hermite插值方法对所述关节变量序列进行角度插补。Furthermore, the modified Akima piecewise cubic Hermite interpolation method is used to perform angle interpolation on the joint variable sequence.

根据本申请实施例的第二方面，提供一种满足笛卡尔空间约束的五自由度机械臂指向动作实现装置，包括：According to a second aspect of an embodiment of the present application, there is provided a device for realizing pointing motion of a five-degree-of-freedom manipulator satisfying Cartesian space constraints, comprising:

获取模块，用于获取机械臂的各个关节杆长、待指向目标点、待指向目标点轨迹序列；An acquisition module is used to acquire the length of each joint rod of the robot arm, the target point to be pointed to, and the trajectory sequence of the target point to be pointed to;

构建模块，用于以世界坐标系、当前5R机械臂关节坐标系间关系以及各个关节间杆长为参数，以所述待指向目标点作为变量，以腕部坐标系向外坐标轴与待指向目标点共线为主要优化目标，将针对机器人本体的笛卡尔空间约束、针对环境的笛卡尔空间约束、各个关节的角度约束转换为非线性优化方程组的限制条件，构建非线性优化方程组；A construction module is used to use the relationship between the world coordinate system, the current 5R robot arm joint coordinate system, and the rod length between each joint as parameters, the target point to be pointed to as a variable, and the outward coordinate axis of the wrist coordinate system and the target point to be pointed to be collinear as the main optimization goal, convert the Cartesian space constraints for the robot body, the Cartesian space constraints for the environment, and the angle constraints of each joint into the restriction conditions of the nonlinear optimization equation group, and construct the nonlinear optimization equation group;

求解模块，用于以所述待指向目标点轨迹序列作为输入，使用序列最小二乘法对所述非线性优化方程组进行优化求解；A solution module, used for taking the trajectory sequence of the target point to be pointed to as input and optimizing and solving the nonlinear optimization equation group using a sequence least square method;

角度插补模块，用于若优化求解得到的关节变量和上一帧的关节变量的变化量超出可允许范围，则选用上一帧的关节变量赋到关节变量序列中；若优化求解得到的关节变量和上一帧的关节变量的变化量在所述可允许范围内，则对将优化求解得到的关节变量加入关节变量序列中，并对所述关节变量序列进行角度插补；An angle interpolation module is used to select the joint variables of the previous frame and assign them to the joint variable sequence if the variation of the joint variables obtained by optimization and solution and the joint variables of the previous frame exceeds the allowable range; if the variation of the joint variables obtained by optimization and solution and the joint variables of the previous frame is within the allowable range, add the joint variables obtained by optimization and solution to the joint variable sequence, and perform angle interpolation on the joint variable sequence;

传输模块，用于将进行角度插补后的关节角度序列数据传输到机器人工控机上，以使用伺服控制的方法驱动5R机械臂指向目标点轨迹。The transmission module is used to transmit the joint angle sequence data after angle interpolation to the robot industrial computer, so as to drive the 5R robot arm to point to the target point trajectory using the servo control method.

根据本申请实施例的第三方面，提供一种电子设备，包括：According to a third aspect of an embodiment of the present application, there is provided an electronic device, including:

一个或多个处理器；one or more processors;

存储器，用于存储一个或多个程序；A memory for storing one or more programs;

当所述一个或多个程序被所述一个或多个处理器执行，使得所述一个或多个处理器实现如第一方面所述的方法。When the one or more programs are executed by the one or more processors, the one or more processors implement the method as described in the first aspect.

根据本申请实施例的第四方面，提供一种计算机可读存储介质，其上存储有计算机指令，该指令被处理器执行时实现如第一方面所述方法的步骤。According to a fourth aspect of an embodiment of the present application, a computer-readable storage medium is provided, on which computer instructions are stored, and when the instructions are executed by a processor, the steps of the method described in the first aspect are implemented.

本申请的实施例提供的技术方案可以包括以下有益效果：The technical solution provided by the embodiments of the present application may have the following beneficial effects:

由上述实施例可知，本申请采用序列最小二乘方法求解所构建的指向动作非线性方程，解决逆运动学无法针对无姿态信息点得到逆解及环境存在空间约束的问题，达到机器人能够由非线性方程的求解结果直接指向给定的无姿态指向点。实现了5R机械臂针对无姿态信息目标点轨迹的在线指向动作，解决了无姿态信息目标点的机械臂在线指向问题，能够避开机械臂运动学奇异点同时满足三维空间约束。As can be seen from the above embodiments, the present application uses the sequential least squares method to solve the constructed nonlinear equations of pointing action, solves the problem that inverse kinematics cannot obtain an inverse solution for points without posture information and that there are spatial constraints in the environment, and achieves that the robot can directly point to a given non-attitude pointing point by the solution of the non-linear equation. The online pointing action of the 5R manipulator for the trajectory of the target point without posture information is realized, the problem of the manipulator's online pointing for the target point without posture information is solved, and the kinematic singularity of the manipulator can be avoided while satisfying the three-dimensional space constraints.

应当理解的是，以上的一般描述和后文的细节描述仅是示例性和解释性的，并不能限制本申请。It should be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the present application.

附图说明BRIEF DESCRIPTION OF THE DRAWINGS

此处的附图被并入说明书中并构成本说明书的一部分，示出了符合本申请的实施例，并与说明书一起用于解释本申请的原理。The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present application and, together with the description, serve to explain the principles of the present application.

图1是根据一示例性实施例示出的一种满足笛卡尔空间约束的五自由度机械臂指向动作实现方法的流程图。Fig. 1 is a flow chart showing a method for realizing a pointing motion of a five-degree-of-freedom robotic arm satisfying Cartesian space constraints according to an exemplary embodiment.

图2是根据一示例性实施例示出的导览机器人的示意图。Fig. 2 is a schematic diagram of a tour guide robot according to an exemplary embodiment.

图3是根据一示例性实施例示出的机器人构型的示意图。Fig. 3 is a schematic diagram showing a robot configuration according to an exemplary embodiment.

图4是根据一示例性实施例示出的一种满足笛卡尔空间约束的五自由度机械臂指向动作实现装置的框图。Fig. 4 is a block diagram of a device for realizing pointing motion of a five-degree-of-freedom manipulator satisfying Cartesian space constraints according to an exemplary embodiment.

图5是根据一示例性实施例示出的一种电子设备的示意图。Fig. 5 is a schematic diagram of an electronic device according to an exemplary embodiment.

具体实施方式DETAILED DESCRIPTION

这里将详细地对示例性实施例进行说明，其示例表示在附图中。下面的描述涉及附图时，除非另有表示，不同附图中的相同数字表示相同或相似的要素。以下示例性实施例中所描述的实施方式并不代表与本申请相一致的所有实施方式。Here, exemplary embodiments are described in detail, and examples thereof are shown in the accompanying drawings. When the following description refers to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The implementations described in the following exemplary embodiments do not represent all implementations consistent with the present application.

在本申请使用的术语是仅仅出于描述特定实施例的目的，而非旨在限制本申请。在本申请和所附权利要求书中所使用的单数形式的“一种”、“所述”和“该”也旨在包括多数形式，除非上下文清楚地表示其他含义。还应当理解，本文中使用的术语“和/或”是指并包含一个或多个相关联的列出项目的任何或所有可能组合。The terms used in this application are for the purpose of describing specific embodiments only and are not intended to limit this application. The singular forms of "a", "said" and "the" used in this application and the appended claims are also intended to include plural forms unless the context clearly indicates other meanings. It should also be understood that the term "and/or" used herein refers to and includes any or all possible combinations of one or more associated listed items.

应当理解，尽管在本申请可能采用术语第一、第二、第三等来描述各种信息，但这些信息不应限于这些术语。这些术语仅用来将同一类型的信息彼此区分开。例如，在不脱离本申请范围的情况下，第一信息也可以被称为第二信息，类似地，第二信息也可以被称为第一信息。取决于语境，如在此所使用的词语“如果”可以被解释成为“在……时”或“当……时”或“响应于确定”。It should be understood that although the terms first, second, third, etc. may be used in the present application to describe various information, these information should not be limited to these terms. These terms are only used to distinguish the same type of information from each other. For example, without departing from the scope of the present application, the first information may also be referred to as the second information, and similarly, the second information may also be referred to as the first information. Depending on the context, the word "if" as used herein may be interpreted as "at the time of" or "when" or "in response to determining".

图1是根据一示例性实施例示出的一种满足笛卡尔空间约束的五自由度机械臂指向动作实现方法的流程图，如图1所示，该方法通过终端实现，应用于如图2所示的导览机器人，机器人构型如图3所示，该方法可以包括以下步骤：FIG1 is a flow chart of a method for realizing a pointing action of a five-degree-of-freedom manipulator satisfying Cartesian space constraints according to an exemplary embodiment. As shown in FIG1 , the method is realized by a terminal and applied to a navigation robot as shown in FIG2 . The robot configuration is shown in FIG3 . The method may include the following steps:

步骤S10：获取机械臂的各个关节杆长、待指向目标点、待指向目标点轨迹序列；Step S10: Obtain the length of each joint rod of the robot arm, the target point to be pointed to, and the trajectory sequence of the target point to be pointed to;

步骤S11：以世界坐标系、当前5R机械臂关节坐标系间关系以及各个关节间杆长为参数，以所述待指向目标点作为变量，以腕部坐标系向外坐标轴与待指向目标点共线为主要优化目标，将针对机器人本体的笛卡尔空间约束、针对环境的笛卡尔空间约束、各个关节的角度约束转换为非线性优化方程组的限制条件，构建非线性优化方程组；Step S11: Taking the relationship between the world coordinate system, the current 5R robot arm joint coordinate system and the rod length between each joint as parameters, taking the target point to be pointed to as a variable, taking the outward coordinate axis of the wrist coordinate system and the target point to be pointed to be collinear as the main optimization goal, converting the Cartesian space constraints for the robot body, the Cartesian space constraints for the environment, and the angle constraints of each joint into the constraint conditions of the nonlinear optimization equation group, and constructing the nonlinear optimization equation group;

步骤S12：以所述待指向目标点轨迹序列作为输入，使用序列最小二乘法对所述非线性优化方程组进行优化求解；Step S12: using the trajectory sequence of the target point to be pointed to as input, and using the sequence least squares method to optimize and solve the nonlinear optimization equation group;

步骤S13：若优化求解得到的关节变量和上一帧的关节变量的变化量超出可允许范围，则选用上一帧的关节变量赋到关节变量序列中；若优化求解得到的关节变量和上一帧的关节变量的变化量在所述可允许范围内，则对将优化求解得到的关节变量加入关节变量序列中，并对所述关节变量序列进行角度插补；Step S13: if the variation of the joint variables obtained by optimization and the joint variables of the previous frame exceeds the allowable range, the joint variables of the previous frame are selected and assigned to the joint variable sequence; if the variation of the joint variables obtained by optimization and the joint variables of the previous frame is within the allowable range, the joint variables obtained by optimization and the joint variables are added to the joint variable sequence, and the angle interpolation of the joint variable sequence is performed;

步骤S14：将进行角度插补后的关节角度序列数据传输到机器人工控机上，以使用伺服控制的方法驱动5R机械臂指向目标点轨迹。Step S14: Transmit the joint angle sequence data after angle interpolation to the robot industrial computer, so as to drive the 5R robot arm to point to the target point trajectory using a servo control method.

由上述实施例可知，本申请采用序列最小二乘方法求解所构建的指向动作非线性方程，解决逆运动学无法针对无姿态信息点得到逆解及环境存在空间约束的问题，达到机器人能够由非线性方程的求解结果直接指向给定的无姿态指向点。实现了5R机械臂针对无姿态信息目标点轨迹的在线指向动作，解决了无姿态信息目标点的机械臂在线指向问题，能够避开机械臂运动学奇异点同时满足三维空间约束。As can be seen from the above embodiments, the present application uses the sequential least squares method to solve the constructed nonlinear equations of pointing action, solves the problem that inverse kinematics cannot obtain an inverse solution for points without posture information and that there are spatial constraints in the environment, and achieves that the robot can directly point to a given non-attitude pointing point by the solution of the non-linear equation. The online pointing action of the 5R manipulator for the trajectory of the target point without posture information is realized, the problem of the manipulator's online pointing for the target point without posture information is solved, and the kinematic singularity of the manipulator can be avoided while satisfying the three-dimensional space constraints.

在步骤S10的具体实施中，获取机械臂的各个关节杆长、待指向目标点、待指向目标点轨迹序列；In the specific implementation of step S10, the length of each joint rod of the robot arm, the target point to be pointed to, and the trajectory sequence of the target point to be pointed to are obtained;

具体地，实时运行过程中的待指向目标点需要由机器人所进行任务决定，一般由视觉建图提供的三维目标点作为待指向目标点，待指向目标点轨迹序列由离线编程得到，由固定的一组三维目标点或三维目标点的动态曲线表示。Specifically, the target point to be pointed to during real-time operation needs to be determined by the task performed by the robot. Generally, the three-dimensional target point provided by visual mapping is used as the target point to be pointed to. The trajectory sequence of the target point to be pointed to is obtained by offline programming and is represented by a fixed set of three-dimensional target points or a dynamic curve of the three-dimensional target points.

在步骤S11的具体实施中，以世界坐标系、当前5R机械臂关节坐标系间关系以及各个关节间杆长为参数，以所述待指向目标点作为变量，以腕部坐标系向外坐标轴与待指向目标点共线为主要优化目标，将针对机器人本体的笛卡尔空间约束、针对环境的笛卡尔空间约束、各个关节的角度约束转换为非线性优化方程组的限制条件，构建非线性优化方程组；In the specific implementation of step S11, the relationship between the world coordinate system, the current 5R robot arm joint coordinate system and the rod length between each joint are used as parameters, the target point to be pointed to is used as a variable, and the outward coordinate axis of the wrist coordinate system and the target point to be pointed to are collinear as the main optimization goal. The Cartesian space constraints for the robot body, the Cartesian space constraints for the environment, and the angle constraints of each joint are converted into constraint conditions of a nonlinear optimization equation group, and a nonlinear optimization equation group is constructed;

具体地，此步骤可以包括以下子步骤：Specifically, this step may include the following sub-steps:

步骤S21：根据5R机械臂的世界坐标系、各关节坐标系、关节间杆长建立5R机械臂的正向运动学模型，得到机械臂末端、各关节坐标系原点位于世界坐标系下的位置关于五个关节变量的解析式（即5R机械臂腕部坐标系和世界坐标系的齐次变换）；Step S21: A forward kinematics model of the 5R robotic arm is established according to the world coordinate system, the coordinate systems of each joint, and the length of the rod between the joints, and an analytical expression of the positions of the end of the robotic arm and the origin of each joint coordinate system in the world coordinate system with respect to five joint variables is obtained (i.e., a homogeneous transformation between the wrist coordinate system of the 5R robotic arm and the world coordinate system);

Figure SMS_32
Figure SMS_32

一般通过DH建模、旋量方法就可以得到每个关节对应于上一个关节坐标系的齐次变换（表示为T），

Figure SMS_33
为腕部关节对应世界坐标系的齐次变换。Generally, the homogeneous transformation (expressed as T) of each joint corresponding to the previous joint coordinate system can be obtained through DH modeling and the screw method.
Figure SMS_33
is the homogeneous transformation of the wrist joint to the world coordinate system.

这里将

Figure SMS_34
汇总到一起，表示将肩部相对机器人坐标系的齐次变换表示为经过
Figure SMS_35
三个关节变量的齐次变换结果。Here will
Figure SMS_34
Taken together, the homogeneous transformation of the shoulder relative to the robot coordinate system is expressed as
Figure SMS_35
Homogeneous transformation results of the three joint variables.

步骤S22：给定世界坐标系下所述待指向目标点的位置，通过所述正向运动学模型，得到所述待指向目标点位于世界坐标系的三维坐标，将针对机器人本体的笛卡尔空间约束、针对环境的笛卡尔空间约束、各个关节的角度约束转换为非线性优化方程组的限制条件，构建非线性优化方程组，所建立的优化目标包含：使待指向目标点位于腕部坐标系z轴正方向上以及最小化待指向目标点位于腕部坐标系x,y轴上的偏移量、所指向目标点与腕部坐标系原点组成的矢量与腕部坐标系x,y轴的内积、与上一次优化求解结果之间的偏差。Step S22: Given the position of the target point to be pointed to in the world coordinate system, the three-dimensional coordinates of the target point to be pointed to in the world coordinate system are obtained through the forward kinematics model, and the Cartesian space constraints for the robot body, the Cartesian space constraints for the environment, and the angle constraints of each joint are converted into constraints of a nonlinear optimization equation group, and a nonlinear optimization equation group is constructed. The established optimization objectives include: making the target point to be pointed to be located in the positive direction of the z-axis of the wrist coordinate system and minimizing the offset of the target point to be pointed to on the x, y axis of the wrist coordinate system, the inner product of the vector composed of the target point to be pointed to and the origin of the wrist coordinate system and the x, y axis of the wrist coordinate system, and the deviation from the previous optimization solution.

具体地，针对机器人本体的笛卡尔空间约束可以表示为：Specifically, the Cartesian space constraints for the robot body can be expressed as:

Figure SMS_36
Figure SMS_36

式中，

Figure SMS_37
表示机器人肩部关节对应于世界坐标系的位置，
Figure SMS_38
表示机器人肘部关节对应于世界坐标系的位置，
Figure SMS_39
表示机器人肩部关节对应于世界坐标系的位置，
Figure SMS_40
可以表示为针对机器人本体结构的线性约束或非线性约束条件，例如机器人本体碰撞约束。In the formula,
Figure SMS_37
represents the position of the robot shoulder joint corresponding to the world coordinate system,
Figure SMS_38
represents the position of the robot elbow joint corresponding to the world coordinate system,
Figure SMS_39
represents the position of the robot shoulder joint corresponding to the world coordinate system,
Figure SMS_40
It can be expressed as a linear constraint or nonlinear constraint on the robot body structure, such as a robot body collision constraint.

针对环境的笛卡尔空间约束可以表示为：The Cartesian space constraints for the environment can be expressed as:

Figure SMS_41
Figure SMS_41

式中,

Figure SMS_42
可以表示为针对环境的线性约束或非线性约束条件，例如场景中存在的障碍物、场景中的坐标限制。In the formula,
Figure SMS_42
It can be expressed as linear constraints or nonlinear constraints on the environment, such as obstacles in the scene and coordinate restrictions in the scene.

关节约束可以表示为：The joint constraints can be expressed as:

Figure SMS_43
，1≤j≤5
Figure SMS_43
, 1≤j≤5

式中，

Figure SMS_44
为5R机械臂第j个关节变量的最小值，
Figure SMS_45
为5R机械臂第j个关节变量实际值，
Figure SMS_46
为5R机械臂第j个关节变量最大值。In the formula,
Figure SMS_44
is the minimum value of the j-th joint variable of the 5R robot arm,
Figure SMS_45
is the actual value of the jth joint variable of the 5R robot arm,
Figure SMS_46
is the maximum value of the j-th joint variable of the 5R robot arm.

在步骤S12的具体实施中，以所述待指向目标点轨迹序列作为输入，使用序列最小二乘法对所述非线性优化方程组进行优化求解；In the specific implementation of step S12, the trajectory sequence of the target point to be pointed to is used as input, and the nonlinear optimization equation group is optimized and solved using the sequence least squares method;

具体地，以待指向目标点轨迹序列作为输入，步骤S11中以腕部坐标系向外坐标轴与待指向目标点共线为主要优化目标，此外，为提高指向动作轨迹的平滑度，引入关节变量与前次求解结果之间偏差的L2范数作为次优化目标，从而，所构建的非线性优化方程组为：Specifically, the trajectory sequence of the target point to be pointed to is used as input. In step S11, the main optimization goal is that the outward coordinate axis of the wrist coordinate system is collinear with the target point to be pointed to. In addition, in order to improve the smoothness of the pointing action trajectory, the L2 norm of the deviation between the joint variables and the previous solution results is introduced as a secondary optimization goal. Thus, the constructed nonlinear optimization equation group is:

Figure SMS_47
，
Figure SMS_47
,

其中

Figure SMS_50
分别为肩部的三个关节角、肘部的关节角和腕部的关节角，
Figure SMS_56
为
Figure SMS_64
对应的权重系数，
Figure SMS_49
为待指向目标点相对于世界坐标系原点在Z轴方向上的偏移，
Figure SMS_57
、
Figure SMS_65
同理；
Figure SMS_72
表示腕部坐标系相对于世界坐标系的变换矩阵，
Figure SMS_51
表示腕部X轴在世界坐标系下的表示，
Figure SMS_60
表示腕部Y轴在世界坐标系下的表示，
Figure SMS_68
表示腕部Z轴在世界坐标系下的表示，
Figure SMS_75
表示腕部坐标系相对世界坐标系的原点偏移，
Figure SMS_53
、
Figure SMS_59
、
Figure SMS_67
为腕部坐标系原点相对于世界坐标系原点的位置，
Figure SMS_74
表示待指向目标点相对于相对世界坐标系的原点偏移，
Figure SMS_55
、
Figure SMS_62
、
Figure SMS_70
、
Figure SMS_76
、
Figure SMS_48
、
Figure SMS_58
、
Figure SMS_66
同理；
Figure SMS_73
为第j个关节的第i次优化结果，
Figure SMS_54
为第j个关节针对待指向目标点的第i-1次优化结果，
Figure SMS_61
为针对环境的笛卡尔空间约束，
Figure SMS_71
为针对机器人本体的笛卡尔空间约束，
Figure SMS_77
、
Figure SMS_52
分别为
Figure SMS_63
和
Figure SMS_69
对应的权重系数。in
Figure SMS_50
They are the three joint angles of the shoulder, the joint angle of the elbow and the joint angle of the wrist.
Figure SMS_56
for
Figure SMS_64
The corresponding weight coefficient is,
Figure SMS_49
is the offset of the target point to be pointed to relative to the origin of the world coordinate system in the Z-axis direction,
Figure SMS_57
,
Figure SMS_65
Similarly;
Figure SMS_72
Represents the transformation matrix of the wrist coordinate system relative to the world coordinate system,
Figure SMS_51
Indicates the wrist X-axis in the world coordinate system.
Figure SMS_60
Indicates the wrist Y-axis in the world coordinate system.
Figure SMS_68
Indicates the wrist Z axis in the world coordinate system.
Figure SMS_75
Indicates the origin offset of the wrist coordinate system relative to the world coordinate system.
Figure SMS_53
,
Figure SMS_59
,
Figure SMS_67
is the position of the wrist coordinate system origin relative to the world coordinate system origin,
Figure SMS_74
Indicates the offset of the target point to be pointed to relative to the origin of the relative world coordinate system.
Figure SMS_55
,
Figure SMS_62
,
Figure SMS_70
,
Figure SMS_76
,
Figure SMS_48
,
Figure SMS_58
,
Figure SMS_66
Similarly;
Figure SMS_73
is the i-th optimization result of the j-th joint,
Figure SMS_54
is the i-1th optimization result of the jth joint for the target point to be pointed to,
Figure SMS_61
is the Cartesian space constraint for the environment,
Figure SMS_71
is the Cartesian space constraint for the robot body,
Figure SMS_77
,
Figure SMS_52
They are
Figure SMS_63
and
Figure SMS_69
The corresponding weight coefficient.

具体而言，f1实现机械臂指向待指向目标点时，目标点应位于机械臂腕部转轴方向以外（定义机械臂Z轴表示为机械臂转轴正方向，向外即Z轴正向，Y轴统一定义为机器人左侧，X轴由已确定的X、Y轴做右手定则得到），f2及f3将待指向目标点限制在转轴方向上，f4、f5表示由腕部坐标系到待指向目标点的矢量应与腕部坐标X、Y轴垂直（加强1,2,3条件），f6表示出现两次及以上待指向目标点时，最小化两者关节变量之间的偏差，T表示腕部坐标系相对世界坐标系的齐次变换阵，

Figure SMS_80
表示腕部X轴在世界坐标系下的表示，
Figure SMS_83
表示腕部Y轴在世界坐标系下的表示，
Figure SMS_85
表示腕部Z轴在世界坐标系下的表示，
Figure SMS_79
表示腕部坐标系相对世界坐标系的原点偏移，
Figure SMS_81
、
Figure SMS_84
、
Figure SMS_86
分别表示腕部坐标系原点相对于世界坐标系原点的位置。式中，wrist表示腕部，world表示世界坐标系，上标为参考坐标系，下标为实际坐标系。
Figure SMS_78
为第j个关节的第i次优化结果，
Figure SMS_82
为第j个关节针对待指向目标点的第i-1次优化结果。需要说明的是，如果是非实时地针对待指向目标点轨迹序列做一连串的优化求解，第i次就表示针对序列中第i个点的优化结果，i-1就是针对序列中第i-1个点的优化结果，优化过程中就是最小化相邻两次优化求解结果之间的偏差，比如说针对第一个指向点输出的关节角度，在优化求解第二个指向点的关节角度过程中，最小化与第一次求解关节角度之间的偏差；如果是实时地针对待指向目标点做优化求解关节角，第i次表示当前的优化结果，第i-1次就表示我上一次的优化结果。Specifically, when f 1 realizes the robot arm pointing to the target point to be pointed to, the target point should be located outside the rotation axis direction of the robot arm wrist (the robot arm Z axis is defined as the positive direction of the robot arm rotation axis, the outward direction is the positive direction of the Z axis, the Y axis is uniformly defined as the left side of the robot, and the X axis is obtained by the right-hand rule of the determined X and Y axes), f 2 and f 3 limit the target point to be pointed to in the direction of the rotation axis, f 4 and f 5 indicate that the vector from the wrist coordinate system to the target point to be pointed to should be perpendicular to the X and Y axes of the wrist coordinate system (strengthening conditions 1, 2, and 3), f 6 indicates that when the target point to be pointed to appears twice or more, the deviation between the joint variables of the two is minimized, and T represents the homogeneous transformation matrix of the wrist coordinate system relative to the world coordinate system.
Figure SMS_80
Indicates the wrist X-axis in the world coordinate system.
Figure SMS_83
Indicates the wrist Y-axis in the world coordinate system.
Figure SMS_85
Indicates the wrist Z axis in the world coordinate system.
Figure SMS_79
Indicates the origin offset of the wrist coordinate system relative to the world coordinate system.
Figure SMS_81
,
Figure SMS_84
,
Figure SMS_86
They represent the position of the wrist coordinate system origin relative to the world coordinate system origin. In the formula, wrist represents the wrist, world represents the world coordinate system, the superscript is the reference coordinate system, and the subscript is the actual coordinate system.
Figure SMS_78
is the i-th optimization result of the j-th joint,
Figure SMS_82
It is the i-1th optimization result of the j-th joint for the target point to be pointed to. It should be noted that if a series of optimization solutions are performed for the trajectory sequence of the target point to be pointed to in non-real time, the i-th time represents the optimization result for the i-th point in the sequence, and i-1 is the optimization result for the i-1th point in the sequence. The optimization process is to minimize the deviation between the two adjacent optimization solution results. For example, for the joint angle output for the first pointing point, when optimizing the joint angle for the second pointing point, minimize the deviation between the joint angle and the first solution; if the joint angle is optimized for the target point to be pointed to in real time, the i-th time represents the current optimization result, and the i-1-th time represents the last optimization result.

通过序列最小二乘法对上述优化求解方程进行求解，得到肩部的三个关节角，肘部 一个关节角和腕部的一个关节角。The above optimization equations are solved by sequential least squares method to obtain three joint angles of the shoulder, one joint angle of the elbow and one joint angle of the wrist.

在步骤S13的具体实施中，若优化求解得到的关节变量和上一帧的关节变量的变化量超出可允许范围，则选用上一帧的关节变量赋到关节变量序列中；若优化求解得到的关节变量和上一帧的关节变量的变化量在所述可允许范围内，则对将优化求解得到的关节变量加入关节变量序列中，并对所述关节变量序列进行角度插补；In the specific implementation of step S13, if the variation of the joint variables obtained by optimization and the joint variables of the previous frame exceeds the allowable range, the joint variables of the previous frame are selected and assigned to the joint variable sequence; if the variation of the joint variables obtained by optimization and the joint variables of the previous frame is within the allowable range, the joint variables obtained by optimization and the joint variables are added to the joint variable sequence, and the angle interpolation of the joint variable sequence is performed;

具体地，本方法可以在两帧之间进行实时插补，也可以在得到一个关节变量序列之后再非实时地进行整个序列的插补。Specifically, the method can perform real-time interpolation between two frames, or can perform non-real-time interpolation of the entire sequence after obtaining a joint variable sequence.

对于整个序列的插补，当得到优化后的关节变量序列后，由于序列具有一定的离散性，为保证机械臂动作的平滑性，使用修正Akima分段三次Hermite插值方法得到较为密集的关节轨迹，其得到的关节变量序列能够避免过冲，达到比五次样条插值更好的效果。For the interpolation of the entire sequence, after the optimized joint variable sequence is obtained, since the sequence has a certain discreteness, in order to ensure the smoothness of the robot movement, the modified Akima piecewise cubic Hermite interpolation method is used to obtain a more dense joint trajectory. The joint variable sequence obtained can avoid overshoot and achieve better results than quintic spline interpolation.

更具体地，对动作关键帧进行修正Akima分段三次Hermite插值，当前位置与目标位置对应的角度满足如下式的关系：More specifically, the action keyframes are modified by Akima piecewise cubic Hermite interpolation, and the angles corresponding to the current position and the target position satisfy the following relationship:

Figure SMS_87
Figure SMS_87

式中，

Figure SMS_88
表示连接当前角度
Figure SMS_89
（对应时间
Figure SMS_90
）与下一角度
Figure SMS_91
（对应时间
Figure SMS_92
）关于时间
Figure SMS_93
的斜率，w1,w2为Akima插值修正权重，当两个具有不同斜率的平台区相遇时，对原始Akima 算法所做的修改会对斜率更接近于零的一侧赋予更多权重，此修正优先考虑更接近水平的一侧，这样更直观并可避免过冲。特别是，每当有三个或更多连续共线点时，该算法将这些点用一条直线连接，从而避免过冲。采样点θi处的导数di的值通过给出的两修正权重加权得到。In the formula,
Figure SMS_88
Indicates the current angle of the connection
Figure SMS_89
(corresponding to time
Figure SMS_90
) and the next angle
Figure SMS_91
(corresponding to time
Figure SMS_92
) About time
Figure SMS_93
The slope of , w1, w2 are Akima interpolation correction weights. When two platform areas with different slopes meet, the modification made to the original Akima algorithm gives more weight to the side with a slope closer to zero. This correction gives priority to the side closer to the horizontal, which is more intuitive and avoids overshoot. In particular, whenever there are three or more consecutive collinear points, the algorithm connects these points with a straight line to avoid overshoot. The value of the derivative di at the sampling point θi is weighted by the two correction weights given.

进一步地，得到Further, we get

Figure SMS_94
Figure SMS_94

该式为改进akima算法的通用公式，将插值结果表示为三次多项式，由前面获得的导数结果计算公式的权重c.This formula is a general formula for improving the Akima algorithm. The interpolation result is expressed as a cubic polynomial, and the weight c of the formula is calculated by the derivative result obtained previously.

根据所述三次多项式的多项式系数，可以使5R机械臂按照一定的时间间隔生成机械臂的关节角度序列、关节角速度序列、关节角加速度序列，实现机械臂在改进akima插值方法生成的关键帧间的转换。According to the polynomial coefficients of the cubic polynomial, the 5R robotic arm can generate the joint angle sequence, joint angular velocity sequence, and joint angular acceleration sequence of the robotic arm at certain time intervals, thereby realizing the conversion of the robotic arm between key frames generated by the improved Akima interpolation method.

在步骤S14的具体实施中，将进行角度插补后的关节角度序列数据传输到机器人工控机上，以使用伺服控制的方法驱动5R机械臂指向目标点轨迹。In the specific implementation of step S14, the joint angle sequence data after angle interpolation is transmitted to the robot industrial computer, so as to drive the 5R robot arm to point to the target point trajectory using a servo control method.

需要说明的是，步骤S14的具体实施为本领域的常规技术手段，此处不作赘述。It should be noted that the specific implementation of step S14 is a conventional technical means in the art and will not be elaborated here.

与前述的满足笛卡尔空间约束的五自由度机械臂指向动作实现方法的实施例相对应，本申请还提供了满足笛卡尔空间约束的五自由度机械臂指向动作实现装置的实施例。Corresponding to the aforementioned embodiment of the method for realizing the pointing motion of a five-degree-of-freedom robotic arm satisfying Cartesian space constraints, the present application also provides an embodiment of a device for realizing the pointing motion of a five-degree-of-freedom robotic arm satisfying Cartesian space constraints.

图4是根据一示例性实施例示出的一种满足笛卡尔空间约束的五自由度机械臂指向动作实现装置框图。参照图4，该装置可以包括：FIG4 is a block diagram of a device for realizing a pointing motion of a five-degree-of-freedom manipulator satisfying Cartesian space constraints according to an exemplary embodiment. Referring to FIG4 , the device may include:

获取模块21，用于获取机械臂的各个关节杆长、待指向目标点、待指向目标点轨迹序列；An acquisition module 21 is used to acquire the length of each joint rod of the robot arm, the target point to be pointed to, and the trajectory sequence of the target point to be pointed to;

构建模块22，用于以世界坐标系、当前5R机械臂关节坐标系间关系以及各个关节间杆长为参数，以所述待指向目标点作为变量，以腕部坐标系向外坐标轴与待指向目标点共线为主要优化目标，将针对机器人本体的笛卡尔空间约束、针对环境的笛卡尔空间约束、各个关节的角度约束转换为非线性优化方程组的限制条件，构建非线性优化方程组；A construction module 22 is used to use the relationship between the world coordinate system, the current 5R robot arm joint coordinate system, and the rod length between each joint as parameters, the target point to be pointed to as a variable, and the outward coordinate axis of the wrist coordinate system and the target point to be pointed to be collinear as the main optimization goal, convert the Cartesian space constraints for the robot body, the Cartesian space constraints for the environment, and the angle constraints of each joint into the restriction conditions of the nonlinear optimization equation group, and construct the nonlinear optimization equation group;

求解模块23，用于以所述待指向目标点轨迹序列作为输入，使用序列最小二乘法对所述非线性优化方程组进行优化求解；A solution module 23, configured to use the trajectory sequence of the target point to be pointed to as input and use a sequence least square method to optimize and solve the nonlinear optimization equation group;

角度插补模块24，用于若优化求解得到的关节变量和上一帧的关节变量的变化量超出可允许范围，则选用上一帧的关节变量赋到关节变量序列中；若优化求解得到的关节变量和上一帧的关节变量的变化量在所述可允许范围内，则对将优化求解得到的关节变量加入关节变量序列中，并对所述关节变量序列进行角度插补；Angle interpolation module 24 is used for selecting joint variables of the previous frame to be assigned to the joint variable sequence if the variation of joint variables obtained by optimization and solution and joint variables of the previous frame exceeds the allowable range; if the variation of joint variables obtained by optimization and solution and joint variables of the previous frame is within the allowable range, adding joint variables obtained by optimization and solution to the joint variable sequence, and performing angle interpolation on the joint variable sequence;

传输模块25，用于将进行角度插补后的关节角度序列数据传输到机器人工控机上，以使用伺服控制的方法驱动5R机械臂指向目标点轨迹。The transmission module 25 is used to transmit the joint angle sequence data after angle interpolation to the robot industrial computer, so as to drive the 5R robot arm to point to the target point trajectory using a servo control method.

关于上述实施例中的装置，其中各个模块执行操作的具体方式已经在有关该方法的实施例中进行了详细描述，此处将不做详细阐述说明。Regarding the device in the above embodiment, the specific manner in which each module performs operations has been described in detail in the embodiment of the method, and will not be elaborated here.

对于装置实施例而言，由于其基本对应于方法实施例，所以相关之处参见方法实施例的部分说明即可。以上所描述的装置实施例仅仅是示意性的，其中所述作为分离部件说明的单元可以是或者也可以不是物理上分开的，作为单元显示的部件可以是或者也可以不是物理单元，即可以位于一个地方，或者也可以分布到多个网络单元上。可以根据实际的需要选择其中的部分或者全部模块来实现本申请方案的目的。本领域普通技术人员在不付出创造性劳动的情况下，即可以理解并实施。For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can refer to the partial description of the method embodiments. The device embodiments described above are merely schematic, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the present application. A person of ordinary skill in the art can understand and implement it without creative work.

相应的，本申请还提供一种电子设备，包括：一个或多个处理器；存储器，用于存储一个或多个程序；当所述一个或多个程序被所述一个或多个处理器执行，使得所述一个或多个处理器实现如上述的满足笛卡尔空间约束的五自由度机械臂指向动作实现方法。如图5所示，为本发明实施例提供的一种满足笛卡尔空间约束的五自由度机械臂指向动作实现方法所在任意具备数据处理能力的设备的一种硬件结构图，除了图5所示的处理器、内存以及网络接口之外，实施例中装置所在的任意具备数据处理能力的设备通常根据该任意具备数据处理能力的设备的实际功能，还可以包括其他硬件，对此不再赘述。Correspondingly, the present application also provides an electronic device, including: one or more processors; a memory for storing one or more programs; when the one or more programs are executed by the one or more processors, the one or more processors implement the above-mentioned five-degree-of-freedom robotic arm pointing action implementation method that satisfies Cartesian space constraints. As shown in Figure 5, a hardware structure diagram of any device with data processing capability in which a five-degree-of-freedom robotic arm pointing action implementation method that satisfies Cartesian space constraints is provided in an embodiment of the present invention, in addition to the processor, memory and network interface shown in Figure 5, any device with data processing capability in which the device in the embodiment is located can also include other hardware according to the actual function of the device with data processing capability, which will not be described in detail.

相应的，本申请还提供一种计算机可读存储介质，其上存储有计算机指令，该指令被处理器执行时实现如上述的满足笛卡尔空间约束的五自由度机械臂指向动作实现方法。所述计算机可读存储介质可以是前述任一实施例所述的任意具备数据处理能力的设备的内部存储单元，例如硬盘或内存。所述计算机可读存储介质也可以是外部存储设备，例如所述设备上配备的插接式硬盘、智能存储卡（Smart Media Card，SMC）、SD卡、闪存卡（FlashCard）等。进一步的，所述计算机可读存储介还可以既包括任意具备数据处理能力的设备的内部存储单元也包括外部存储设备。所述计算机可读存储介质用于存储所述计算机程序以及所述任意具备数据处理能力的设备所需的其他程序和数据，还可以用于暂时地存储已经输出或者将要输出的数据。Correspondingly, the present application also provides a computer-readable storage medium on which computer instructions are stored, and when the instructions are executed by the processor, the five-degree-of-freedom manipulator pointing action implementation method that satisfies Cartesian space constraints as described above is implemented. The computer-readable storage medium can be an internal storage unit of any device with data processing capabilities described in any of the aforementioned embodiments, such as a hard disk or a memory. The computer-readable storage medium can also be an external storage device, such as a plug-in hard disk, a smart memory card (Smart Media Card, SMC), an SD card, a flash card (FlashCard), etc. equipped on the device. Furthermore, the computer-readable storage medium can also include both an internal storage unit and an external storage device of any device with data processing capabilities. The computer-readable storage medium is used to store the computer program and other programs and data required by any device with data processing capabilities, and can also be used to temporarily store data that has been output or is to be output.

本领域技术人员在考虑说明书及实践这里公开的内容后，将容易想到本申请的其它实施方案。本申请旨在涵盖本申请的任何变型、用途或者适应性变化，这些变型、用途或者适应性变化遵循本申请的一般性原理并包括本申请未公开的本技术领域中的公知常识或惯用技术手段。Those skilled in the art will readily appreciate other embodiments of the present application after considering the specification and practicing the contents disclosed herein. The present application is intended to cover any variations, uses or adaptations of the present application, which follow the general principles of the present application and include common knowledge or customary technical means in the art that are not disclosed in the present application.

应当理解的是，本申请并不局限于上面已经描述并在附图中示出的精确结构，并且可以在不脱离其范围进行各种修改和改变。It should be understood that the present application is not limited to the exact construction that has been described above and shown in the drawings, and that various modifications and changes may be made without departing from the scope thereof.

Claims (9)

1.一种满足笛卡尔空间约束的五自由度机械臂指向动作实现方法，其特征在于，包括：1. A method for realizing a pointing motion of a five-degree-of-freedom manipulator satisfying Cartesian space constraints, characterized by comprising: 获取机械臂的各个关节杆长、待指向目标点、待指向目标点轨迹序列；Obtain the length of each joint rod of the robot arm, the target point to be pointed to, and the trajectory sequence of the target point to be pointed to; 以世界坐标系、当前5R机械臂关节坐标系间关系以及各个关节间杆长为参数，以所述待指向目标点作为变量，以腕部坐标系向外坐标轴与待指向目标点共线为主要优化目标，将针对机器人本体的笛卡尔空间约束、针对环境的笛卡尔空间约束、各个关节的角度约束转换为非线性优化方程组的限制条件，构建非线性优化方程组；Taking the relationship between the world coordinate system, the current 5R robot arm joint coordinate system and the rod length between each joint as parameters, taking the target point to be pointed to as a variable, taking the outward coordinate axis of the wrist coordinate system and the target point to be pointed to be collinear as the main optimization goal, converting the Cartesian space constraints for the robot body, the Cartesian space constraints for the environment, and the angle constraints of each joint into the restriction conditions of the nonlinear optimization equation group, and constructing the nonlinear optimization equation group; 以所述待指向目标点轨迹序列作为输入，使用序列最小二乘法对所述非线性优化方程组进行优化求解；Taking the trajectory sequence of the target point to be pointed to as input, the nonlinear optimization equation group is optimized and solved using the sequential least squares method; 若优化求解得到的关节变量和上一帧的关节变量的变化量超出可允许范围，则选用上一帧的关节变量赋到关节变量序列中；若优化求解得到的关节变量和上一帧的关节变量的变化量在所述可允许范围内，则对将优化求解得到的关节变量加入关节变量序列中，并对所述关节变量序列进行角度插补；If the variation of the joint variables obtained by the optimization solution and the joint variables of the previous frame exceeds the allowable range, the joint variables of the previous frame are selected and assigned to the joint variable sequence; if the variation of the joint variables obtained by the optimization solution and the joint variables of the previous frame is within the allowable range, the joint variables obtained by the optimization solution are added to the joint variable sequence, and the angle interpolation of the joint variable sequence is performed; 将进行角度插补后的关节角度序列数据传输到机器人工控机上，以使用伺服控制的方法驱动5R机械臂指向目标点轨迹。The joint angle sequence data after angle interpolation is transmitted to the robot industrial computer, so as to drive the 5R robot arm to point to the target point trajectory using the servo control method. 2.根据权利要求1所述的方法，其特征在于，根据5R机械臂的世界坐标系、各关节坐标系、关节间杆长建立5R机械臂的正向运动学模型，根据所述正向运动学模型得到所述世界坐标系、当前5R机械臂关节坐标系间关系。2. The method according to claim 1 is characterized in that a forward kinematics model of the 5R robotic arm is established based on the world coordinate system, each joint coordinate system, and the rod length between joints of the 5R robotic arm, and the relationship between the world coordinate system and the current 5R robotic arm joint coordinate system is obtained based on the forward kinematics model. 3.根据权利要求1所述的方法，其特征在于，所述主要优化目标具体为：使待指向目标点位于腕部坐标系z轴正方向上以及最小化待指向目标点位于腕部坐标系x,y轴上的偏移量、所指向目标点与腕部坐标系原点组成的矢量与腕部坐标系x,y轴的内积、与上一次优化求解结果之间的偏差。3. The method according to claim 1 is characterized in that the main optimization objectives are: to make the target point to be pointed to be located in the positive direction of the z-axis of the wrist coordinate system and to minimize the offset of the target point to be pointed to on the x, y axes of the wrist coordinate system, the inner product of the vector composed of the target point to be pointed to and the origin of the wrist coordinate system and the x, y axes of the wrist coordinate system, and the deviation from the previous optimization solution result. 4.根据权利要求1所述的方法，其特征在于，在构建非线性优化方程组前，引入关节变量与前次求解结果之间偏差的L2范数作为次优化目标。4. The method according to claim 1 is characterized in that before constructing the nonlinear optimization equation group, the L2 norm of the deviation between the joint variable and the previous solution result is introduced as a sub-optimization target. 5.根据权利要求4所述的方法，其特征在于，所构建的非线性优化方程组为：5. The method according to claim 4, characterized in that the constructed nonlinear optimization equations are:
Figure QLYQS_1
，
Figure QLYQS_1
, 其中
Figure QLYQS_2
分别为肩部的三个关节角、肘部的关节角和腕部的关节角，
Figure QLYQS_11
为
Figure QLYQS_20
对应的权重系数，
Figure QLYQS_6
为待指向目标点相对于世界坐标系原点在Z轴方向上的偏移，
Figure QLYQS_16
、
Figure QLYQS_24
同理；
Figure QLYQS_30
表示腕部坐标系相对于世界坐标系的变换矩阵，
Figure QLYQS_9
表示腕部X轴在世界坐标系下的表示，
Figure QLYQS_17
表示腕部Y轴在世界坐标系下的表示，
Figure QLYQS_25
表示腕部Z轴在世界坐标系下的表示，
Figure QLYQS_31
表示腕部坐标系相对世界坐标系的原点偏移，
Figure QLYQS_7
、
Figure QLYQS_12
、
Figure QLYQS_19
为腕部坐标系原点相对于世界坐标系原点的位置，
Figure QLYQS_28
表示待指向目标点相对于相对世界坐标系的原点偏移，
Figure QLYQS_5
、
Figure QLYQS_10
、
Figure QLYQS_18
、
Figure QLYQS_26
、
Figure QLYQS_4
、
Figure QLYQS_13
、
Figure QLYQS_21
同理；
Figure QLYQS_27
为第j个关节的第i次优化结果，
Figure QLYQS_3
为第j个关节针对待指向目标点的第i-1次优化结果，
Figure QLYQS_14
为针对环境的笛卡尔空间约束，
Figure QLYQS_22
为针对机器人本体的笛卡尔空间约束，
Figure QLYQS_29
、
Figure QLYQS_8
分别为
Figure QLYQS_15
和
Figure QLYQS_23
对应的权重系数。in
Figure QLYQS_2
They are the three joint angles of the shoulder, the joint angle of the elbow and the joint angle of the wrist.
Figure QLYQS_11
for
Figure QLYQS_20
The corresponding weight coefficient is,
Figure QLYQS_6
is the offset of the target point to be pointed to relative to the origin of the world coordinate system in the Z-axis direction,
Figure QLYQS_16
,
Figure QLYQS_24
Similarly;
Figure QLYQS_30
Represents the transformation matrix of the wrist coordinate system relative to the world coordinate system,
Figure QLYQS_9
Indicates the wrist X-axis in the world coordinate system.
Figure QLYQS_17
Indicates the wrist Y-axis in the world coordinate system.
Figure QLYQS_25
Indicates the wrist Z axis in the world coordinate system.
Figure QLYQS_31
Indicates the origin offset of the wrist coordinate system relative to the world coordinate system.
Figure QLYQS_7
,
Figure QLYQS_12
,
Figure QLYQS_19
is the position of the wrist coordinate system origin relative to the world coordinate system origin,
Figure QLYQS_28
Indicates the offset of the target point to be pointed to relative to the origin of the relative world coordinate system.
Figure QLYQS_5
,
Figure QLYQS_10
,
Figure QLYQS_18
,
Figure QLYQS_26
,
Figure QLYQS_4
,
Figure QLYQS_13
,
Figure QLYQS_21
Similarly;
Figure QLYQS_27
is the i-th optimization result of the j-th joint,
Figure QLYQS_3
is the i-1th optimization result of the jth joint for the target point to be pointed to,
Figure QLYQS_14
is the Cartesian space constraint for the environment,
Figure QLYQS_22
is the Cartesian space constraint for the robot body,
Figure QLYQS_29
,
Figure QLYQS_8
They are
Figure QLYQS_15
and
Figure QLYQS_23
The corresponding weight coefficient. 6.根据权利要求1所述的方法，其特征在于，利用修正Akima分段三次Hermite插值方法对所述关节变量序列进行角度插补。6. The method according to claim 1 is characterized in that the angle interpolation of the joint variable sequence is performed using a modified Akima piecewise cubic Hermite interpolation method. 7.一种满足笛卡尔空间约束的五自由度机械臂指向动作实现装置，其特征在于，包括：7. A device for realizing pointing motion of a five-degree-of-freedom manipulator satisfying Cartesian space constraints, characterized by comprising: 获取模块，用于获取机械臂的各个关节杆长、待指向目标点、待指向目标点轨迹序列；An acquisition module is used to acquire the length of each joint rod of the robot arm, the target point to be pointed to, and the trajectory sequence of the target point to be pointed to; 构建模块，用于以世界坐标系、当前5R机械臂关节坐标系间关系以及各个关节间杆长为参数，以所述待指向目标点作为变量，以腕部坐标系向外坐标轴与待指向目标点共线为主要优化目标，将针对机器人本体的笛卡尔空间约束、针对环境的笛卡尔空间约束、各个关节的角度约束转换为非线性优化方程组的限制条件，构建非线性优化方程组；A construction module is used to use the relationship between the world coordinate system, the current 5R robot arm joint coordinate system, and the rod length between each joint as parameters, the target point to be pointed to as a variable, and the outward coordinate axis of the wrist coordinate system and the target point to be pointed to be collinear as the main optimization goal, convert the Cartesian space constraints for the robot body, the Cartesian space constraints for the environment, and the angle constraints of each joint into the restriction conditions of the nonlinear optimization equation group, and construct the nonlinear optimization equation group; 求解模块，用于以所述待指向目标点轨迹序列作为输入，使用序列最小二乘法对所述非线性优化方程组进行优化求解；A solution module, used for taking the trajectory sequence of the target point to be pointed to as input and optimizing and solving the nonlinear optimization equation group using a sequence least square method; 角度插补模块，用于若优化求解得到的关节变量和上一帧的关节变量的变化量超出可允许范围，则选用上一帧的关节变量赋到关节变量序列中；若优化求解得到的关节变量和上一帧的关节变量的变化量在所述可允许范围内，则对将优化求解得到的关节变量加入关节变量序列中，并对所述关节变量序列进行角度插补；An angle interpolation module is used to select the joint variables of the previous frame and assign them to the joint variable sequence if the variation of the joint variables obtained by optimization and solution and the joint variables of the previous frame exceeds the allowable range; if the variation of the joint variables obtained by optimization and solution and the joint variables of the previous frame is within the allowable range, add the joint variables obtained by optimization and solution to the joint variable sequence, and perform angle interpolation on the joint variable sequence; 传输模块，用于将进行角度插补后的关节角度序列数据传输到机器人工控机上，以使用伺服控制的方法驱动5R机械臂指向目标点轨迹。The transmission module is used to transmit the joint angle sequence data after angle interpolation to the robot industrial computer, so as to drive the 5R robot arm to point to the target point trajectory using the servo control method. 8.一种电子设备，其特征在于，包括：8. An electronic device, comprising: 一个或多个处理器；one or more processors; 存储器，用于存储一个或多个程序；A memory for storing one or more programs; 当所述一个或多个程序被所述一个或多个处理器执行，使得所述一个或多个处理器实现如权利要求1-6任一项所述的方法。When the one or more programs are executed by the one or more processors, the one or more processors implement the method according to any one of claims 1 to 6. 9.一种计算机可读存储介质，其上存储有计算机指令，其特征在于，该指令被处理器执行时实现如权利要求1-6中任一项所述方法的步骤。9. A computer-readable storage medium having computer instructions stored thereon, wherein when the instructions are executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.
CN202310432715.3A 2023-04-21 2023-04-21 Method for realizing pointing action of five-degree-of-freedom mechanical arm meeting Cartesian space constraint Active CN116141341B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202310432715.3A CN116141341B (en) 2023-04-21 2023-04-21 Method for realizing pointing action of five-degree-of-freedom mechanical arm meeting Cartesian space constraint

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202310432715.3A CN116141341B (en) 2023-04-21 2023-04-21 Method for realizing pointing action of five-degree-of-freedom mechanical arm meeting Cartesian space constraint

Publications (2)

Publication Number Publication Date
CN116141341A true CN116141341A (en) 2023-05-23
CN116141341B CN116141341B (en) 2023-08-08

Family

ID=86362220

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202310432715.3A Active CN116141341B (en) 2023-04-21 2023-04-21 Method for realizing pointing action of five-degree-of-freedom mechanical arm meeting Cartesian space constraint

Country Status (1)

Country Link
CN (1) CN116141341B (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN118305813A (en) * 2024-06-12 2024-07-09 苏州远昌智能科技有限公司 Teleoperation control method and system for humanoid robot

Citations (12)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2005069734A (en) * 2003-08-20 2005-03-17 Tokyo Univ Of Marine Science & Technology Teaching method of spatial position of object by pointing action
US20130211597A1 (en) * 2012-02-14 2013-08-15 Jerry Neil SOMMERVILLE Control System That Guides A Robot Or Articulated Device With A Laser Distance Meter For 3D Motion, Or Guides A Robot Or Articulated Device With A Computer Pointing Device (Such As A Mouse) For 2D Motion
CN105068536A (en) * 2015-08-13 2015-11-18 吉林大学 Moving substrate track planner achieved based on nonlinear optimization method
CN105773641A (en) * 2014-12-24 2016-07-20 肖伟 Finger pointer
CN107398903A (en) * 2017-09-04 2017-11-28 杭州电子科技大学 The method for controlling trajectory of industrial machinery arm actuating station
CN111185923A (en) * 2020-01-14 2020-05-22 深圳众为兴技术股份有限公司 Robot control device and control method
US20210053220A1 (en) * 2019-08-23 2021-02-25 Realtime Robotics, Inc. Motion planning for robots to optimize velocity while maintaining limits on acceleration and jerk
WO2021065196A1 (en) * 2019-10-03 2021-04-08 Mitsubishi Electric Corporation Method and system for trajectory optimization for nonlinear robotic systems with geometric constraints
CN112805127A (en) * 2018-10-06 2021-05-14 百超激光有限公司 Method and apparatus for creating robot control program
US20210308862A1 (en) * 2020-04-03 2021-10-07 Fanuc Corporation Fast robot motion optimization with distance field
CN115778445A (en) * 2022-12-07 2023-03-14 佗道医疗科技有限公司 Laser guidance verification method for tail end of mechanical arm
CN115922728A (en) * 2023-01-03 2023-04-07 之江实验室 Robot pointing action control method, device, electronic device and storage medium

Patent Citations (13)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2005069734A (en) * 2003-08-20 2005-03-17 Tokyo Univ Of Marine Science & Technology Teaching method of spatial position of object by pointing action
US20130211597A1 (en) * 2012-02-14 2013-08-15 Jerry Neil SOMMERVILLE Control System That Guides A Robot Or Articulated Device With A Laser Distance Meter For 3D Motion, Or Guides A Robot Or Articulated Device With A Computer Pointing Device (Such As A Mouse) For 2D Motion
CN105773641A (en) * 2014-12-24 2016-07-20 肖伟 Finger pointer
CN105068536A (en) * 2015-08-13 2015-11-18 吉林大学 Moving substrate track planner achieved based on nonlinear optimization method
CN107398903A (en) * 2017-09-04 2017-11-28 杭州电子科技大学 The method for controlling trajectory of industrial machinery arm actuating station
CN112805127A (en) * 2018-10-06 2021-05-14 百超激光有限公司 Method and apparatus for creating robot control program
US20210053220A1 (en) * 2019-08-23 2021-02-25 Realtime Robotics, Inc. Motion planning for robots to optimize velocity while maintaining limits on acceleration and jerk
WO2021065196A1 (en) * 2019-10-03 2021-04-08 Mitsubishi Electric Corporation Method and system for trajectory optimization for nonlinear robotic systems with geometric constraints
CN114502335A (en) * 2019-10-03 2022-05-13 三菱电机株式会社 Method and system for trajectory optimization of a non-linear robotic system with geometric constraints
CN111185923A (en) * 2020-01-14 2020-05-22 深圳众为兴技术股份有限公司 Robot control device and control method
US20210308862A1 (en) * 2020-04-03 2021-10-07 Fanuc Corporation Fast robot motion optimization with distance field
CN115778445A (en) * 2022-12-07 2023-03-14 佗道医疗科技有限公司 Laser guidance verification method for tail end of mechanical arm
CN115922728A (en) * 2023-01-03 2023-04-07 之江实验室 Robot pointing action control method, device, electronic device and storage medium

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
廖波;尚建忠;ERNEST APPLETON;王晓明;: "基于遍历迭代法的五自由度拟人手臂逆运动学求解", 机械设计与研究, no. 05 *

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN118305813A (en) * 2024-06-12 2024-07-09 苏州远昌智能科技有限公司 Teleoperation control method and system for humanoid robot

Also Published As

Publication number Publication date
CN116141341B (en) 2023-08-08

Similar Documents

Publication Publication Date Title
WO2020098551A1 (en) Robot operation method and apparatus, robot, electronic device and readable medium
CN109976347B (en) Visual servo path planning method based on rapid expansion random tree and potential field method
De Luca et al. Image-based visual servoing schemes for nonholonomic mobile manipulators
CN114571452B (en) Industrial robot trajectory planning method, electronic device and readable storage medium
CN111553239A (en) Robot joint visual servo control method, terminal device and storage medium
Mbakop et al. Path planning and control of mobile soft manipulators with obstacle avoidance
Ruchanurucks et al. Humanoid robot motion generation with sequential physical constraints
CN113043277B (en) Multi-joint mechanism trajectory planning method and device, electronic equipment and storage medium
CN116141341A (en) Method for realizing pointing action of five-degree-of-freedom mechanical arm meeting Cartesian space constraint
Pan et al. Collision-free and curvature-continuous path smoothing in cluttered environments
Lam et al. Motion planning for tree climbing with inchworm‐like robots
Yang et al. Optimal configuration for mobile robotic grinding of large complex components based on redundant parameters
Wu et al. Novel adaptive zeroing neural dynamics schemes for temporally-varying linear equation handling applied to arm path following and target motion positioning
Wang et al. Design of stable visual servoing under sensor and actuator constraints via a Lyapunov-based approach
Zhou et al. Motion planning method of redundant dual-chain manipulator with multiple constraints
Siradjuddin et al. A real-time model based visual servoing application for a differential drive mobile robot using beaglebone black embedded system
Huang et al. Telepresence augmentation for visual and haptic guided immersive teleoperation of industrial manipulator
CN114055467A (en) Space pose online simulation system based on five-degree-of-freedom robot
Vahrenkamp et al. Planning and execution of grasping motions on a humanoid robot
Borras et al. Singularity-invariant leg rearrangements in Stewart–Gough platforms
Bhuiyan et al. Towards real-time motion planning for industrial robots in collaborative environments
Vijayan et al. Comparative study on the performance of neural networks for prediction in assisting visual servoing
Borgstadt et al. Visual servoing: path interpolation by homography decomposition
Zhang et al. Trajectory planning of collaborative robot for 3c products assembly
Chan et al. Trajectory specification via sparse waypoints for eye-in-hand robots requiring continuous target visibility

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