CN103085069A

CN103085069A - Novel robot kinematics modeling method

Info

Publication number: CN103085069A
Application number: CN2012105442146A
Authority: CN
Inventors: 贾庆轩; 吴楚锋; 陈钢; 孙汉旭; 禇明
Original assignee: Beijing University of Posts and Telecommunications
Current assignee: Beijing University of Posts and Telecommunications
Priority date: 2012-12-17
Filing date: 2012-12-17
Publication date: 2013-05-08
Anticipated expiration: 2032-12-17
Also published as: CN103085069B

Abstract

The invention discloses a novel robot kinematics modeling method. Its core includes: only need to establish the robot reference coordinate system and the end tool coordinate system, and express the parameters of the robot kinematics model through the position vector and pointing vector; use the implicit joint coordinate system to deduce the transformation relationship between the joints; and then, through the matrix transformation The relationship solves the pose transformation matrix and Jacobian matrix of the end tool coordinate system of the robot relative to the reference coordinate system for a given joint position. The invention solves the problem of robot kinematics modeling, and its modeling process is simple and efficient, only needing to model a reference coordinate system and an end tool coordinate system, while having an intuitive expression form and clear physical meaning.

Description

A New Robot Kinematics Modeling Method

技术领域 technical field

本发明涉及一种机器人运动学建模方法，属于机器人建模技术领域。 The invention relates to a robot kinematics modeling method, belonging to the technical field of robot modeling. the

背景技术 Background technique

随着机器人技术的快速发展，机器人的应用领域越来越广泛。在机器人应用领域中，机器人的运动学特性是机器人操作与控制的基础，而运动学建模是机器人运动学分析的前提。另外，随着机器人应用领域的发展，机器人的操作人员呈现大众化发展，机器人本身呈现多样化，多自由度发展，因此开展高效通用易懂的运动学建模方法研究具有重要意义。 With the rapid development of robot technology, the application fields of robots are becoming more and more extensive. In the field of robot application, the kinematic characteristics of the robot are the basis of robot operation and control, and kinematic modeling is the premise of robot kinematic analysis. In addition, with the development of the application field of robots, the popularity of robot operators appears, and the robot itself presents diversification and multi-degree-of-freedom development. Therefore, it is of great significance to carry out research on efficient, general and easy-to-understand kinematic modeling methods. the

因内外学者围绕机器人运动学建模已经开展了相关研究工作。传统的机器人运动学建模方法主要为选择参考坐标系及末端工具坐标系后在机器人各连杆上建立固定于连杆的坐标系，通过求解连杆坐标系、参考坐标系及末端工具坐标系之间的变换矩阵，而进求解末端工具坐标系相对于参考坐标系的位姿及机器人雅克比矩阵等信息完成机器人运动学建模。其中最为经典的建模方法为DH法，由Denavit与Hartenberg提出，该方法通过一系列规定在机器人连杆上建立连杆坐标系，采用四个变量描述机器人连杆之间的变化关系，但该方法建立连杆坐标系过程太过复杂，对多自由度机器人，这个问题更加突出。Richard M.Murray采用旋量理论完成机器人运动学建模，该方法将机器人各关节运动视为运动旋量，通过旋量运算计算机器人运动传递。旋量方法只需建立机器人参考坐标系及末端工具坐标系，但该方法中间推导过程复杂，物理意义不明确，编程实现难度较大。 Scholars at home and abroad have carried out related research work around robot kinematics modeling. The traditional robot kinematics modeling method is mainly to select the reference coordinate system and the end tool coordinate system and then establish the coordinate system fixed on the connecting rod on each connecting rod of the robot. By solving the connecting rod coordinate system, reference coordinate system and end tool coordinate system The transformation matrix between them, and then solve the position and orientation of the end tool coordinate system relative to the reference coordinate system and the Jacobian matrix of the robot to complete the robot kinematics modeling. The most classic modeling method is the DH method, proposed by Denavit and Hartenberg. This method establishes a link coordinate system on the robot link through a series of regulations, and uses four variables to describe the changing relationship between the robot links. Method The process of establishing the link coordinate system is too complicated, and this problem is more prominent for multi-degree-of-freedom robots. Richard M. Murray used the screw theory to complete the robot kinematics modeling. This method regards the motion of each joint of the robot as a motion screw, and calculates the robot motion transfer through screw operations. The screw method only needs to establish the robot reference coordinate system and the end tool coordinate system, but the middle derivation process of this method is complicated, the physical meaning is not clear, and the programming is difficult to realize. the

针对上述情况，本发明在结合现有机器人运动学建模技术优点的基础上，提出了一种只需明确建立机器人参考坐标系及末端工具坐标系，中间坐标系自主生成且隐含于推导计算过程的运动学建模方法。该方法建模过程简单易懂，推导简明，物理意义明确，易于编程实现，适合于实际应用。 In view of the above situation, on the basis of combining the advantages of the existing robot kinematics modeling technology, the present invention proposes a method that only needs to clearly establish the robot reference coordinate system and the end tool coordinate system, and the intermediate coordinate system is automatically generated and implicit in the derivation calculation. Kinematic modeling methods for processes. The modeling process of this method is simple and easy to understand, the derivation is concise, the physical meaning is clear, and it is easy to program and realize, which is suitable for practical application. the

发明内容 Contents of the invention

本发明的目的是针对现有运动学建模方法繁琐复杂的不足，提供一种简单易懂的运动学建模方法。 The purpose of the present invention is to provide an easy-to-understand kinematics modeling method for the cumbersome and complicated shortcomings of the existing kinematics modeling method. the

本发明所采用的技术方案是：首先根据任务需求建模机器人参考坐标系及末端工具坐标系；其次由机器人零位构型(机器人所有关节位置为0时机器人的形态)及其尺寸参数，采用位置矢量及指向矢量(这两个矢量合称机器人运动学模型参数)在参考坐标系下对机器人各关节进行描述；然后通过所得的模型参数推导隐含关节坐标系及隐含关节坐标系之间的变换关系；最终通过矩阵变换，在给定机器人关节位置情况下，求解机器人末端工具坐标系相对于参考坐标系的位姿变换矩阵及雅克比矩阵。 The technical scheme adopted in the present invention is: firstly, model the robot reference coordinate system and the end tool coordinate system according to the task requirements; secondly, the zero configuration of the robot (the shape of the robot when all the joint positions of the robot are 0) and its size parameters, adopt The position vector and pointing vector (these two vectors are collectively called the robot kinematics model parameters) describe each joint of the robot in the reference coordinate system; Transformation relationship; Finally, through matrix transformation, in the case of a given robot joint position, the pose transformation matrix and Jacobian matrix of the end tool coordinate system of the robot relative to the reference coordinate system are solved. the

具体建模方法如下： The specific modeling method is as follows:

(1)根据任务需求建立参考坐标系及末端工具坐标系，获取机器人零位构型下末端工具坐标系相对于参考坐标系的位姿及机器人各关节在参考坐标系下的描述M_i＝[P_i Z_i]，i＝1…n，n为机器人关节数量。 (1) Establish the reference coordinate system and the end tool coordinate system according to the task requirements, obtain the position and orientation of the end tool coordinate system relative to the reference coordinate system in the zero configuration of the robot and the description of each joint of the robot in the reference coordinate system M _i =[ P _i Z _i ], i=1...n, n is the number of robot joints.

(2)结合参考坐标系和末端工具坐标系，推导机器人各关节隐含坐标系及各坐标系间的变换关系。 (2) Combining the reference coordinate system and the end tool coordinate system, deduce the implicit coordinate system of each joint of the robot and the transformation relationship between each coordinate system. the

(3)根据矩阵变换关系，求解机器人在给定关节位置情况下末端工具坐标系相对于参考坐标系的位姿变换矩阵及雅克比矩阵。 (3) According to the matrix transformation relationship, solve the pose transformation matrix and Jacobian matrix of the end tool coordinate system relative to the reference coordinate system of the robot under the given joint position. the

本发明的优点 Advantages of the present invention

本发明主要涉及一种机器人的运动学建模方法，其优势在于(1)只需建立机器人参考坐标系及末端工具坐标系，无需建立机器人连杆坐标系；(2)通过关节隐含坐标系，由所得的模型参数直接推导各坐标系之间在零位构型下的变换矩阵；(3)表达形式清晰简洁，具有明确的物理意义，易于编程实现。将此方法应用于8自由度模块化机器人运动学建模，相比DH 建模方法，其建模过程简单易懂(见实施例1)。 The present invention mainly relates to a kinematics modeling method of a robot. Its advantage is that (1) it is only necessary to establish a robot reference coordinate system and an end tool coordinate system, and there is no need to establish a robot link coordinate system; , the transformation matrix between coordinate systems in the zero configuration is directly deduced from the obtained model parameters; (3) the expression form is clear and concise, has clear physical meaning, and is easy to program. Applying this method to 8-DOF modular robot kinematics modeling, compared with the DH modeling method, its modeling process is simple and easy to understand (see embodiment 1). the

附图说明 Description of drawings

图1是任意自由度机器人示意图及本发明建模方法说明图； Fig. 1 is a schematic diagram of an arbitrary degree of freedom robot and an explanatory diagram of the modeling method of the present invention;

图2是实例机器人零位构型及建模所得结果，其中， Fig. 2 is the result obtained from the zero position configuration and modeling of the example robot, in which,

图2-A是实例机器人零位构型图； Figure 2-A is a zero-position configuration diagram of an example robot;

图2-B是实例机器人零位简化图及坐标系选取； Figure 2-B is a simplified diagram of the zero position of the example robot and the selection of the coordinate system;

图2-C是实例机器人建模结果。 Figure 2-C is the modeling result of the example robot. the

具体实施方式 Detailed ways

本发明提供了一种新型的机器人运动学建模方法，下面结合附图对本发明作进一步说明。机器人由多个关节和连杆组成，其结构表示以及各杆件、关节以及坐标系的符号说明如图1所示，其中∑₀为机器人参考坐标系，∑_end为机器人末端工具坐标系，M_i为所提出建模方法第个关节的建模参数，P_i为第i个关节的位置矢量，Z_i为第i个关节的指向矢量，i＝1…n，n为机器人的关节数。 The present invention provides a novel robot kinematics modeling method, and the present invention will be further described below in conjunction with the accompanying drawings. The robot is composed of multiple joints and connecting rods. Its structure representation and the symbol description of each member, joint and coordinate system are shown in Fig. 1, where ∑ ₀ is the robot reference coordinate system, ∑ _end is the end tool coordinate system of the robot, and M _i is the modeling parameter of the th joint of the proposed modeling method, P _i is the position vector of the i th joint, Z _i is the pointing vector of the i th joint, i=1...n, n is the number of joints of the robot.

(1)根据任务需求建立参考坐标系及末端工具坐标系。 (1) Establish the reference coordinate system and the end tool coordinate system according to the task requirements. the

(2)确定零位构型下机器人末端工具坐标系相对于参考坐标系下的位姿及机器人模型参数。 (2) Determine the pose and robot model parameters of the robot end tool coordinate system relative to the reference coordinate system in the zero configuration. the

末端工具坐标系相对于参考坐标系位姿为： The pose of the end tool coordinate system relative to the reference coordinate system is:

⁰PE＝{x，y，z，α，β，γ} (1) ⁰ PE = {x, y, z, α, β, γ} (1)

其中x，y，z为末端工具坐标系原点在参考坐标系下的xyz位置矢量，α，β，γ为末端工具坐标系相对于参考坐标系的zyx欧拉角。 Where x, y, z are the xyz position vectors of the origin of the end tool coordinate system in the reference coordinate system, α, β, γ are the zyx Euler angles of the end tool coordinate system relative to the reference coordinate system. the

机器人模型参数： Robot model parameters:

M_i＝[P_i Z_i]，i＝1…n (2) M _i =[P _i Z _i ], i=1...n (2)

n为机器人自由度数，P_i、Z_i分别为零位构型下，第i个关节的位置矢量和指向矢量。位置矢量表示关节轴线上任意一点的位置，指向矢量表示关节指向。指向矢量，对于转动关节而言，由关节转动的转轴在参考坐标系下的单位矢量表示，对于移动关节而言，为关节运动方向在参考坐标系下的单位矢量表示。 n is the number of degrees of freedom of the robot, P _i and Z _i are the position vector and pointing vector of the i-th joint in the zero configuration, respectively. The position vector represents the position of any point on the joint axis, and the pointing vector represents the joint orientation. The pointing vector, for a rotary joint, is represented by the unit vector of the axis of rotation of the joint in the reference coordinate system, and for a moving joint, it is represented by the unit vector of the joint motion direction in the reference coordinate system.

(3)推导机器人各关节隐含坐标系及参考坐标系、各隐含坐标系与末端工具坐标系之间的变换矩阵。 (3) Deduce the transformation matrix between the implicit coordinate system of each joint of the robot and the reference coordinate system, each implicit coordinate system and the end tool coordinate system. the

选择机器人第i个关节的关节位置矢量P_i为机器人第i个关节固连坐标系的原点，第i个关节的指向矢量Z_i为机器人第i个关节固连坐标系的Z轴方向矢量，将其与参考坐标系的X₀轴或Y₀轴叉乘，所得结果作为第i个关节固连坐标系的X轴X_i，再将X_i与Z_i叉乘可得第i个关节固连坐标系的Y轴Y_i。最终，可得零位构型下机器人各关节坐标系在参考坐系下的位姿变换矩阵i＝１…n： Select the joint position vector P _i of the i-th joint of the robot as the origin of the fixed coordinate system of the i-th joint of the robot, and the pointing vector Z _i of the i-th joint is the Z-axis direction vector of the i-th joint of the robot’s fixed coordinate system, Cross-multiply it with the X ₀ axis or Y ₀ axis of the reference coordinate system, and the result is taken as the X-axis X _i of the i-th joint fixed coordinate system, and then cross-multiply X _i and Z _i to get the i-th joint fixed Connect the Y axis Y _i of the coordinate system. Finally, the pose transformation matrix of each joint coordinate system of the robot in the reference coordinate system in the zero configuration can be obtained i=1...n:

${T T}_{00}^{i i}_{00} = = [\begin{matrix} {Z Z}_{i i} \times \times {W W}_{00} & {Z Z}_{i i} \times \times (({Z Z}_{i i} \times \times {W W}_{00})) & {Z Z}_{i i} & {P P}_{i i} \\ 00 & 00 & 00 & 11 \end{matrix}] - - - - - - ((33))$

其中，W₀＝X₀＝{1，0，0}或W₀＝Y₀＝{0，1，0} Wherein, W ₀ =X ₀ ={1,0,0} or W ₀ =Y ₀ ={0,1,0}

由矩阵变换关系，有： According to the matrix transformation relationship, there are:

${T T}_{00}^{i i + + 11}_{00} = = {T T}_{00}^{i i}_{00} \cdot \cdot {T T}_{i i}^{i i + + 11}_{00} - - - - - - ((44))$

为零位状态下相邻关节隐含坐标系之间的位姿变换矩阵。

is the pose transformation matrix between the implicit coordinate systems of adjacent joints in the zero state.

由上式(4)可得： From the above formula (4), it can be obtained:

${T T}_{i i}^{i i + + 11}_{00} = = {(({T T}_{00}^{i i}_{00}))}^{- - 11} {T T}_{00}^{i i + + 11}_{00},, i i = = 11 \cdot &Center Dot; \cdot &Center Dot; \cdot \cdot n no - - - - - - ((55))$

同理由零位构型下最后一个关节坐标系相对于参考坐标系的位姿变换矩阵

及末端工具坐标系相对于参考坐标系的位姿变换矩阵

有

可得： For the same reason, the pose transformation matrix of the last joint coordinate system relative to the reference coordinate system in the zero configuration

and the pose transformation matrix of the end tool coordinate system relative to the reference coordinate system

have

Available:

${T T}_{n no}^{end end}_{00} = = {(({T T}_{00}^{n no}_{00}))}^{- - 11} \cdot \cdot {T T}_{00}^{end end}_{00} - - - - - - ((66))$

结合

i＝1，…，n的表达式，可得出机器人各关节坐标系之间的变换矩阵

i＝1…n、第1个关节与参考坐标系的变换矩阵以及最后一个关节到末端工具坐标系的变换矩阵

的表达式。至此完成由给定的模型参数推导隐含关节坐标系之间的固定变换矩阵。整个过程中，并不需要主动建立坐标系，也不知道假定的关节坐标系的具体指向，推导简单易懂。所得的变换矩阵为固定不变值，在机器人运动学分析中只需求解一次。 combine

The expression of i=1,...,n can get the transformation matrix between the coordinate systems of each joint of the robot

i=1...n, the transformation matrix of the first joint and the reference coordinate system and the transformation matrix of the last joint to the end tool coordinate system

the expression. So far, the fixed transformation matrix between implicit joint coordinate systems has been deduced from the given model parameters. In the whole process, there is no need to actively establish a coordinate system, and the specific direction of the assumed joint coordinate system is not known, and the derivation is simple and easy to understand. The resulting transformation matrix is a fixed value, and only needs to be solved once in the robot kinematics analysis.

(4)通过所得的变换矩阵，求解给定关节位置情况下，机器人末端工具坐标系相对于参考坐标系的位姿变换矩阵及雅克比矩阵。 (4) Solve the pose transformation matrix and the Jacobian matrix of the end tool coordinate system of the robot relative to the reference coordinate system under the given joint position through the obtained transformation matrix. the

机器人运动学正解为给定机器人各关节位置求解末端工具坐标系相对于参考坐标系的位置及姿态的问题。由于假定关节坐标系与关节固连，关节运动将引起坐标系相应的运动，而假定关节坐标系之间的变换矩阵固定不变，且由模型参数可直接求得。因此由矩阵变换关系，得到假定关节坐标系之间的变换矩阵后，结合关节位置q＝[x₁ x₂…x_n]，可得机器人末端工具坐标系相对于参考坐标系的位姿变换矩阵，即求解得出机器人运动学正解的表达式： The forward solution of robot kinematics is the problem of solving the position and attitude of the end tool coordinate system relative to the reference coordinate system for the given position of each joint of the robot. Since it is assumed that the joint coordinate system is fixedly connected with the joint, joint movement will cause the corresponding movement of the coordinate system, and the transformation matrix between the joint coordinate systems is assumed to be fixed, and can be obtained directly from the model parameters. Therefore, from the matrix transformation relationship, after obtaining the transformation matrix between the assumed joint coordinate systems, combined with the joint position q=[x ₁ x ₂ …x _n ], the pose transformation matrix of the tool coordinate system at the end of the robot relative to the reference coordinate system can be obtained , that is, solve the expression to obtain the positive solution of robot kinematics:

${T T}_{00}^{end end} = = {T T}_{00}^{11}_{00} {A A}_{11} {T T}_{11}^{22}_{00} {A A}_{22} {T T}_{22}^{33}_{00} \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot; {A A}_{n no} {T T}_{n no}^{end end}_{00} - - - - - - ((77))$

其中，A_i，i＝1…n为第i个关节运动产生的位姿变换矩阵。 Wherein, A _i , i=1...n is the pose transformation matrix generated by the movement of the i-th joint.

若第i个关节为旋转关节， $A_{i} = [\begin{matrix} \cos x_{i} & - \sin x_{i} & 0 & 0 \\ \sin x_{i} & \cos x_{i} & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{matrix}],$ x_i为第i个关节的角度。 If the i-th joint is a revolving joint, $A_{i} = [\begin{matrix} \cos x_{i} & - \sin x_{i} & 0 & 0 \\ \sin x_{i} & \cos x_{i} & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{matrix}],$ x _i is the angle of the i-th joint.

若第i个关节为移动关节， $A_{i} = [\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & x_{i} \\ 0 & 0 & 0 & 1 \end{matrix}],$ x_i为第i个关节的位移。 If the i-th joint is a moving joint, $A_{i} = [\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & x_{i} \\ 0 & 0 & 0 & 1 \end{matrix}],$ x _i is the displacement of the i-th joint.

由Whitney提出的矢量积法可知机器人雅克比矩阵第i列的表达式，对于移动关节而言， The vector product method proposed by Whitney shows the expression of the i-th column of the Jacobian matrix of the robot. For the moving joint,

${J J}_{i i} = = [\begin{matrix} {Z Z}_{i i}^{q q} \\ 00 \end{matrix}] - - - - - - ((88))$

对于转动关节而言， For revolving joints,

${J J}_{i i} = = [\begin{matrix} {Z Z}_{i i}^{q q} \times \times (({R R}_{00}^{i i} \cdot &Center Dot; {P P}_{i i}^{end end})) \\ {Z Z}_{i i}^{q q} \end{matrix}] - - - - - - ((99))$

其中^qZ_i、

分别为关节处于位置q时，机器人第i个关节的指向矢量，机器人第i个关节坐标系相对于参考坐标系的姿态变换矩阵及第i个关节位置到末端工具坐标系原点处的矢量。 where ^q Z _i ,

Respectively, when the joint is at position q, the pointing vector of the i-th joint of the robot, the attitude transformation matrix of the i-th joint coordinate system of the robot relative to the reference coordinate system, and the vector from the i-th joint position to the origin of the end tool coordinate system.

由式(7)推导所得的机器人运动学正解表达式，令可得： The positive solution expression of robot kinematics derived from formula (7), let Available:

${T T}_{i i} = = {T T}_{00}^{11}_{00} {A A}_{11} {T T}_{11}^{22}_{00} {A A}_{22} {T T}_{22}^{33}_{00} \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot; {A A}_{i i},, {T T}_{i i}^{end end} = = {T T}_{i i}^{i i + + 11}_{00} {A A}_{i i + + 11} {T T}_{i i + + 11}^{i i + + 22}_{00} \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot; {A A}_{n no} {T T}_{n no}^{end end}_{00} - - - - - - ((1010))$

由^qZ_i、的含义可知，^qZ_i为T_i第三列前三个元素组成的矢量，即位姿变换矩阵T_i中Z轴的方向矢量；为T_i前三行三列组成的姿态变换矩阵；

为第四列前三个元素组成的矢量，即位姿变换矩阵

的位置矢量。将求解所得的^qZ_i、

代入(8)或(9)可得雅克比矩阵各列的值。 By ^q Z _i , It can be seen from the meaning that ^q Z _i is the vector composed of the first three elements in the third column of T _i , that is, the direction vector of the Z axis in the pose transformation matrix T _i ; is the attitude transformation matrix composed of the first three rows and three columns of T _i ;

for The vector composed of the first three elements in the fourth column is the pose transformation matrix

The position vector of . The obtained ^q Z _i ,

Substitute into (8) or (9) to get the value of each column of the Jacobian matrix.

通过以上推导，可得出具有n个自由度的机器人的雅克比矩阵： Through the above derivation, the Jacobian matrix of a robot with n degrees of freedom can be obtained:

J＝[J₁ J₂…J_n] (11) J＝[J ₁ J ₂ ...J _n ] (11)

至此，得到了机器人运动学模型以及末端工具坐标系相对于参考坐标系的位姿变换矩阵和雅克比矩阵。 So far, the robot kinematics model and the pose transformation matrix and Jacobian matrix of the end tool coordinate system relative to the reference coordinate system are obtained. the

实施例1： Example 1:

根据本发明所建立的机器人运动学建模方法，以8自由度模块化机器人为研究对象展开验证。 According to the robot kinematics modeling method established in the present invention, the 8-degree-of-freedom modular robot is used as the research object for verification. the

该模块化机器人包括8个自由度，结构如图2-A所示，机器人每个自由度均为转动属性。根据所提出的建模方法，首先选择机器人根部中心为机器人参考坐标系原点，参考系Z轴垂直于根部所在平面向上，X轴垂直于Z轴水平向右，Y轴由所得Z轴和X轴基于右手坐标系确定。末端工具坐标系原点定于机器人末端中心，选择其X，Y和Z三轴与参考坐标系X，Y和Z三轴同向。所得建模结果如图2-B所示，图中还标出了各关节转动方向。所图2-C所示，为8R模块化机器人运动学建模结果，其中∑₀为机器人参考坐标系，∑_end为机器人末端工具坐标系，P_i为第i个关节的位置矢量，Z_i为第i个关节的指向矢量，i＝1…8，a，b，c，d，e，f为机器人的尺寸参数。 The modular robot includes 8 degrees of freedom, the structure is shown in Figure 2-A, and each degree of freedom of the robot is a rotation attribute. According to the proposed modeling method, the center of the robot root is first selected as the origin of the robot reference coordinate system, the Z axis of the reference system is perpendicular to the plane where the root is located, the X axis is perpendicular to the Z axis and horizontally to the right, and the Y axis is obtained from the Z axis and the X axis Determined based on the right-handed coordinate system. The origin of the end tool coordinate system is set at the center of the end of the robot, and its X, Y, and Z axes are selected to be in the same direction as the reference coordinate system's X, Y, and Z axes. The obtained modeling results are shown in Figure 2-B, and the rotation direction of each joint is also marked in the figure. As shown in Figure 2-C, it is the kinematics modeling result of the 8R modular robot, where ∑ ₀ is the robot reference coordinate system, ∑ _end is the end tool coordinate system of the robot, P _i is the position vector of the i-th joint, Z _i is the pointing vector of the i-th joint, i=1...8, a, b, c, d, e, f are the size parameters of the robot.

采用xyz位置矢量及zyx欧拉角描述机器人末端工具坐标系相对于参考坐标系的位姿，由于零位构型下末端坐标系三轴与参考坐标系平行且同向，可得零位构型下机器人末端位姿为：⁰PE＝{-b，0，a+c+d+e+f，0，0，0}，结合机器人的零位构型及其尺寸参数可得出建模所得的模型参数M_i＝[P_i Z_i]。 Use the xyz position vector and zyx Euler angle to describe the pose of the robot end tool coordinate system relative to the reference coordinate system. Since the three axes of the end coordinate system in the zero configuration are parallel and in the same direction as the reference coordinate system, the zero configuration can be obtained The end pose of the lower robot is: ⁰ PE={-b, 0, a+c+d+e+f, 0, 0, 0}, combined with the robot’s zero configuration and its size parameters, the modeling result can be obtained The model parameters of M _i =[P _i Z _i ].

Claims

1. novel robot kinematics's modeling method is characterized in that the method comprises the following steps:

(1) set up robot reference frame and end-of-arm tooling coordinate system, adopt position vector and pointing vector to represent the model parameter of modeling gained;

(2) by the supposition joint coordinate system, the combination model parameter, module and carriage transformation matrix between the derivation assumed coordinate system, and then complete robot end's tool coordinates system with respect to module and carriage transformation matrix and the robot Jacobian matrix of reference frame by matrixing.

2. a kind of novel robot kinematics's modeling method according to claim 1, it is characterized in that: described modeling parameters is obtained simply, explicit physical meaning.Rotating shaft direction or moving direction to each joint of robot under reference frame are described, and can get the pointing vector in each joint of robot.Select some location point as each joint of robot on pointing vector, and then can the description of this location point under reference frame, the i.e. position vector in each joint of robot.The position vector of gained and pointing vector are the model parameter of robot modeling's gained.

3. a kind of novel robot kinematics's modeling method according to claim 1 is characterized in that described robot normal solution and Jacobian matrix are found the solution to comprise the following steps:

(1) according to the model parameter of Kinematic Model gained, suppose each joint of robot coordinate system that is connected, the transformation matrix between current each assumed coordinate system of deriving;

(2) by the transformation matrix that obtains, in conjunction with joint of robot positional value (joint angles or joint amount of movement), finding the solution robot end's tool coordinates by matrix operation is with respect to the module and carriage transformation matrix of reference frame and the Jacobian matrix of robot.