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Industrial robot arm kinematics

Date: 2018-12-25 11:36    Clicks:     Autor: IKVROBOT    

Overview

Kinematics studies the motion of objects and does not discuss the forces that cause motion. Kinematics focuses on the higher-order differentiation of position, velocity, acceleration, and positional variables over time or other variables.

In the kinematics of robotics, it mainly includes two parts: positive kinematics and inverse kinematics.

Positive kinematics refers to the calculation of the position and attitude of the robotic end effector described by Cartesian space from the joint space description of the robot. This problem is usually a geometric problem. Given a set of joint angles, the end coordinate system is calculated relative to the base coordinate system. The position and posture.

Inverse kinematics refers to the inverse calculation of the joint angle of the robot joint space from the position and attitude of the robot end effector described by Cartesian space, which is a basic problem for robot control. Usually because the forward kinematics equation is nonlinear, the inverse kinematics problem is more difficult, and it is difficult to obtain a closed solution or even a solution. The image space of positive kinematics forms a solution space for inverse kinematics, called the workspace of robots.

Position is an abbreviation for position and posture.

Robotic kinematics

Robotic kinematics is a single-shot mapping of a set of images of the original image in the robotic joint space at the end of the robot's Cartesian space. Obtaining robotic kinematics has the following steps:

robotic kinematics

1. A fixed base coordinate system is established on the fixed end of the robot. The coordinate system is a Cartesian coordinate system, and the end positions of the robot are represented by three coordinate values of x, y and z.

2. At each joint of the robot, a coordinate system that is fixed with the joint and moves in the base coordinate system as the joint moves, and determines the DH (Denavit-Hartenberg) parameter of the robot, that is, the link angle of the robot arm to which the joint is attached \alpha_i, link length a_i, link offset b_i, and joint angle \theta_i of the joint, the first three parameters are the link parameters determined by the specific structure of the robot, and the last one is the joint control parameters of the robot.

3.The DH parameter is used to calculate the homogeneous matrix between the joint coordinate systems at both ends of the robot arm. The homogeneous matrix is a 4*4 matrix, which is composed of a 3*3 rotation matrix, a 3*1 translation matrix, and a lower right corner. composition.
^{i-1}_iT=Rot(X,\alpha_{i-1})Trans(X,a_{i-1})Rot(Z,\theta_i)Trans(Z,b_i)

4. Multiplying all homogeneous matrices sequentially to obtain a homogeneous matrix transformation relationship between the robot's end coordinate system and the base coordinate system, thereby calculating the coordinate values of any point in the base coordinate system in the base coordinate system, and the vector in any end coordinate system. The vector in the coordinate system.

Robot inverse kinematics

Robot inverse kinematics refers to the combination of the position and attitude of the robot end effector described by Cartesian space to calculate the joint angle combination that the robot joint space should reach. Robot inverse kinematics has multiple solutions, that is, corresponding to a specific end pose, robot joint angle can be achieved in various combinations, usually the robot selects the "shortest stroke solution" when executing, that is, the amount of movement of each joint The smallest solution.

The acquisition of inverse kinematics is usually difficult. The solution of inverse kinematics is divided into closed solution and numerical solution. A closed solution is a solution to an analytical form or a solution that is not higher than a fourth-order polynomial without iteration.

The main research in inverse kinematics is that all tandem 6-degree-of-freedom mechanisms with rotating joints and moving joints can be solved. 6 The full condition of the joint robot with a closed solution is that the adjacent three joint axes intersect at one point. So today's 6-DOF robots have three intersecting axes.

Precision;

Accuracy is divided into positioning accuracy (accuracy) and repeatability (precision). Repeatability is obtained by a "teaching-reproduction" process that requires the robot to reach a particular Cartesian spatial position given the joint angle of the robot. The positioning accuracy is the position of the given Cartesian space, and the robot is required to calculate the joint angle using inverse kinematics and achieve the way to reach the position. Usually, the repeatability of the robot is high and the positioning accuracy is poor.

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