Kinematics Research Of Series Robots Based On Mesh Of Workspace

The workspace of the robot is the basis of the study of the kinematics of the robot.When the robot moves to the singularity in the workspace,it might lead to a large error of the inverse solution of the robot,the speed increased,and the output torque infinite.Therefore,it is important to study the robot's singularity based on the workspace and show them in the graph visually,which is of great theoretical and practical significance for the smooth movement of the robot.The serial robot is discussed in this passage.Based on its singularity of the workspace,the interface of the visualization of the singular space is constructed.Based on the interface,the kinematics and trajectory planning of the robots are analyzed and simulated.The main contents are as follows:Using the D-H parameters,the serial robots are modeled under the Matlab platform.Based on the posture described by three Euler angles,the formulas of the positive solution are solved.And the characteristics and their adaptive ranges of the existing inverse kinematics algorithms are simulated by the program.For the two posture,the regular and the posture near the singularity,the inverse methods are compared by the solvability and the time.Finally,a suitable inverse method for our robot is selected after the comparison.This paper focuses on the meshing of the workspace of the robot and the visualization of the singular position in the space.According to the established manipulator model,the workspace of the robot is obtained by geometrical method,and the appropriate grid element is selected and the grid unit node number is formed by the outer contour shape of the working space.According to the different types of robotic tasks,the singularity of single pose and multi-pose is studied respectively.The evaluation index of singularity in multi-pose is proposed based on its Jacobian matrix and its condition number.According to the numerical value of the evaluation index,the singularity of the space is visualized by color rendering,and then the relationship of the fluctuation of the inverse solution of the robot with the change of the number of conditions is studied by using the matrix perturbation theorem,validating the rationality of the evaluation index specified in this paper.The study of the trajectory planning of the robot includes two kinds of planning methods:such as Cartesian planning and joint space trajectory planning.This paper studies the respective characteristics and applicable conditions of the two methods.Based on the existing singular spatial visualized graphs,the trajectory planning method avoiding the singularity in Cartesian space is discussed.Based on the Jacobian matrix of the robot,the condition of the angle avoiding the singularty in joint space is studied and simulated.Based on the study of grid meshing in the working space of serial robot,the singularity evaluation index of single pose and multi-pose is put forward based on the number of conditions.In the graphical interface,the singular position in space is visualized,providing a theoretical basis for the singularity problem for robot trajectory planning.The algorithm is verified by the program of matrix perturbation theory,which proves the rationality of the algorithm.