Research On The Kinematics And Trajectory Planning Of Redundant Robots

The robot’s forward-inverse kinematics and trajectory planning is always the fundamental issue for controlling the robot’s motion and implementing all kinds of tasks. In this paper, the redundant robot’s inverse kinematics and trajectory planning are solved, the research results can be divided into two aspects:The first aspect is about the solution and optimization of the redundant robot’s inverse kinematics. For improving the computation speed to make the methods available online, this paper places emphasis on deriving the inverse solutions in the analytic way. According to the reasons of producing redundant problems, the problem can be divided into two types:the redundant optimal problems because of the robot’s incomplete tip pose, and that because the robot itself owns more than six degrees of freedom (DOF).In the second chapter, aim to the redundant optimal problems because of the robot’s incomplete tip pose, using a six-DOF pingpong robot’s arm as an example, by analyzing the solid geometrical configuration of the robot’s arm and the relationship between each link, the kinetic energy is minimized. The posture of the end-effector is solved so that the complete tip matrix is obtained, which is the important precondition of solving the robot’s inverse kinematics, then the inverse kinematics can be solved.In the third chapter, aim to the redundant optimal problems because the robot itself owns more than six degrees of freedom, using a seven-DOF space craft robot as an example, according to its special structure that there are three adjacent joint axes parallel to each other, an analytic approach of solving inverse kinematics based on screw theory is proposed, all the solutions of the inverse kinematics are denoted by a joint angle parameter. Then a common optimization method for multi-solution problem is introduced, so that the optimal solution for the given objective function can be obtained from all the feasible solutions.The second aspect is the trajectory planning problem of redundant robots. according to the characteristics of the given task’s requirements, the problem can be divided into two aspects:trajectory planning in the joint space and trajectory planning in Cartesian space.In the fourth chapter, aim to the problem of the trajectory planning in joint space, the minimum-acceleration trajectory planning from the arbitrary initial state to the arbitrary target state is solved, while all given kinematic constraints of velocity, acceleration and jerk are taking into account. the sufficient and necessary condition of the solution existence is given, meanwhile, it is proven that the method can generate the minimum-acceleration trajectory planning by theory, and the joint limit problem is discussed at last.In the fifth chapter, aim to the problem of the trajectory planning in Cartesian space, the traditional method based on the Jacobian matrix is improved, so that the error drift problem can be decreased. Moreover, the singularity problem is also analyzed and coped with, at last the relationship between the inverse kinematics and trajectory planning is concluded.