Pseudoinverse-based jerk-level solutions of D3Z0, D2Z1, D1Z2 and D0Z3 types to redundant manipulator´s inverse kinematics

The pseudoinverse-based method, as a conventional method, is generally used in the motion planning and control of velocity and/or acceleration level(s) to solve the complicated inverse-kinematics (IK) problem. In this paper, we firstly propose a simple pseudoinverse-based solution at the jerk level to solve the IK problem by using direct derivative dynamics (DDD or D³ for short) thrice and without using Zhang dynamics (ZD), which is thus termed D3Z0 type. Note that, though the D3Z0 solution is simple, it has some inherent weaknesses, such as low control precision and lack of necessary feedbacks. Therefore, as an important branch of dynamics methods, ZD is adopted to solve the above weaknesses. According to the number of times of using ZD, three enhanced solutions termed D2Z1, D1Z2 and D0Z3 types are then proposed and investigated. Specifically, D2Z1 means that we use 3D twice and ZD once to construct the solution, and D1Z2 and D0Z3 can be obtained and defined similarly. Moreover, feedbacks of position, velocity and acceleration levels can be partially or fully incorporated into the D2Z1, D1Z2 and D0Z3 solutions. Meanwhile, based on D3Z0, D2Z1, D1Z2 and D0Z3 solutions, a relatively complete framework of DZ-type solutions is thus proposed for solving the IK problem at the jerk level. Finally, simulation results performed on a five-link redundant manipulator substantiate the effectiveness and superiority of the DZ-type solutions for manipulator motion planning and control, which further show both smooth and efficient tracking performance, especially for solving the jerk-level IK redundancy of manipulators.