Robot Manipulator Redundancy Resolution

Chapter 4Z1G1 Type Scheme to JAL Inverse Kinematics

4.1 Introduction

By exploiting the powerful gradient dynamics (GD) method and zeroing dynamics (ZD) method, this chapter presents and investigates the Z1G1 type scheme in an inverse-free manner at the joint-acceleration level for the redundant robot manipulator. The Z1G1 type scheme can effectively solve the inverse kinematics problem of redundant robot manipulators without calculating the computationally expensive inverse of Jacobian matrix. The path-tracking simulations and physical experiments are conducted to further substantiate the effectiveness, high accuracy, and physical realizability of the presented inverse-free solution.

4.2 Problem Formulation and Z1G1 Type Scheme

As mentioned in the Chapter 3, the end-effector position-and-orientation vector in Cartesian space is related to the joint space by a forward kinematics equation as depicted in [60]: , which is expected to track the desired path , that is, . Note that is the ...