Complete framework of jerk-level inverse-free solutions to inverse kinematics of redundant robot manipulators

By applying the gradient dynamics (GD) and Zhang dynamics (ZD) to the motion planning and control for redundant robot manipulators at the joint-jerk level, three novel types of inverse-free solutions, namely Z2G1 type, Z1G2 type and Z0G3 type, are thus proposed, developed and investigated in this paper. These solutions only need to calculate the transpose of Jacobian matrix rather than the complex pseudo-inverse of Jacobian matrix, more efficiently resolving the complicated time-varying inverse-kinematics (IK) problem for robot manipulators. Besides, the path-tracking applications based on a 4-link robot manipulator show that the manipulator's motion is pretty smooth, fully illustrating the effectiveness, accuracy and superiority of such inverse-free solutions. Moreover, it is the first time for the researchers to propose a relatively complete inverse-free solution framework at the joint-jerk level. The proposed approaches can provide effective solutions to the motion planning and control at different levels (e.g., the joint-velocity, joint-acceleration and joint-jerk levels), having a wider application range and also obtaining a perfect tracking performance for redundant robot manipulators.