Jerk-level solutions to manipulator inverse kinematics with mathematical equivalence of operations discovered

Abstract

By applying direct derivative dynamics (DDD or D <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ), gradient neural dynamics (GND) and Zhang neural dynamics (ZND) at joint-jerk level, three novel solutions (namely, of types Z1D1G1-D1Z1G1, D2Z1-D1Z1D1-Z1D2 and D1Z2-Z1D1Z1-Z2D1) are proposed, developed and investigated in this paper. It is the first time that a relatively complete hybrid solution framework is proposed at the joint-jerk level. Then, a mathematical equivalence of Z1D1 and D1Z1 operations is discovered. Besides, the path-tracking applications performed on a 5-link robot manipulator sufficiently illustrate the efficacy, accuracy and superiority of these solutions.