Stable Numerical Solution of Inverse Kinematics in Singular Posture and Unsolvable Problem Based on Minimization of Elastic Energy of Virtual Spring

Abstract

In this paper, we attempt to explicate a numerical solution of inverse kinematics from the concept of virtual spring- damper hypothesis and joint damping control. Based on the minimization of elastic energy of the virtual spring, the sufficient condition for the stable convergence in the discrete time system is derived. Furthermore, we proposed two methods and a termination condition based on the stability condition. Simulation experiments are carried out to verify that calculation results are stably converged even in singular postures, unsolvable problems, and the redundant manipulator. Additionally, it is also clear that the proposed methods complete the calculation with a small number of iterations.