Singularity avoidance for manipulators with spherical wrists using the approximate damped reciprocal algorithm

Tiantian Yu,Daqing Wang,Lifu Gao

doi:10.1177/1729881421995681

Abstract

Due to the loss of freedom, the stability and tracking ability of the manipulator around the singularity become worse. This article aims at improving the accuracy of the manipulator and ensuring the stability of the system with the damped reciprocal method. Firstly, the singularities are separated into forearm and wrist singularities to obtain the singular factors of the manipulator respectively. Secondly, a new mathematical function of the approximate damped reciprocal of the singular factor is proposed. Thirdly, the singularities are avoided by modifying the Jacobian matrixes of the manipulator with the approximate damped reciprocal algorithm. Finally, the effectiveness and the stability of the system are proved by the simulations on a manipulator with the spherical wrist. The simulation results prove that this method can largely improve the accuracy of the end-effector and can ensure the stability of the system around the singular region.

Highlights

The kinematic singularity is an inherent characteristic of a manipulator, in which bounded Cartesian speeds lead to infinite joint speeds, and bounded Cartesian accelerations lead to infinite end-effector forces
Many methods have been proposed to avoid the singularity: (a) methods based on the geometry,[1,2] which can intuitively reflect the configuration of singularities, but cannot obtain the mathematical expression of singularities; (b) methods based on task space control,[3,4,5,6,7,8] in which singularities are avoided by motion planning, but it is difficult to find the proper parameters; (c) methods based on optimization,[9,10,11] which take the singularity avoidance problem as an optimization problem, but are relatively timeconsuming; (d) methods based on the Jacobian matrix,[12,13,14] such as pseudoinverse method,[15] Jacobian transpose,[16,17] and damped least-squares inverse of the Jacobian matrix.[18]
The singularities are avoided by modifying the Jacobian matrixes of the manipulator with the approximate damped reciprocal algorithm

Summary

Introduction

The kinematic singularity is an inherent characteristic of a manipulator, in which bounded Cartesian speeds lead to infinite joint speeds, and bounded Cartesian accelerations lead to infinite end-effector forces. Improving the tracking accuracy and the stability of the manipulator are important to the control of the manipulator during the singularity avoidance. A Jacobian transpose method based on the damped reciprocal[19] was proposed, which had less computation complexity, but the piecewise damped reciprocal function had some discontinuity.[20] the Gaussian distribution damped reciprocal algorithm[21] was introduced to improve the continuity of the singularity avoidance. After that the improved Gaussian distribution damped reciprocal algorithm was proposed to improve the tracking accuracy of the end-effector.[22] the accuracy of those methods based on the damped reciprocal still need to be improved

Objectives

Findings

Discussion

Conclusion