Torque efficient motion through singularity

Abstract

Constraint on the actuation and power resources is often the critical limiting factor for a robot to perform desired tasks. Increasing torque and energy capacity may be a solution, but is seldom viable for robots already built. An attractive alternative is to carefully generate motion trajectories that maximally leverages upon the limited torque and energy resources. In this endeavor, singularity, which is deemed undesirable due to lose of manipulability, could be utilized to an advantage. This paper presents analysis of force and momentum generated through contact in relation to the singularity. The analysis shows that a motion at or near singularity not only maximally leverages the torque limits to generate forces in quasi-static motions, but is also optimally energy efficient for dynamical motion when it comes to momentum generation. Based on a simplified model, we discuss mechanical advantage aspects of a robotic leg and describe range of feasible forces that can be generated together with directions in which singular position becomes minimum torque configuration. Then we define stroke motion and establish upper bounds on the momentum generated through contact. Collinear stroke, where motion is along a straight line, is examined with respect to singularity.