Stability of the Tracking Problem with Task-Priority Inverse Kinematics

Abstract

The multiple task-priority inverse kinematics framework using the Moore-Penrose pseudoinverse has been shown to be asymptotically stable for the regulation problem with certain conditions on the tasks. In this article we present a theorem that extends this to the tracking problem by including an additional criterion that we term fully represented in the null-space. We show the effect of this on a simulation with a snake-like robot manipulator with 30 links for 3 compatible tasks, and an example of 2 tasks that are compatible as a regulation problem but incompatible as a tracking problem. As the tracking problem is more affected by the linearization assumption, we also include an example showing that the effect of linearization can be detrimental during tracking.