Stability of the Tracking Problem with Task-Priority Inverse Kinematics

https://doi.org/10.1016/j.ifacol.2018.11.528Get rights and content

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.

Keywords

Inverse kinematic problem
Stability analysis
Control (closed-loop)
Robot kinematics
Industrial robots
Robot arm

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The work reported in this paper was based on activities within centre for research based innovation SFI Manufacturing in Norway, and is partially funded by the Research Council of Norway under contract number 237900.

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