Departmental Papers (ESE)

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Abstract

We develop a dynamical systems approach to prioritizing multiple tasks in the context of a mobile robot. We take navigation as our prototypical task, and use vector field planners derived from navigation functions to encode control policies that achieve each individual task. We associate a scalar quantity with each task, representing its current importance to the robot; this value evolves in time as the robot achieves tasks. In our framework, the robot uses as its control input a convex combination of the individual task vector fields. The weights of the convex combination evolve dynamically according to a decision model adapted from the bio-inspired literature on swarm decision making, using the task values as an input. We study a simple case with two navigation tasks and derive conditions under which a stable limit cycle can be proven to emerge. While owing along the limit cycle, the robot periodically navigates to each of the two goal locations; moreover, numerical study suggests that the basin of attraction is quite large so that significant perturbations are recovered with a reliable return to the desired task coordination pattern.

For more information: Kod*lab and http://www.paulreverdy.com/2018/05/11/motivation-dynamics-simulations/

Sponsor Acknowledgements

This work was supported in part by Air Force Research Laboratory grant FA865015D1845 (subcontract 669737-1).

Document Type

Working Paper

Subject Area

GRASP, Kodlab

Date of this Version

2018

Publication Source

SIAM J. Appl. Dyn. Syst

Volume

17

Issue

2

Start Page

1683

Last Page

1715

DOI

https://doi.org/10.1137/17M111972X

Copyright/Permission Statement

First Published in SIAM Journal on Applied Dynamical Systems in volume 17, number 2, published by the Society for Industrial and Applied Mathematics (SIAM)

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Date Posted: 01 August 2018

This document has been peer reviewed.