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/
This work was supported in part by Air Force Research Laboratory grant FA865015D1845 (subcontract 669737-1).
Date of this Version
SIAM J. Appl. Dyn. Syst
First Published in SIAM Journal on Applied Dynamical Systems in volume 17, number 2, published by the Society for Industrial and Applied Mathematics (SIAM)
Date Posted: 01 August 2018
This document has been peer reviewed.