A Dynamical System for Prioritizing and Coordinating Motivations

Abstract

We develop a dynamical systems approach to prioritizing and selecting multiple recurring tasks with the aim of conferring a degree of deliberative goal selection to a mobile robot confronted with competing objectives. We take navigation as our prototypical task and use reactive (i.e., vector field) planners derived from navigation functions to encode control policies that achieve each individual task. We associate a scalar "value" with each task representing its current urgency and let that quantity evolve in time as the robot evaluates the importance of its assigned task relative to competing tasks. The robot's motion control input is generated as a convex combination of the individual task vector fields. Their weights, in turn, evolve dynamically according to a decision model adapted from the literature on bioinspired swarm decision making, driven by the values. In this paper we study a simple case with two recurring, competing navigation tasks and derive conditions under which it can be guaranteed that the robot will repeatedly serve each in turn. Specifically, we provide conditions sufficient for the emergence of a stable limit cycle along which the robot repeatedly and alternately navigates to the two goal locations. 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.