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We develop a dynamical systems approach to prioritizing and selectingmultiple recurring tasks with the aim of conferring a degree of deliberativegoal selection to a mobile robot confronted with competing objectives. We takenavigation as our prototypical task, and use reactive (i.e., vector field)planners derived from navigation functions to encode control policies thatachieve each individual task. We associate a scalar "value" with each taskrepresenting its current urgency and let that quantity evolve in time as therobot evaluates the importance of its assigned task relative to competingtasks. The robot's motion control input is generated as a convex combination ofthe individual task vector fields. Their weights, in turn, evolve dynamicallyaccording to a decision model adapted from the literature on bioinspired swarmdecision making, driven by the values. In this paper we study a simple casewith two recurring, competing navigation tasks and derive conditions underwhich it can be guaranteed that the robot will repeatedly serve each in turn.Specifically, we provide conditions sufficient for the emergence of a stablelimit cycle along which the robot repeatedly and alternately navigates to thetwo goal locations. Numerical study suggests that the basin of attraction isquite large so that significant perturbations are recovered with a reliablereturn to the desired task coordination pattern.

A dynamical system for prioritizing and coordinating motivations