  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.
