Reactive Motion Planning For Temporal Logic Tasks Without Workspace Discretization

The curse of dimensionality is a challenge in many applications of Linear Temporal Logic robot motion planning, and is linked to the discretization of the robot's workspace. The discretization aggravates the problem by introducing a multitude of atomic propositions. This paper argues that a large portion of these atomic propositions is unnecessary. It demonstrates this point by introducing local navigation functions within a temporal logic planning framework, and utilizing register automata for reactive motion planning without explicit, high-resolution workspace discretization. Motivation for this approach comes from applications in pediatric motor rehabilitation involving play-based social child-robot interactions, where the appropriate robot behavior in response to child actions is best described in temporal logic terms. A simulation example drawn from the aforementioned pediatric rehabilitation studies illustrates the advantages of the approach.