Optimal mission planner with timed temporal logic constraints

In this paper, we present an optimization based method for path planning of a mobile robot subject to time bounded temporal constraints, in a dynamic environment. Temporal logic (TL) can address very complex task specification such as safety, coverage, motion sequencing etc. We use metric temporal logic (MTL) to encode the task specifications with timing constraints. We then translate the MTL formulae into mixed integer linear constraints and solve the associated optimization problem using a mixed integer linear program solver. This approach is different from the automata based methods which generate a finite abstraction of the environment and dynamics, and use an automata theoretic approach to formally generate a path that satisfies the TL specifications. We have applied our approach on several case studies in complex dynamical environments subjected to timed temporal specifications.