Optimal motion planning with temporal logic and switching constraints

This paper proposes a method for automatic generation of time-optimal robot motion trajectories for the task of collecting and moving a finite number of objects to particular spots in space, while maintaining predefined temporal logic constraints. The continuous robot dynamics change upon an object pick-up or drop-off. The temporal constraints are expressed as syntactically co-safe Linear Temporal Logic (scLTL) formulas over the set of object and drop-off sites. We propose an approach based on constructing a discrete abstraction of the hybrid system modeling the robot in the form of a finite weighted transition system. Then, by employing tools from automata-based model checking, we obtain an automaton containing only paths that satisfy the specification. The shortest path in this automaton is found by graph search and corresponds directly to the time-optimal hybrid trajectory. The method is applied to a case study with a mobile ground robot and a case study involving a quadrotor moving in an environment with obstacles, thus reflecting its computational advantage over a direct optimization approach.