Integrated Motion Planning and Control Under Metric Interval Temporal Logic Specifications

This paper proposes an approach that combines motion planning and hybrid feedback control design in order to find and follow trajectories fulfilling a given complex mission involving time constraints. We use Metric Interval Temporal Logic (MITL) as a rich and rigorous formalism to specify such missions. The solution builds on three main steps: (i) using sampling-based motion planning methods and the untimed version of the mission specification in the form of Zone automaton, we find a sequence of waypoints in the workspace; (ii) based on the clock zones from the satisfying run on the Zone automaton, we compute time-stamps at which these waypoints should be reached; and (iii) to control the system to connect two waypoints in the desired time, we design a low-level feedback controller leveraging Time-varying Control Barrier Functions. Illustrative simulation results are included.