Formal Methods for Robot Motion Planning with Time and Space Constraints (Extended Abstract)

Abstract

Motion planning is one of the core problems in a wide range of robotic applications. We discuss the use of temporal logics to include complex objectives, constraints, and preferences in motion planning algorithms and focus on three topics: the first one addresses computational tractability of Linear Temporal Logic (LTL) motion planning in systems with uncertain non-holonomic dynamics, i.e. systems whose ability to move in space is constrained. We introduce feedback motion primitives and heuristics to guide motion planning and demonstrate its use on a rover in 2D and a fixed-wing drone in 3D. Second, we introduce combined motion planning and hybrid feedback control design in order to find and follow trajectories under Metric Interval Temporal Logic (MITL) specifications. Our solution creates a path to be tracked, a sequence of obstacle-free polytopes and time stamps, and a controller that tracks the path while staying in the polytopes. Third, we focus on motion planning with spatio-temporal preferences expressed in a fragment of Signal Temporal Logic (STL). We introduce a cost function for a of a path reflecting the satisfaction/violation of the preferences based on the notion of STL spatial and temporal robustness. We integrate the cost into anytime asymptotically optimal motion planning algorithm RRT\(^\star \) and we show the use of the algorithm in integration with an autonomous exploration planner on a UAV.