Sampling-based Motion Planning with Temporal Logic Missions and Spatial Preferences

Abstract While motion planning under temporal logic specifications has been addressed in several state-of-the-art works, spatial aspects have been so far largely neglected. In this work, we enrich the semantics of robot motion specifications by including preferences on spatial relations between its trajectory and various elements in its environment. The spatial preferences are given in a fragment of Signal Temporal Logic (STL) on top of complex missions in syntactically co-safe Linear Temporal Logic (scLTL). We propose a cost function with user-specified parameters, which determines the compromise between efficiency and spatial robustness of a trajectory. The proposed modification of the incremental sampling-based RRT* driven by this cost function guarantees that the motion plan (if found) simultaneously satisfies the mission and asymptotically minimize the cost. The paper includes several case studies showcasing the effects of the user-adjustable parameters on the resulting trajectories.