Planning in Discrete and Continuous Spaces: From LTL Tasks to Robot Motions

Enabling robots to accomplish sophisticated tasks requires enhancing their capability to plan at multiple levels of discrete and continuous abstractions. Toward this goal, the proposed approach couples the ability of sampling-based motion planning to handle the complexity arising from high-dimensional robotic systems, nonlinear dynamics, and collision avoidance with the ability of discrete planning to handle discrete specifications. The approach makes it possible to specify tasks via Linear Temporal Logic (LTL) and automatically computes collision-free and dynamically-feasible motions that enable the robot to carry out assigned tasks. While discrete planning guides sampling-based motion planning, the latter feeds back information to further refine the guide and advance the search. Sampling is also used in the discrete space to shorten the length of the discrete plans and to expand the search toward new discrete states. Experiments with high-dimensional dynamical robot models performing various LTL tasks show significant computational speedups over related work.