Task Planning with Continuous Actions and Nondeterministic Motion Planning Queries

We present a new probabilistic tree-of-roadmaps (PTR) planner that integrates discrete task planning and continuous motion planning using a probabilistic forward search. PTR is explicitly designed with two characteristics in mind: 1) it allows tasks to take continuously variable parameters as input, such as the location of contact points for a robot manipulator executing an object pickup task; 2) it accounts for variability in the feasibility and difficulty of motion planning for each task. To do so, it uses a sample-based tree planner to explore tasks, and uses a probabilistic roadmap planner to explore the feasible space defined by each task. We prove that PTR is probabilistically complete under relatively weak conditions with a convergence rate that improves with the abundance of actions that admit easy motion planning queries. Because these conditions are not explicitly dependent on dimensionality, PTR scales well to high dimensional problems. We demonstrate the application of PTR to a manipulation task on the Honda ASIMO humanoid robot.