Authors: Caelan Garrett, Tomas Lozano-Perez, Leslie Kaelbling
There has been a great deal of progress in developing probabilistically complete methods that move beyond motion planning to multi-modal problems including various forms of task planning. This paper presents a general-purpose formulation of a large class of discrete-time planning problems, with hybrid state and action spaces. The formulation characterizes conditions on the submanifolds in which solutions lie, leading to a characterization of robust feasibility that incorporates dimensionality-reducing constraints. It then connects those conditions to corresponding conditional samplers that are provided as part of a domain specification. We present domain-independent sample-based planning algorithms and show that they are both probabilistically complete and computationally efficient on a set of challenging benchmark problems.