Soft Subdivision Search in Motion Planning

The main paradigm for practical motion planning in the last two decades is Probabilistic Road Map (PRM). We propose an alternative paradigm called Soft Subdivision Search (SSS). The SSS approach is based on two ingredients: the standard subdivision of space, coupled with soft predicates. Such predicates are conservative and convergent relative to exact predicates. This leads to a new class of resolution-exact planners. We view PRM and SSS as frameworks for broad classes of planners. There are many parallels between SSS and PRM: both frameworks are versatile, practical, easy to implement, with adaptive local complexity. The critical difference is that SSS avoids the Halting Problem of PRM. We address three issues: (1) We axiomatize some basic properties that allow resolutionexact planners to be constructed in the SSS framework. (2) We show how soft predicates can be effectively and correctly implemented using numerical approximations. (3) We recover exact planners by extending our framework. The SSS framework is a theoretically sound basis for new classes of algorithms in motion planning and beyond. We discuss the prospects of SSS planners being able to solve currently challenging problems and their relation to PRM.