A Unifying Algorithm for Conditional, Probabilistic Planning

Several recent papers describe algorithms for generating conditional and/or probabilistic plans. In this paper, we synthesize this work, and present a unifying algorithm that incorporates and clarifies the main techniques that have been developed in the previous literature. Our algorithm decouples the search-control strategy for conditional and/or probabilistic planning from the underlying plan-refinement process. A similar decoupling has proven to be very useful in the analysis of classical planning algorithms, and we suspect it can be at least as useful here, where the search-control decisions are even more crucial. We describe an extension of conditional, probabilistic planning, to provide candidates for decision-theoretic assessment, and describe the reasoning about failed branches and side-effects that is needed for this purpose

Optimal Sampling-Based Motion Planning under Differential Constraints: the Driftless Case

Motion planning under differential constraints is a classic problem in robotics. To date, the state of the art is represented by sampling-based techniques, with the Rapidly-exploring Random Tree algorithm as a leading example. Yet, the problem is still open in many aspects, including guarantees on the quality of the obtained solution. In this paper we provide a thorough theoretical framework to assess optimality guarantees of sampling-based algorithms for planning under differential constraints. We exploit this framework to design and analyze two novel sampling-based algorithms that are guaranteed to converge, as the number of samples increases, to an optimal solution (namely, the Differential Probabilistic RoadMap algorithm and the Differential Fast Marching Tree algorithm). Our focus is on driftless control-affine dynamical models, which accurately model a large class of robotic systems. In this paper we use the notion of convergence in probability (as opposed to convergence almost surely): the extra mathematical flexibility of this approach yields convergence rate bounds - a first in the field of optimal sampling-based motion planning under differential constraints. Numerical experiments corroborating our theoretical results are presented and discussed