In this paper, generalized versions of the probabilistic sampling-based planners, i.e., probabilistic roadmaps and rapidly exploring random tree, are presented. The generalized planners, i.e., generalized probabilistic roadmap and the generalized rapidly exploring random tree, result in hybrid hierarchical feedback planners that are robust to the uncertainties in the robot motion model and in the robot map or workspace. The proposed planners are analyzed and shown to probabilistically be complete. The algorithms are tested on fully actuated and underactuated robots on several maps of varying degrees of difficulty, and the results show that the generalized methods have a significant advantage over the traditional methods when planning under uncertainty.
