Motion Planning for Carlike Robots Using a Probabilistic Learning Approach

Abstract

In this article, a recently developed learning approach for robot motion planning is extended and applied to two types of carlike robots: normal ones, and robots that can only move for ward. In this learning approach the motion planning process is split into two phases: the learning phase and the query phase. In the learning phase, a probabilistic roadmap is incremen tally constructed in configuration space. This roadmap is an undirected graph where nodes correspond to randomly chosen configurations in free space and edges correspond to simple collision-free paths between the nodes. These simple motions are computed using a fast local method. In the query phase, this roadmap can be used to find paths between different pairs of configurations. The approach can be applied to normal carlike robots (with nonholonomic constraints) by using suitable local methods that compute paths feasible for the robots. Application to carlike robots that can move only forward demands a more fundamen tal adaptation of the learning method; that is, the roadmaps must be stored in directed graphs instead of undirected ones. We have implemented the planners, and we present experi mental results that demonstrate their efficiency for both robot types, even in cluttered workspaces. Also, we prove probabilis tic completeness of the planners. 1. A robot is fully controllable iff the existence of a path in the open free C space implies the existence of a feasible path. 2. By "metric," we simply mean a function of type C x C → R+ without any restrictions. 3. Formally, this requires a minor adaptation of the general outline of the learning algorithm, as presented in Section 3.1. Line 7. will be: if -connected(c, n) Λ L( c, n) ⊂ free C space then E = E U {( c, n)}. 4. This does not necessarily hold if P1 consists of just one or two circular arcs of maximal curvature. In this case, however, P1 can be found directly with the local planner. 5. We say a path Q lies within distance ∈ of a path R, iff ∀ q ∈ Q : ∃r ∈ R : |q - r| ≤ ∈ (in C space).