Graph-based Path Planning for Mobile Robots

Abstract

In this thesis, questions of navigation, planning and control of real-world mobile robotic systems are addressed.

Chapter II contains the first contribution in this thesis, which is a modification of the canonical two-layer hybrid architecture: deliberative planning on top, with reactive behaviors underneath. Deliberative is used to describe higher-level reasoning that includes experiential memory and regional or global objectives. Alternatively, reactive describes low-level controllers that operate on information spatially and temporally immediate to the robot. In the traditional architecture, information is passed top down, with the deliberative layer dictating to the reactive layer. Chapter II presents our work on introducing feedback in the opposite direction, allowing the behaviors to provide information to the planning module(s).

The path planning problem, particularly as it as solved by the visibility graph, is addressed first in Chapter III. Our so-called oriented visibility graph is a combinatorial planner with emphasis on dynamic re-planning in unknown environments at the expensive of guaranteed optimality at all times. An example of single source planning -- where the goal location is known and static -- this approach is compared to related approaches (e.g. the reduced visibility graph).

The fourth chapter further develops the work presented in the Chapter III; the oriented visibility graph is extended to the hierarchical oriented visibility graph. This work directly addresses some of the limitations of the oriented visibility graph, particularly the loss of optimality in the case where obstacles are non-convex and where the convex hulls of obstacles overlap. This results in an approach that is a kind of middle-ground between the oriented visibility graph which was designed to handle dynamic updates very fast, and the reduced visibility graph, an old standard in path planning that guarantees optimality.

Chapter V investigates path planning at a higher level of abstraction. Given is a weighted colored graph where vertices are assigned a color (or class) that indicates a feature or quality of the environment associated with that vertex. The question is then asked, ``what is the globally optimal path through this weighted colored graph?' We answer this question with a mapping from classes and edge weights to a real number, and use Dijkstra's Algorithm to compute the best path. Correctness is proven and an implementation is highlighted.