Multi-robot path planning is dificult due to the combinatorial explosion of the search space with every new robot added. Complete search of the combined state-space soon becomes intractable. In this paper we present a novel form of abstraction that allows us to plan much more eficiently. The key to this abstraction is the partitioning of the map into subgraphs of known structure with entry and exit restrictions which we can represent compactly. Planning then becomes a search in the much smaller space of subgraph configurations. Once an abstract plan is found, it can be quickly resolved into a correct (but possibly sub-optimal) concrete plan without the need for further search. We prove that this technique is sound and complete and demonstrate its practical effiectiveness on a real map. A contending solution, prioritised planning, is also evaluated and shown to have similar performance albeit at the cost of completeness. The two approaches are not necessarily conflicting; we demonstrate how they can be combined into a single algorithm which out-performs either approach alone.
@cite_18: Sensor based motion planning incorporates sensor information reflecting the state of a robot's environment into its planning process, whereas traditional approaches assume complete prior knowledge of the robot's environment. Recent research has focused on the development and incremental construction of the hierarchical generalized Voronoi graph (HGVG), which is a concise representation of a robot's environment. The HGVG is advantageous in that it lends itself to sensor based construction in a rigorous and provably correct manner. With this approach, a robot can enter an unknown environment, incrementally construct the HGVG, and then use the HGVG for future excursions in the environment. Simulations and experiments validate this approach.
@cite_4: This paper addresses the question how robot planning (e.g. for navigation) can be done with hierarchical maps. We present an algorithm for hierarchical path planning for stochastic tasks, based on Markov decision processes (MDPs) and dynamic programming. It is more efficient than standard dynamic programming for "flat" MDPs, because it reduces the state space for all levels in its hierarchy and it allows reuse of previously computed partial policies. This computational advantage comes at the cost of some extra memory and overhead to represent and coordinate the hierarchical system, and in some cases somewhat longer paths to target locations. We demonstrate the method on artificially generated MDP data, and on real robot data from our vision-controlled robot navigating in an office environment.
@cite_22: Hierarchical approximate cell decomposition is a popular approach to the geometric robot motion planning problem. In many cases, the search effort expended at a particular iteration can be greatly reduced by exploiting the work done during previous iterations. In this paper, we describe how this exploitation of past computation can be effected by the use of a dynamically maintained single-source shortest paths tree. We embed a single-source shortest paths tree in the connectivity graph of the approximate representation of the robot configuration space. This shortest paths tree records the most promising path to each vertex in the connectivity graph from the vertex corresponding to the robot's initial configuration. At each iteration, some vertex in the connectivity graph is replaced with a new set of vertices, corresponding to a more detailed representation of the configuration space. Our new, dynamic algorithm is then used to update the single-source shortest paths tree to reflect these changes to the underlying connectivity graph. >
@cite_0: This paper addresses the problem of automatic construction of a hierarchical map from images. Our approach departs from a large collection of omnidirectional images taken at many locations in a building. First, a low-level map is built that consists of a graph in which relations between images are represented. For this, we use a metric based on visual landmarks (SIFT features) and geometrical constraints. Then, we use a graph partitioning method to cluster nodes and in this way construct the high-level map. Experiments on real data show that meaningful higher and lower level maps are obtained, which can be used for accurate localization and planning.
@cite_23: Considers the problem of robot motion planning using an approximate cell decomposition method for Cspace representation. By means of a hierarchical multilevel discretization the authors are able to reduce the complexity of the problem and to provide a practically feasible procedure for its solution. Hierarchical discretization is based on the use of a multisource distance field that is introduced and described in the paper. The developed procedure, used as an heuristic, systematically reduces the amount of memory needed for implementing the motion planning algorithm. Using such a procedure, several instances of the motion planning problem, involving for example two three-links manipulators acting in the same tridimensional environment, have been solved in a reasonable amount of time. >
@cite_16: Mobile robot localization and navigation requires a map - the robot's internal representation of the environment. A common problem is that path planning becomes very inefficient for large maps. In this paper we address the problem of segmenting a base-level map in order to construct a higher-level representation of the space which can be used for more efficient planning. We represent the base-level map as a graph for both geometric and appearance based space representations. Then we use a graph partitioning method to cluster nodes of the base-level map and in this way construct a high-level map, which is also a graph. We apply a hierarchical path planning method for stochastic tasks based on Markov decision processes (MDPs) and investigate the effect of choosing different numbers of clusters
@cite_10: This paper introduces a 1-dimensional network of curves termed the generalized Voronoi graph (GVG) and its extension, the hierarchical generalized Voronoi graph (HGVG), which can be used as a basis for a roadmap or retract-like structure. The GVG and HGVG provide a basis for sensor based path planning in an unknown static environment. In this paper, the GVG and HGVG are defined and some of their properties are exploited to show their utility for motion planning. A companion paper describes how to use the GVG and HGVG for the purposes of sensor based planning.
Hierarchical planning has been applied to path-planning before with abstractions such as approximate cell decomposition @cite_22 @cite_23 , generalised Voronoi graphs @cite_10 @cite_18 and general ad-hoc hierarchical maps @cite_4 @cite_0 @cite_16 , but the structures identified in these examples do not carry over well to the multi-robot scenario.