Real-time obstacle avoidance for manipulators and mobile robots
International Journal of Robotics Research
The complexity of robot motion planning
The complexity of robot motion planning
Robot planning and control via potential functions
The robotics review 1
Robot motion planning: a distributed representation approach
International Journal of Robotics Research
On finding narrow passages with probabilistic roadmap planners
WAFR '98 Proceedings of the third workshop on the algorithmic foundations of robotics on Robotics : the algorithmic perspective: the algorithmic perspective
OBPRM: an obstacle-based PRM for 3D workspaces
WAFR '98 Proceedings of the third workshop on the algorithmic foundations of robotics on Robotics : the algorithmic perspective: the algorithmic perspective
Robot Motion Planning
Planning Algorithms
A simple and linear time randomized algorithm for computing sparse spanners in weighted graphs
Random Structures & Algorithms
Spatial Planning: A Configuration Space Approach
IEEE Transactions on Computers
Sampling-based algorithms for optimal motion planning
International Journal of Robotics Research
IEEE Transactions on Robotics
Sampling-Based Roadmap of Trees for Parallel Motion Planning
IEEE Transactions on Robotics
A Little More, a Lot Better: Improving Path Quality by a Path-Merging Algorithm
IEEE Transactions on Robotics
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Asymptotically optimal planners, such as PRM*, guarantee that solutions approach optimal as the number of iterations increases. Roadmaps with this property, however, may grow too large for storing on resource-constrained robots and for achieving efficient online query resolution. By relaxing optimality, asymptotically near-optimal planners produce sparser graphs by not including all edges. The idea stems from graph spanners, which produce sparse subgraphs that guarantee near-optimality. Existing asymptotically optimal and near-optimal planners, however, include all sampled configurations as roadmap nodes, meaning only infinite-size graphs have the desired properties. To address this limitation, this work describes SPARS, an algorithm that returns a sparse roadmap spanner. The method provides the following properties: (a) probabilistic completeness, (b) asymptotic near-optimality and (c) the probability of adding nodes to the spanner converges to zero as iterations increase. The last point suggests that finite-size data structures with asymptotic near-optimality in continuous spaces may indeed exist. The approach builds simultaneously a dense graph similar to PRM* and its roadmap spanner, meaning that upon construction an infinite-size graph is still needed asymptotically. An extension of SPARS is also presented, termed SPARS2, which removes the dependency on building a dense graph for constructing the sparse roadmap spanner and for which it is shown that the same desirable properties hold. Simulations for rigid-body motion planning show that algorithms for constructing sparse roadmap spanners indeed provide small data structures and result in faster query resolution. The rate of node addition is shown to decrease over time and practically the quality of solutions is considerably better than the theoretical bounds. Upon construction, the memory requirements of SPARS2 are significantly smaller but there is a small sacrifice in the size of the final spanner relative to SPARS.