Sampling-based algorithms for optimal motion planning

@article{Karaman2011SamplingbasedAF,
  title={Sampling-based algorithms for optimal motion planning},
  author={Sertaç Karaman and Emilio Frazzoli},
  journal={The International Journal of Robotics Research},
  year={2011},
  volume={30},
  pages={846 - 894}
}
During the last decade, sampling-based path planning algorithms, such as probabilistic roadmaps (PRM) and rapidly exploring random trees (RRT), have been shown to work well in practice and possess theoretical guarantees such as probabilistic completeness. [] Key Result The analysis in this paper hinges on novel connections between stochastic sampling-based path planning algorithms and the theory of random geometric graphs.

The Role of Vertex Consistency in Sampling-based Algorithms for Optimal Motion Planning

A new incremental sampling-based motion planning algorithm based on Rapidly-exploring Random Graphs (RRG), denoted RRT# (RRT "sharp") which also guarantees asymptotic optimality but, in addition, it also ensures that the constructed spanning tree of the geometric graph is consistent after each iteration.

Use of relaxation methods in sampling-based algorithms for optimal motion planning

  • O. ArslanP. Tsiotras
  • Computer Science
    2013 IEEE International Conference on Robotics and Automation
  • 2013
This paper presents a new incremental sampling-based motion planning algorithm based on Rapidly-exploring Random Graphs (RRG), denoted by RRT# (RRT “sharp”), which also guarantees asymptotic optimality, but, in addition, it also ensures that the constructed spanning tree rooted at the initial state contains lowest-cost path information for vertices which have the potential to be part of the optimal solution.

Hybridization of Sampling-based Motion Planning Algorithms

This dissertation hybridizes sampling-based and optimized-based planning in conjunction with the spherical representations for faster convergence speed and particularly considers spherical representations to discretize space for various purpose and exploit those for biased-sampling, probabilistic collision checking, and adaptive sparse graph construction.

Deterministic sampling-based motion planning: Optimality, complexity, and performance

It is shown that PRM is deterministically asymptotically optimal, and that planning with deterministic (or random) low-dispersion sampling generally provides superior performance in terms of path cost and success rate, and extends to other batch-processing algorithms such as FMT*, to non-uniform sampling strategies, to k-nearest-neighbor implementations, and to differentially constrained problems.

Sampling-based algorithms for optimal path planning problems

This dissertation proposes an incremental sampling-based algorithm that is provably correct and probabilistically complete and an incremental local model-checking algorithm for the deterministic μ-calculus, both of which guarantee asymptotic optimality without sacrificing computational efficiency.

Dynamic programming guided exploration for sampling-based motion planning algorithms

  • O. ArslanP. Tsiotras
  • Computer Science
    2015 IEEE International Conference on Robotics and Automation (ICRA)
  • 2015
This paper proposes three sample rejection methods that leverage the classification of the samples according to their potential of being part of the optimal solution to guide the exploration of the motion planner to promising regions of the search space.

Efficient Sampling-Based Approaches to Optimal Path Planning in Complex Cost Spaces

Results presented on several classes of problems show that they converge faster than RRT* toward the optimal path, especially when the topology of the search space is complex and/or when its dimensionality is high.

Adaptive Sampling-based Motion Planning with Control Barrier Functions

This paper combines the effectiveness of RRT-based algorithms with the safety guar-antees provided by CBFs in a method called CBF-RRT, which preserves the probabilistic completeness of R RT ∗ .

Sampling-based Roadmap Planners are Probably Near-Optimal after Finite Computation

A formal bound on the probability that solutions returned by asymptotically optimal roadmap-based methods (e.g., PRM*) are within a bound of the optimal path length I* with clearance {\epsilon} after a finite iteration n is proved.

On Probabilistic Completeness of the Generalized Shape Expansion-Based Motion Planning Algorithm

A detailed mathematical analysis of GSE is elaborates, providing upper bounds on the probability of failure of the GSE algorithm, particularly in terms of number of iterations to reach a feasible path.
...

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