# 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}
}
• Published 5 May 2011
• Computer Science
• The International Journal of Robotics Research
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.
3,182 Citations

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

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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

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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

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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

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• 2015
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

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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

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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

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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

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• 2014
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

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2020 59th IEEE Conference on Decision and Control (CDC)
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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.

## References

SHOWING 1-10 OF 114 REFERENCES

### Optimal kinodynamic motion planning using incremental sampling-based methods

• Computer Science
49th IEEE Conference on Decision and Control (CDC)
• 2010
It is shown that the RRT* algorithm equipped with any local steering procedure that satisfies this condition converges to an optimal solution almost surely, while maintaining the same properties of the standard RRT algorithm.

### Anytime Motion Planning using the RRT*

• Computer Science
2011 IEEE International Conference on Robotics and Automation
• 2011
This paper presents two key extensions to the RRT*, committed trajectories and branch-and-bound tree adaptation, that together enable the algorithm to make more efficient use of computation time online, resulting in an anytime algorithm for real-time implementation.

### Improving Motion-Planning Algorithms by Efficient Nearest-Neighbor Searching

• Computer Science
IEEE Transactions on Robotics
• 2007
This paper presents and implements an algorithm for performing NN queries in Cartesian products of R, S1, and RP3, the most common topological spaces in the context of motion planning, and extends the algorithm based on kd-trees, called ANN, developed by Arya and Mount for Euclidean spaces.

### Sampling-Diagram Automata: A Tool for Analyzing Path Quality in Tree Planners

• Computer Science
WAFR
• 2010
It is proved, for a simple family of obstacle settings, that the popular dual-tree planner Bi-RRT may produce low- quality paths that are arbitrarily worse than optimal with modest but significant probability, and overlook higher-quality paths even when such paths are easy to produce.

### Analysis of probabilistic roadmaps for path planning

• Physics
Proceedings of IEEE International Conference on Robotics and Automation
• 1996
An analysis of a recent path planning method which uses probabilistic roadmaps, which has proven very successful in practice, but the theoretical understanding of its performance is still limited.

### Sampling-based planning, control and verification of hybrid systems

• Computer Science
• 2000
A sampling-based approach to planning, control and verification inspired by robotics motion planning algorithms such as rapidly exploring random trees (RRTs) and probabilistic roadmaps (PRMs) is

### Quasi-randomized path planning

• Computer Science, Mathematics
Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164)
• 2001
Two quasi- random variants of PRM- based planners are proposed: 1) a classical PRM with quasi-random sampling; and 2) a semi-random lazy-PRM, which have been implemented, and are shown through experiments to offer some performance advantages in comparison to their randomized counterparts.

### Current Issues in Sampling-Based Motion Planning

• Mathematics
ISRR
• 2003
A variety of important issues for sampling-based motion planning are discussed, including uniform and regular sampling, topological issues, and search philosophies, and the role of randomization is addressed.

### Sampling-based roadmap of trees for parallel motion planning

• Computer Science
IEEE Transactions on Robotics
• 2005
The planner not only achieves a smooth spectrum between multiple-query and single-query planning, but it combines advantages of both and is significantly more decoupled than PRM and sampling-based tree planners.

### Rapidly-exploring Random Belief Trees for motion planning under uncertainty

• Mathematics
2011 IEEE International Conference on Robotics and Automation
• 2011
The algorithm incrementally constructs a graph of trajectories through state space, while efficiently searching over candidate paths through the graph at each iteration results in a search tree in belief space that provably converges to the optimal path.