Abstract
Path planning has long been one of the major research areas in robotics, with PRM and RRT being two of the most effective path planners. Though they are generally very efficient, these two sample-based planners can become computationally expensive in the important special case of narrow passage problems. This paper develops a path planning paradigm which uses ellipsoids and superquadrics to respectively encapsulate the rigid parts of the robot and obstacles. The main benefit in doing this is that configuration-space obstacles can be parameterized in closed form, thereby allowing prior knowledge to be used to avoid sampling infeasible configurations, in order to solve the narrow passage problem efficiently. Benchmark results for single-body robots show that, remarkably, the proposed method outperforms the sample-based planners in terms of the computational time in searching for a path through narrow corridors. Feasible extensions that integrate with sample-based planners to further solve the high dimensional multi-body problems are discussed, which will require substantial additional theoretical development in the future.
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- 1.
Here the word “arena” denotes the bounded area in which the robot and obstacles are contained.
- 2.
Explicitly, \(\varvec{\omega }= \log ^\vee (R)\), \(R \in \text {SO}(n)\) and \(\mathbf{t} \in \mathbb {R}^n\) (\(\mathbf{t}\) is the actual translation as seen in the world reference frame). And the pair \((R,\mathbf{t})\) forms the “Pose Change Group”, i.e. \(\text {PCG}(n) \doteq \text {SO}(n) \times \mathbb {R}^n\), with the group operation being a direct product, which is different than \(\text {SE}(n) \doteq \text {SO}(n) \rtimes \mathbb {R}^n\) (for more details, see [33]).
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Acknowledgements
The authors would like to thank Dr. Fan Yang, Mr. Thomas W. Mitchel and Mr. Zeyi Wang for useful discussions. This work was performed under National Science Foundation grant IIS-1619050 and Office of Naval Research Award N00014-17-1-2142. The ideas expressed in this paper are solely those of the authors.
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Ruan, S., Ma, Q., Poblete, K.L., Yan, Y., Chirikjian, G.S. (2020). Path Planning for Ellipsoidal Robots and General Obstacles via Closed-Form Characterization of Minkowski Operations. In: Morales, M., Tapia, L., Sánchez-Ante, G., Hutchinson, S. (eds) Algorithmic Foundations of Robotics XIII. WAFR 2018. Springer Proceedings in Advanced Robotics, vol 14. Springer, Cham. https://doi.org/10.1007/978-3-030-44051-0_1
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