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dRRT*: Scalable and informed asymptotically-optimal multi-robot motion planning

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Abstract

Many exciting robotic applications require multiple robots with many degrees of freedom, such as manipulators, to coordinate their motion in a shared workspace. Discovering high-quality paths in such scenarios can be achieved, in principle, by exploring the composite space of all robots. Sampling-based planners do so by building a roadmap or a tree data structure in the corresponding configuration space and can achieve asymptotic optimality. The hardness of motion planning, however, renders the explicit construction of such structures in the composite space of multiple robots impractical. This work proposes a scalable solution for such coupled multi-robot problems, which provides desirable path-quality guarantees and is also computationally efficient. In particular, the proposed \(\mathtt{dRRT^*}\) is an informed, asymptotically-optimal extension of a prior sampling-based multi-robot motion planner, \(\mathtt{dRRT}\). The prior approach introduced the idea of building roadmaps for each robot and implicitly searching the tensor product of these structures in the composite space. This work identifies the conditions for convergence to optimal paths in multi-robot problems, which the prior method was not achieving. Building on this analysis, \(\mathtt{dRRT}\) is first properly adapted so as to achieve the theoretical guarantees and then further extended so as to make use of effective heuristics when searching the composite space of all robots. The case where the various robots share some degrees of freedom is also studied. Evaluation in simulation indicates that the new algorithm, \(\mathtt{dRRT^*}\)  converges to high-quality paths quickly and scales to a higher number of robots where various alternatives fail. This work also demonstrates the planner’s capability to solve problems involving multiple real-world robotic arms.

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Notes

  1. Notice this difference from the original \(\mathtt{dRRT}\) (Solovey et al. 2015a) so as to allow edges where some robots remain motionless.

  2. In the graphs considered here, an edge exists between two nodes, if the nodes are separated by a distance less than the connection radius r(n).

  3. Let \(A_1,A_2\ldots \) be random variables in some probability space and let B be an event depending on \(A_n\). B occurs asymptotically almost surely (a.a.s.) if \(\lim \limits _{n\rightarrow \infty } \Pr [B(A_n)]=1\).

  4. The small-o notation o(1) indicates a function that becomes smaller than any positive constant and thereby asymptotically will become negligible. When this relation holds, the positive constant corresponds to \(\epsilon \).

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Authors and Affiliations

  1. Computer Science Department of Rutgers University, Piscataway, NJ, USA

    Rahul Shome & Kostas E. Bekris

  2. Computer Science Department of Tel Aviv University, Tel Aviv, Israel

    Kiril Solovey & Dan Halperin

  3. Electrical Engineering and Computer Science Department of University of Michigan, Ann Arbor, MI, USA

    Andrew Dobson

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  1. Rahul Shome
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  2. Kiril Solovey
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  3. Andrew Dobson
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  5. Kostas E. Bekris
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Correspondence to Kostas E. Bekris.

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This is one of the several papers published in Autonomous Robots comprising the Special Issue on Multi-Robot and Multi-Agent Systems.

A. Dobson, R. Shome and K. Bekris were supported by NSF IIS 1617744 and CCF 1330789.

K. Solovey and D. Halperin’s work has been supported in part by the Israel Science Foundation (Grant No. 825/15) and by the Blavatnik Computer Science Research Fund. Kiril Solovey has also been supported by the Clore Israel Foundation.

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Shome, R., Solovey, K., Dobson, A. et al. dRRT*: Scalable and informed asymptotically-optimal multi-robot motion planning. Auton Robot 44, 443–467 (2020). https://doi.org/10.1007/s10514-019-09832-9

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