On the Power of Manifold Samples in Exploring Configuration Spaces and the Dimensionality of Narrow Passages

Salzman, Oren; Hemmer, Michael; Halperin, Dan

doi:10.1109/tase.2014.2331983

Cited by 26 publications

(11 citation statements)

References 47 publications

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“…With the advent of robot swarms, practical solutions to these problems became more important and the robotics community started to develop practical sampling-based algorithms [31,49,50,59,60,64,70] which, while working well in practice, are not guaranteed to find an (optimal) solution. In another recent work, Yu and Rus [75] present a practical algorithm based on a fine-grained discretization combined with an IP for the resulting discrete problem to provide near-optimal solutions even for densely populated environments.…”

Section: Related Workmentioning

confidence: 99%

Coordinated Motion Planning: Reconfiguring a Swarm of Labeled Robots with Bounded Stretch

Demaine¹,

Fekete²,

Keldenich³

et al. 2019

SIAM J. Comput.

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We present a number of breakthroughs for coordinated motion planning, in which the objective is to reconfigure a swarm of labeled convex objects by a combination of parallel, continuous, collision-free translations into a given target arrangement. Problems of this type can be traced back to the classic work of Schwartz and Sharir (1983), who gave a method for deciding the existence of a coordinated motion for a set of disks between obstacles; their approach is polynomial in the complexity of the obstacles, but exponential in the number of disks. Other previous work has largely focused on sequential schedules, in which one robot moves at a time.We provide constant-factor approximation algorithms for minimizing the execution time of a coordinated, parallel motion plan for a swarm of robots in the absence of obstacles, provided some amount of separability.Our algorithm achieves constant stretch factor: If all robots are at most d units from their respective starting positions, the total duration of the overall schedule is O(d). Extensions include unlabeled robots and different classes of robots. We also prove that finding a plan with minimal execution time is NP-hard, even for a grid arrangement without any stationary obstacles. On the other hand, we show that for densely packed disks that cannot be well separated, a stretch factor Ω(N 1/4 ) may be required. On the positive side, we establish a stretch factor of O(N 1/2 ) even in this case.

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Section: Related Workmentioning

confidence: 99%

Coordinated Motion Planning: Reconfiguring a Swarm of Labeled Robots with Bounded Stretch

Demaine¹,

Fekete²,

Keldenich³

et al. 2019

SIAM J. Comput.

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show abstract

“…In contrast to that, centralized approaches (Kloder and Hutchinson, 2005;O'Donnell and Lozano-Pérez, 1989;Salzman et al, 2015;Solovey et al, 2015a;Svestka and Overmars, 1998;Wagner and Choset, 2013) usually work in the combined high-dimensional configuration space, and thus tend to be slower than decoupled techniques. However, centralized algorithms often come with stronger theoretical guarantees, such as completeness.…”

Section: Prior Workmentioning

confidence: 99%

“…Such an approach suffers from inefficiency as it overlooks aspects of multi-robot planning, and hence can handle only a very small number of robots. Several techniques tailored for instances of MMP involving a small number of robots have been described (Hirsch and Halperin, 2004;Salzman et al, 2015).…”

Section: Prior Workmentioning

confidence: 99%

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

et al. 2019

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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 dRRT * is an informed, asymptotically-optimal extension of a prior sampling-based multi-robot motion planner, 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.A. Dobson, R. Shome and K.

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“…Multi-robot motion planning research has approached the problem with decentralized solutions [7], [8], [9], [10], [11], [12] which reduce search space size by partitioning the problem into several sub-problems but typically lack completeness and optimality guarantees. In contrast, centralized approaches [13], [14], [15], [16], [17], [18] usually work in the combined high-dimensional configuration spaces, and thus tend to be slower than decoupled techniques but provide stronger theoretical guarantees.…”

Section: A Foundationsmentioning

confidence: 99%

Anytime Multi-arm Task and Motion Planning for Pick-and-Place of Individual Objects via Handoffs

Shome¹,

Bekris²

2019

2019 International Symposium on Multi-Robot and Multi-Agent Systems (MRS)

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Automation applications are pushing the deployment of many high DoF manipulators in warehouse and manufacturing environments. This has motivated many efforts on optimizing manipulation tasks involving a single arm. Coordinating multiple arms for manipulation, however, introduces additional computational challenges arising from the increased DoFs, as well as the combinatorial increase in the available operations that many manipulators can perform, including handoffs between arms. The focus here is on the case of pickand-place tasks, which require a sequence of handoffs to be executed, so as to achieve computational efficiency, asymptotic optimality and practical anytime performance. The paper leverages recent advances in multi-robot motion planning for high DoF systems to propose a novel multi-modal extension of the dRRT * algorithm. The key insight is that, instead of naively solving a sequence of motion planning problems, it is computationally advantageous to directly explore the composite space of the integrated multi-arm task and motion planning problem, given input sets of possible pick and handoff configurations. Asymptotic optimality guarantees are possible by sampling additional picks and handoffs over time. The evaluation shows that the approach finds initial solutions fast and improves their quality over time. It also succeeds in finding solutions to harder problem instances relative to alternatives and can scale effectively as the number of robots increases.

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On the Power of Manifold Samples in Exploring Configuration Spaces and the Dimensionality of Narrow Passages

Cited by 26 publications

References 47 publications

Coordinated Motion Planning: Reconfiguring a Swarm of Labeled Robots with Bounded Stretch

Coordinated Motion Planning: Reconfiguring a Swarm of Labeled Robots with Bounded Stretch

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

Anytime Multi-arm Task and Motion Planning for Pick-and-Place of Individual Objects via Handoffs

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