Distributed Optimization with Pairwise Constraints and its Application to Multi-robot Path Planning

Bhattacharya, Subhrajit; Kumar, Vijay; Likhachev, Maxim

doi:10.15607/rss.2010.vi.023

Cited by 17 publications

(13 citation statements)

References 9 publications

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“…Multiple problems coupled by constraints can be decoupled and solved in parallel threads, while performing cross-validation for constraint satisfaction in a central main thread, until a solution satisfying the coupling constraints is found. An interested reader may refer to Samar et al (2007) and Bhattacharya et al (2010) for similar approaches.…”

Section: Methodsmentioning

confidence: 99%

A topological approach to using cables to separate and manipulate sets of objects

Bhattacharya

Kim

Heidarsson

et al. 2015

The International Journal of Robotics Research

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Abstract-In this paper we study the problem of manipulating and transporting multiple objects on the plane using a cable attached at each end to a mobile robot. This problem is motivated by the use of boats with booms in skimming operations for cleaning oil spills or removing debris on the surface of the water. The goal in this paper is to automate the task of separating the objects of interest from a collection of objects by manipulating them with cables that are actuated only at the ends, and then transporting them to specified destinations. Because the cable is flexible, the shape of the cable must be explicitly modeled in the problem. Further, the robots must cooperatively plan motions to achieve the required cable shape and gross position/orientation to separate the objects of interest and then transport them as specified. The theoretical foundation for the problem is derived from topological invariants, homology and homotopy. We first derive the necessary topological conditions for achieving the desired separation of objects. We then propose a distributed search-based planning technique for finding optimal robot trajectories for separation and transportation. We demonstrate the applicability of this method using a dynamic simulation platform with explicit models of the cable dynamics, the contact between the cable and one or more objects, and the surface drag on the cable and on the objects. We also describe our preliminary efforts to develop an experimental platform consisting of a system of two cooperating autonomous boats.

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Section: Methodsmentioning

confidence: 99%

A topological approach to using cables to separate and manipulate sets of objects

Bhattacharya

Kim

Heidarsson

et al. 2015

The International Journal of Robotics Research

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“…Here we mention selected works specifically related to distributed optimization or game-theoretic methods for robot networks. Reference [16] utilizes distributed optimization for trajectory optimization with pairwise coupling constraints, e.g., stemming from formation maintenance or rendezvous. Reference [17] considers convex optimization for motion coordination of large numbers of robots.…”

Section: Related Literaturementioning

confidence: 99%

“…These attractive and repulsive forces were generated by efficiently utilizing the potential functions defined in (16) and (17). The resulting problem that was solved at each time step was a submodular minimization problem.…”

Section: Multiagent Pursuit-evasion Using Submodular Minimizationmentioning

confidence: 99%

Distributed Optimization for Robot Networks: From Real-Time Convex Optimization to Game-Theoretic Self-Organization

Jaleel

Shamma

2020

Proc. IEEE

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Recent advances in sensing, communication, and computing technologies have enabled the use of multi-robot systems for practical applications like surveillance, area mapping, and search and rescue. For such systems, a major challenge is to design decision rules that are real-time implementable, require local information only, and guarantee some desired global performance. Distributed optimization provides a framework for designing such local decision making rules for multi-robot systems. In this tutorial, we present a collection of selected results for distributed optimization for robot networks. We will focus on two special classes of problems: (i) real-time path planning for multi-robot systems and (ii) self-organization in multi-robot systems using game-theoretic approaches. For multirobot path planning, we will present some recent approaches that are based on approximately solving distributed optimization problems over continuous and discrete domains of actions. The main idea underlying these approaches is that a variety of path planning problems can be formulated as convex optimization and submodular minimization problems over continuous and discrete action spaces, respectively. To generate local update rules that are efficiently implementable in real time, these approaches rely on approximate solutions to the global problems that can still guarantee some level of desired global performance. For game theoretic self-organization, we will present a sampling of results for area coverage and real-time target assignment. In these results, the problems are formulated as games and online updating rules are designed to enable teams of robots to achieve the collective objective in a distributed manner.

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“…Complete MAPF solvers (optimal and sub-optimal) were proposed for different variations of the problem (Wang & Botea, 2011;de Wilde, ter Mors, & Witteveen, 2014;Luna & Bekris, 2011;Felner et al, 2017). Taking some of the kinematics of real robots into account, the multi-robot path finding problem was studied as well (Grady, Bekris, & Kavraki, 2010;Bhattacharya, Kumar, & Likhachev, 2010). Finally, also uncertainty of the position or the movements was taken into account (Wagner & Choset, 2017).…”

Section: Related Workmentioning

confidence: 99%

Implicitly Coordinated Multi-Agent Path Finding under Destination Uncertainty: Success Guarantees and Computational Complexity

Nebel

Bolander²,

Engesser

et al. 2019

jair

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In multi-agent path finding (MAPF), it is usually assumed that planning is performed centrally and that the destinations of the agents are common knowledge. We will drop both assumptions and analyze under which conditions it can be guaranteed that the agents reach their respective destinations using implicitly coordinated plans without communication. Furthermore, we will analyze what the computational costs associated with such a coordination regime are. As it turns out, guarantees can be given assuming that the agents are of a certain type. However, the implied computational costs are quite severe. In the distributed setting, we either have to solve a sequence of NP-complete problems or have to tolerate exponentially longer executions. In the setting with destination uncertainty, bounded plan existence becomes PSPACE-complete. This clearly demonstrates the value of communicating about plans before execution starts.

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Distributed Optimization with Pairwise Constraints and its Application to Multi-robot Path Planning

Cited by 17 publications

References 9 publications

A topological approach to using cables to separate and manipulate sets of objects

A topological approach to using cables to separate and manipulate sets of objects

Distributed Optimization for Robot Networks: From Real-Time Convex Optimization to Game-Theoretic Self-Organization

Implicitly Coordinated Multi-Agent Path Finding under Destination Uncertainty: Success Guarantees and Computational Complexity

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