2,100 research outputs found
Distributed Online Rollout for Multivehicle Routing in Unmapped Environments
In this work we consider a generalization of the well-known multivehicle
routing problem: given a network, a set of agents occupying a subset of its
nodes, and a set of tasks, we seek a minimum cost sequence of movements subject
to the constraint that each task is visited by some agent at least once. The
classical version of this problem assumes a central computational server that
observes the entire state of the system perfectly and directs individual agents
according to a centralized control scheme. In contrast, we assume that there is
no centralized server and that each agent is an individual processor with no a
priori knowledge of the underlying network (including task and agent
locations). Moreover, our agents possess strictly local communication and
sensing capabilities (restricted to a fixed radius around their respective
locations), aligning more closely with several real-world multiagent
applications. These restrictions introduce many challenges that are overcome
through local information sharing and direct coordination between agents. We
present a fully distributed, online, and scalable reinforcement learning
algorithm for this problem whereby agents self-organize into local clusters and
independently apply a multiagent rollout scheme locally to each cluster. We
demonstrate empirically via extensive simulations that there exists a critical
sensing radius beyond which the distributed rollout algorithm begins to improve
over a greedy base policy. This critical sensing radius grows proportionally to
the function of the size of the network, and is, therefore, a small
constant for any relevant network. Our decentralized reinforcement learning
algorithm achieves approximately a factor of two cost improvement over the base
policy for a range of radii bounded from below and above by two and three times
the critical sensing radius, respectively
Coordinated Motion Planning: Reconfiguring a Swarm of Labeled Robots with Bounded Stretch
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. Despite a broad range of other non-trivial results for multi-object motion planning, previous work has largely focused on sequential schedules, in which one robot moves at a time, with objectives such as the number of moves; attempts to minimize the overall makespan of a coordinated parallel motion schedule (with many robots moving simultaneously) have defied all attempts at establishing the complexity in the absence of obstacles, as well as the existence of efficient approximation methods.
We resolve these open problems by developing a framework that provides 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 their arrangement entails some amount of separability. In fact, our algorithm achieves constant stretch factor: If all robots want to move at most d units from their respective starting positions, then the total duration of the overall schedule (and hence the distance traveled by each robot) is O(d). Various extensions include unlabeled robots and different classes of robots. We also resolve the complexity of finding a reconfiguration plan with minimal execution time by proving that this 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 Omega(N^{1/4}) may be required. On the positive side, we establish a stretch factor of O(N^{1/2}) even in this case. The intricate difficulties of computing precise optimal solutions are demonstrated by the seemingly simple case of just two disks, which is shown to be excruciatingly difficult to solve to optimality
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