We study a form of the pursuit-evasion problem, in which one or more searchers must move through a given environment so as to guarantee detection of any and all evaders, which can move arbitrarily fast. Our goal is to develop techniques for coordinating teams of robots to execute this task in application domains such as clearing a building, for reasons of security or safety. To this end, we introduce a new class of searcher, the #-searcher, which can be readily instantiated as a physical mobile robot. We present a detailed analysis of the pursuit-evasion problem using #-searchers. We show that computing the minimum number of #-searchers required to search a given environment is NP-hard, and present the first complete search algorithm for a single #-searcher. We show how this algorithm can be extended to handle multiple searchers, and give examples of computed trajectories.

This paper examines the problem of locating a mobile, non-adversarial target in an indoor environment using multiple robotic searchers. One way to formulate this problem is to assume a known environment and choose searcher paths most likely to intersect with the path taken by the target. We refer to this as the Multi-robot Efficient Search Path Planning (MESPP) problem. Such path planning problems are NP-hard, and optimal solutions typically scale exponentially in the number of searchers. We present an approximation algorithm that utilizes finite-horizon planning and implicit coordination to achieve linear scalability in the number of searchers. We prove that solving the MESPP problem requires maximizing a nondecreasing, submodular objective function, which leads to theoretical bounds on the performance of our approximation algorithm. We extend our analysis by considering the scenario where searchers are given noisy non-line-of-sight ranging measurements to the target. For this scenario, we derive and integrate online Bayesian measurement updating into our framework. We demonstrate the performance of our framework in two large-scale simulated environments, and we further validate our results using data from a novel ultra-wideband ranging sensor. Finally, we provide an analysis that demonstrates the relationship between MESPP and the intuitive average capture time metric. Results show that our proposed linearly scalable approximation algorithm generates searcher paths competitive with those generated by exponential algorithms. 1

This technical report presents an anytime algorithm for solving the multi-robot guaranteed search problem. Guaranteed search requires a team of robots to clear an environment of a potentially adversarial target. In other words, a team of searchers must generate a search strategy guaranteed to find a target. This problem is known to be NP-complete on arbitrary graphs but can be solved in linear-time on trees. Our proposed algorithm reduces an environment to a graph representation and then randomly generates a spanning tree of the graph. Guards are then placed on nodes in the graph to eliminate non-tree edges, and a search strategy for the remaining tree is found using a linear-time algorithm from prior work. To reduce the number of guards, our algorithm takes advantage of the temporal characteristics of the search schedule to reuse guards no longer necessary at their previous locations. Many spanning trees are analyzed prior to search to determine the tree that yields the best search strategy. At any time, spanning tree generation can be stopped yielding the best strategy thus far. Our proposed algorithm is demonstrated on two complex graphs derived from physical environments, and several methods for generating candidate spanning trees are compared.

Abstract — In this paper, we examine the problem of locating a non-adversarial target using multiple robotic searchers. This problem is relevant to many applications in robotics including emergency response and aerial surveillance. Assuming a known environment, this problem becomes one of choosing searcher paths that are most likely to intersect with the path taken by the target. We refer to this as the Multi-robot Efficient Search Path Planning (MESPP) problem. Such path planning problems are NP-hard, and optimal solutions typically scale exponentially in the number of searchers. We present a finitehorizon path enumeration algorithm for solving the MESPP problem that utilizes sequential allocation to achieve linear scalability in the number of searchers. We show that solving the MESPP problem requires the maximization of a nondecreasing, submodular objective function, which directly leads to theoretical guarantees on paths generated by sequential allocation. We also demonstrate how our algorithm can run online to incorporate noisy measurements of the target’s position during search. We verify the performance of our algorithm both in simulation and in experiments with a novel radio sensor capable of providing range through walls. Our results show that our linearly scalable MESPP algorithm generates searcher paths competitive with those generated by exponential algorithms. I.

Abstract — Here we present an anytime algorithm for clearing an environment using multiple searchers. Prior methods in the literature treat multi-agent search as either a worst-case problem (i.e., clear an environment of an adversarial evader with potentially infinite speed), or an average-case problem (i.e., minimize average capture time given a model of the target’s motion). We introduce an algorithm that combines finite-horizon planning with spanning tree traversal methods to generate plans that clear the environment of a worst-case adversarial target and have good average-case performance considering a target motion model. Our algorithm is scalable to large teams of searchers and yields theoretically bounded average-case performance. We have tested our proposed algorithm through a large number of experiments in simulation and with a team of robot and human searchers in an office building. Our combined search algorithm both clears the environment and reduces average capture times by up to 75 % when compared to a purely worst-case approach. I.

Using concepts from both robotics and graph theory, we formulate the problem of indoor pursuit / evasion in terms of searching a graph for a mobile evader. We present an offline, greedy, iterative algorithm which performs guaranteed search, i.e. no matter how the evader moves, it will eventually be captured; in fact our algorithm can be applied to either an adversarial (actively trying to avoid capture) or randomly moving evader. Furthermore the algorithm produces an internal search (the searchers move only along the edges of the graph, “teleporting” is not used) and can accommodate “extended” (across nodes) visibility and finite or infinite evader speed. We present search experiments for several indoor environments, some of them quite complicated, in all of which the algorithm succeeds in clearing the graph (i.e. capturing the evader).

... Trees (GSST), an anytime algorithm for multi-robot search. The problem is as follows: clear the environment of any adversarial target using the fewest number of searchers. This problem is NP-hard on arbitrary graphs but can be solved in linear-time on trees. Our algorithm generates spanning trees of a graphical representation of the environment to guide the search. At any time, spanning tree generation can be stopped yielding the best strategy so far. The resulting strategy can be modified online if additional information becomes available. Though GSST does not have performance guarantees after its first iteration, we prove that several variations will find an optimal solution given sufficient runtime. We test GSST in simulation and on a human-robot search team using a distributed implementation. GSST quickly generates clearing schedules with as few as 50 % of the searchers used by competing algorithms.

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This paper examines the problem of locating a mobile, nonadversarial target in an indoor environment using multiple robotic searchers. One way to formulate this problem is to assume a known environment and choose searcher paths most likely to intersect with the path taken by the target. We refer to this as the multi-robot efficient search path planning (MESPP) problem. Such path planning problems are NP-hard, and optimal solutions typically scale exponentially in the number of searchers. We present an approximation algorithm that utilizes finite-horizon planning and implicit coordination to achieve linear scalability in the number of searchers. We prove that solving the MESPP problem requires maximizing a nondecreasing, submodular objective function, which leads to theoretical bounds on the performance of our approximation algorithm. We extend our analysis by considering the scenario where searchers are