Proofs and Experiments in Scalable, Near-Optimal Search by Multiple Robots

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 finite-horizon 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.