MRSAM: A Quadratically Competitive Multi Robots Navigation Algorithm

We explore an on-line problem where a group of robots has to find a target whose position is unknown in an unknown planar environment whose geometry is acquired by the robots during task execution. The critical parameter in such a problem is the physical motion time, which, under the assumption of uniform velocity of all the robots, corresponds to length or cost of the path traveled by the robot which finds the target. The Competitiveness of an online algorithm measures its performance relative to the optimal off-line solution to the problem. While competitiveness usually means constant relative performance, this paper uses generalized competitiveness, i.e. any functional relationship between online performance and optimal off-line solution. Given an online task, its Competitive Complexity Class is a pair of lower and upper bounds on the competitive performance of all online algorithms for the task, such that the two bounds satisfy the same functional relationship. We classify a common online motion planning problem into competitive class. In particular, it is shown that navigation to a target whose position is recognized only upon arrival belongs to a quadratic competitive class. This paper describes a new on-line navigation algorithm, called MRSAM, which requires linear memory and has a quadratic competitive performance. Moreover, it is shown that in general any on-line navigation algorithm must have at least a quadratic competitive performance. The MRSAM algorithm achieves the quadratic lower bound and thus has optimal competitiveness. The algorithm is improved with some practical speedups and its performance is illustrated in office-like environments. I