Optimal motion strategies for range-only distributed target tracking

In this paper we study the problem of optimal trajectory generation for a team of mobile robots that tracks a moving target using range-only measurements. We propose an adaptive-relaxation algorithm for determining the set of feasible locations that each robot must move to in order to collect the most informative measurements; i.e., distance measurements that minimize the uncertainty about the position of the target. We prove that the motion strategy that minimizes the trace of the position error covariance matrix is equivalent to the one that minimizes its maximum eigenvalue. The proposed method is applicable regardless of the process model employed for describing the motion of the target while its computational complexity is linear in the number of robots. Extensive simulation results are presented, demonstrating that the performance attained with the proposed method is comparable to that obtained with exhaustive search whose computational cost is exponential in the number of robots.