Distributed trajectory estimation with privacy and communication constraints: A two-stage distributed Gauss-Seidel approach

We propose a distributed algorithm to estimate the 3D trajectories of multiple cooperative robots from relative pose measurements. Our approach leverages recent results [1] which show that the maximum likelihood trajectory is well approximated by a sequence of two quadratic subproblems. The main contribution of the present work is to show that these subproblems can be solved in a distributed manner, using the distributed Gauss-Seidel (DGS) algorithm. Our approach has several advantages. It requires minimal information exchange, which is beneficial in presence of communication and privacy constraints. It has an anytime flavor: after few iterations the trajectory estimates are already accurate, and they asymptotically convergence to the centralized estimate. The DGS approach scales well to large teams, and it has a straightforward implementation. We test the approach in simulations and field tests, demonstrating its advantages over related techniques.