Bearing-Based Relative Localization for Robotic Swarm With Partially Mutual Observations

Mutual localization provides a consensus of reference frame as an essential basis for cooperation in multi-robot systems. Previous works have developed certifiable and robust solvers relative transformation estimation between each pair robots. However, recovering poses robotic swarm with partially mutual observations is still unexploited problem. In this letter, we present complete algorithm it optimality, scalability robustness. Firstly, fuse all odometry bearing measurements unified minimization problem among the Stiefel manifold. Furthermore, relax original non-convex into semi-definite programming (SDP) strict tightness guarantee. Then, to hold exactness noised cases, add convex (linear) rank cost apply iteration algorithm. We compare our approach local optimization methods on extensive simulations different robot amounts under various noise levels show global optimality advantage. Finally, conduct real-world experiments practicality