Certifiably Optimal Mutual Localization With Anonymous Bearing Measurements

Mutual localization is essential for coordination and cooperation in multi-robot systems. Previous works have tackled this problem by assuming available correspondences between measurements and received odometry estimations. However, the correspondence is difficult to acquire, especially for unified robotteams. In this paper, we present a certifiably optimal algorithm using only anonymous bearing measurements to formulate a novel mixed-integer quadratically constrained quadratic problem (MIQCQP). Then, we relax the original nonconvex problem into a semidefinite programming (SDP) problem and obtain a certifiably global optimum. As a result, if we obtain sufficient independent bearing measurements, our method can determine bearing-pose correspondences and furthermore recover initial relative poses between robots with optimality guarantee. We compare our method with local optimization methods on extensive simulations under different noise levels to show our advantage in global optimality and robustness. Real-world experiments are conducted to show the practicality and robustness.