Certifiably Optimal Mutual Localization with Anonymous Bearing Measurements

TL;DR

This paper introduces a certifiably optimal algorithm for mutual localization in multi-robot systems using anonymous bearing measurements, overcoming challenges of measurement correspondence and local optimization sensitivity.

Contribution

It formulates a novel MIQCQP problem and relaxes it into an SDP to achieve certifiably global optimal solutions, enabling robust and accurate mutual localization.

Findings

Outperforms local optimization methods in simulations

Demonstrates robustness under different noise levels

Validates practicality through real-world experiments

Abstract

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, which are difficult to acquire, especially for unified robot teams. Furthermore, most local optimization methods ask for initial guesses and are sensitive to their quality. In this paper, we present a certifiably optimal algorithm that uses 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 using with off-the-shelf solvers. As a result, our method can determine bearing-pose correspondences and furthermore recover the initial relative poses between robots under a certain condition. We compare the performance 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.