Certifiably Optimal Mutual Localization With Anonymous Bearing Measurements

Wang, Yingjian; Wen, Xiangyong; Yin, Longji; Xu, Chao; Cao, Yanjun; Gao, Fei

doi:10.1109/lra.2022.3190079

Cited by 10 publications

(6 citation statements)

References 17 publications

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“…These local optimization methods rely on good initial values to obtain a suitable solution. Our previous work [10] formulates a mixed-integer programming problem to recover optimal relative poses and data associations jointly with an optimality guarantee. However, all the above works realize mutual localization by relative pose estimation between each pair of robots.…”

Section: A Relative Pose Estimationmentioning

confidence: 99%

“…This step aims to eliminate unconstrained variables (translations) and to formulate a rotation-only problem later, which is a common way to restrict all involved variables in the special orthogonal group (SO(3)) [10,16]. Then we denote k j1j2 = g j1 × g j2 and derive an error…”

Section: B Formulation Using Cross Productmentioning

confidence: 99%

“…To marginalize distance variables d which is constraintless, we follow the same procedure in [10] using Schur Complement. We write Q as follows:…”

Section: Problem Formulation Using Schur Complementmentioning

confidence: 99%

“…To simulate bearing measurement, we follow our previous work [10] to generate synthetic data. Firstly we obtain random trajectories for multiple robots.…”

Section: A Experiments On Synthetic Datamentioning

confidence: 99%

“…Relative pose estimation, which seek to recover relative transformations between robots, is a fundamental problem in multi-robot systems. Bearing-based mutual localization [4]- [10] only uses 2D visual detection of robots. Compared with map-based localization [11]- [14], it is less influenced by the environment and needs less bandwidth.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Bearing-based Relative Localization for Robotic Swarm with Partially Mutual Observations

Wang¹,

Wen²,

Cao³

et al. 2022

Preprint

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

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Section: A Relative Pose Estimationmentioning

confidence: 99%

Section: B Formulation Using Cross Productmentioning

confidence: 99%

“…To marginalize distance variables d which is constraintless, we follow the same procedure in [10] using Schur Complement. We write Q as follows:…”

Section: Problem Formulation Using Schur Complementmentioning

confidence: 99%

“…To simulate bearing measurement, we follow our previous work [10] to generate synthetic data. Firstly we obtain random trajectories for multiple robots.…”

Section: A Experiments On Synthetic Datamentioning

confidence: 99%