Mutual localization serves as the foundation for collaborative perception and task assignment in multi-robot systems. Effectively utilizing limited onboard sensors for mutual localization between marker-less robots is a worthwhile goal. However, due to inadequate consideration of large scale variations of the observed robot and localization refinement, previous work has shown limited accuracy when robots are equipped only with RGB cameras. To enhance the precision of localization, this paper proposes a novel rendezvous-based hierarchical architecture for mutual localization (RHAML). Firstly, to learn multi-scale robot features, anisotropic convolutions are introduced into the network, yielding initial localization results. Then, the iterative refinement module with rendering is employed to adjust the observed robot poses. Finally, the pose graph is conducted to globally optimize all localization results, which takes into account multi-frame observations. Therefore, a flexible architecture is provided that allows for the selection of appropriate modules based on requirements. Simulations demonstrate that RHAML effectively addresses the problem of multi-robot mutual localization, achieving translation errors below 2 cm and rotation errors below 0.5 degrees when robots exhibit 5 m of depth variation. Moreover, its practical utility is validated by applying it to map fusion when multi-robots explore unknown environments.

Bearing measurements,as the most common modality in nature, have recently gained traction in multi-robot systems to enhance mutual localization and swarm collaboration. Despite their advantages, challenges such as sensory noise, obstacle occlusion, and uncoordinated swarm motion persist in real-world scenarios, potentially leading to erroneous state estimation and undermining the system's flexibility, practicality, and robustness.In response to these challenges, in this paper we address theoretical and practical problem related to both mutual localization and swarm planning.Firstly, we propose a certifiable mutual localization algorithm.It features a concise problem formulation coupled with lossless convex relaxation, enabling independence from initial values and globally optimal relative pose recovery.Then, to explore how detection noise and swarm motion influence estimation optimality, we conduct a comprehensive analysis on the interplay between robots' mutual spatial relationship and mutual localization. We develop a differentiable metric correlated with swarm trajectories to explicitly evaluate the noise resistance of optimal estimation.By establishing a finite and pre-computable threshold for this metric and accordingly generating swarm trajectories, the estimation optimality can be strictly guaranteed under arbitrary noise. Based on these findings, an optimization-based swarm planner is proposed to generate safe and smooth trajectories, with consideration of both inter-robot visibility and estimation optimality.Through numerical simulations, we evaluate the optimality and certifiablity of our estimator, and underscore the significance of our planner in enhancing estimation performance.The results exhibit considerable potential of our methods to pave the way for advanced closed-loop intelligence in swarm systems.

Mutual localization stands as a foundational component within various domains of multi-robot systems. Nevertheless, in relative pose estimation, time synchronization is usually underappreciated and rarely addressed, although it significantly influences estimation accuracy. In this paper, we introduce time synchronization into mutual localization to recover the time offset and relative poses between robots simultaneously. Under a constant velocity assumption in a short time, we fuse time offset estimation with our previous bearing-based mutual localization by a novel error representation. Based on the error model, we formulate a joint optimization problem and utilize semi-definite relaxation (SDR) to furnish a lossless relaxation. By solving the relaxed problem, time synchronization and relative pose estimation can be achieved when time drift between robots is limited. To enhance the application range of time offset estimation, we further propose an iterative method to recover the time offset from coarse to fine. Comparisons between the proposed method and the existing ones through extensive simulation tests present prominent benefits of time synchronization on mutual localization. Moreover, real-world experiments are conducted to show the practicality and robustness.

This paper presents a robust and secure framework for achieving accurate and reliable mutual localization in multiple unmanned aerial vehicle (UAV) systems. Challenges of accurate localization and security threats are addressed and corresponding solutions are brought forth and accessed in our paper with numerical simulations. The proposed solution incorporates two key components: the Mobility Adaptive Gradient Descent (MAGD) and Time-evolving Anomaly Detectio (TAD). The MAGD adapts the gradient descent algorithm to handle the configuration changes in the mutual localization system, ensuring accurate localization in dynamic scenarios. The TAD cooperates with reputation propagation (RP) scheme to detect and mitigate potential attacks by identifying UAVs with malicious data, enhancing the security and resilience of the mutual localization

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.