We address in this letter the learning of unknown rigid body motions in the Special Euclidian Group SE(3) based on Gaussian Processes. A new covariance kernel for SE(3) is presented and proven to be a valid kernel for Gaussian Process Regression. The learning error of the proposed Gaussian Process model is extended to a highprobability statement on SE(3). We employ it in a visual pursuit scenario of a moving target with unknown velocity in 3D space. Our approach is validated in a simulated 3D environment in Unity, and shows significant better prediction accuracy than the most commonly used Gaussian kernel. When compared to other covariance kernels proposed on SE(3), its advantages are a natural extension of covering numbers to SE(3), that it is computationally more efficient, and that stability of target pursuit can be guaranteed without limiting the target rotational space to SO(2).

Multi-robot systems offer significant advantages for autonomously exploring large-scale, unknown environments. A critical challenge in these applications, however, is ensuring the safety of all agents in a scalable and efficient manner, especially when operating with decentralized coordination and limited communication. To overcome this limitation, this article presents a fully distributed algorithm that enables a multi-robot team to explore cooperatively while maintaining formal safety guarantees. The core of our approach is a framework where each robot individually trains a sparse Bayesian classifier using its local LiDAR data to probabilistically model unsafe regions. To achieve collaborative awareness, the robots exchange these compact, learned models, not high-volume raw data, and fuse them to construct a shared safety map. Safety is then formally guaranteed through a control barrier function (CBF) derived from this collaborative map. The effectiveness of the proposed algorithm are validated through both simulations and experiments with physical ground robots.

This paper considers vision-based cooperative control for robotic networks pursuing a target object based on distributed Gaussian processes. We consider a situation where networked multiple robots are learning unknown motion of the target as a Gaussian process from different datasets. In this scene, some robots may lose sight of the target due to the limited field of view. To address the issue, we introduce a notion of time varying visibility set. Then, we propose a control law based on a distributed Gaussian process model, which is constructed from the Gaussian process model of each robot. By applying the proposed law to the error system, it is shown that the estimation and control errors are ultimately bounded with probability. Finally, the effectiveness of the proposed method is verified by simulation.

This paper considers a pursuit control based on cooperative target motion estimation by robotic networks equipped with visual sensors. First, we propose a cooperative pursuit control law with a vision-based observer using visual sensor networks, called networked visual motion observer. Then, we learn position dependent target motion by a Gaussian process and integrate it within the proposed control law. Second, we show that all rigid bodies converge to desired relative poses when at least one robot can obtain visual information of the target. Furthermore, we prove that the total estimation and control error is ultimately bounded with high probability when integrating a GP model. Finally, we demonstrate the effectiveness of the proposed control law through simulations.

In this paper, we propose a persistent coverage control method to safely explore unknown environments using an environmental model learned by the sparse Bayesian approach. A sparse Bayesian classification model is introduced to estimate safety from the obtained partial environmental data by LiDAR sensors. Then, based on the control barrier function method, we propose a control law to cover the unknown environment while guaranteeing the safety of robots using a sparse Bayesian classification model. We also propose an algorithm sequentially updating the sparse Bayesian classification model with new datasets obtained through safe coverage control. Finally, we verify the effectiveness of the proposed algorithm through simulations.

In this paper, we consider a control architecture for a mobile robot equipped with visual sensors to pursue a target object in an environment with convex-shaped obstacles. The pursuit involves crucial occlusion avoidance and field of view maintenance, referred to as visual safety. Our goal is to achieve this safety through a multi-layered control architecture consisting of a planning layer and a safety layer. We propose functions that represent occlusion avoidance and field of view maintenance and derive conditions for these to act as control barrier functions. Utilizing these functions, we implement an optimal control at the planning layer and an optimization-based control at the safety layer. The effectiveness of this method is verified through two tasks: guiding the target object into a target location and preventing the target object from entering a target location.