Global connectivity control for spatially interacting multi-robot systems with unicycle kinematics

Abstract

In this paper, we consider the problem of connectivity maintenance in multi-robot systems with unicycle kinematics. While previous work has approached this problem through local control techniques, we propose a solution which achieves global connectivity maintenance under nonholonomic constraints. In addition, our formulation only requires intermittent estimation of algebraic connectivity, and accommodates discontinuous spatial interactions among robots. Specifically, we extend a decision-based link maintenance framework to unicycle kinematics and discontinuous potential-based interaction, by exploiting techniques from nonsmooth analysis. Then, we couple this extension with an existing connectivity estimation technique which yields an estimate with tunable precision in finite time, achieving our result. To illustrate the correctness of our methods, we provide a brief simulation result that closes the paper

Distributed Adaptive and Resilient Control of Multi-Robot Systems with Limited Field of View Interactions

“…Theorem 3. Consider an MRS running (15) designed according to a generalized potential function as in (8) with…”

“…The basic idea is that we will show first that the error ẽi is bounded for all time, hence a time-invariant analysis is carried out. Once this is proven, we will move to the second part of the proof of Theorem 4, where we will analyze the Lyapunov stability in the context of UUB, as given by Definition 2, of the complete system using the global Lyapunov function given in (8) and the new, modified control laws in (33).…”

Leader-Follower Consensus of Unicycles With Communication Range Constraints via Smooth Time-Invariant Feedback

“…In [11], position consensus-based formation with connectivity maintenance is achieved using barrier functions but assuming a complete undirected graph, that is, assuming that each agent has access to the information of every other agent in the system at all times, which can prove limiting in realistic practical scenarios. In [12], a discontinuous controller is presented to guarantee connectivity, but consensus is not considered and global parameters must be estimated, thereby increasing the complexity of the controller. Estimation of global parameters is also used in [13] to achieve practical stability of a desired formation, but only position consensus is addressed.…”

Decentralized Global Connectivity Maintenance for Multi-Robot Navigation: A Reinforcement Learning Approach

“…Potential field methods are widely studied to combine connectivity maintenance with system objectives and obstacle avoidance. Williams et al [3] select a dispersive potential with collision avoidance to validate the designed connectivity controller at the presence of discobstacles. Li et al [1] have proposed a potential-based method towards circle obstacles avoidance with connectivity…”