Cyclic pursuit in a multi-agent robotic system with double-integrator dynamics under linear interactions

Abstract

SUMMARYWe investigate the controlled realization of a stable circular pursuit model in a multi-agent robotic system described by double-integrator dynamics with homogeneous controller gains. The dynamic convergence of the system starting from a randomly chosen, non-overlapping initial configuration to a sustained, stable pursuit configuration satisfying velocity matching and uniform inter-agent separation is demonstrated using the proposed control framework. The cyclic pursuit configuration emerges from local, linear, inter-agent interactions and is shown to be robust under stochastic perturbations of small and moderate intensities. The stability criterion discussed in this work is independent of the number of agents, permitting dynamic addition/deletion of agents without affecting overall system stability. Experimental results that validate the key theoretical results are also presented. Potential applications of the results obtained include cooperative perimeter tracking and resource distribution applications such as border patrol and wildfire monitoring.

Second-Order Agents on Ring Digraphs

“…It can be verified that the equation for the intersection writes as x 2 + 2x − γ 2 x = 0, which implies that the absence of intersection (except for the one at the origin) holds true for γ > √ 2. This demonstrates that the consensus condition for second-order agents (1) in cyclic pursuit can be derived easier as compared to, e.g., [7]. The consensus condition for the case of undirected (or, in terms of digraph, two-directional) ring topology is even simpler.…”

“…Although the consensus conditions (5), (7) can be verified in a straightforward way, this may be computationally expensive in the case of a large number of agents. The framework presented below allows to reduce the problem to a couple of simpler ones using the notion of consensus region.…”

“…pursuit. This class of algorithms has a long history (see, e.g., [6], [7], [8], [9], and references therein), and has a wide range of applications including but not limited to numerous formation control tasks as patrolling, boundary mapping, etc. The cyclic pursuit is a strategy where agent i pursues its neighbor i − 1 , while agent 1 pursues agent n, thus the topology of communication is a Hamiltonian cycle.…”

Pursuit Formation of Double-Integrator Dynamics Using Consensus Control Approach

“…In this condition, when the formation radius was large, the agents linear speeds became large which might have not been applicable in the real world. A similar problem existed in the proposed approach in [29], since there was no control on the pursuit angular speed.…”

Method of forbidden regions in the dynamic system matrices root clustering problem

“…The Lyapunov matrix equation of matrix root-clustering was generalized in [1,5]. The problem of root clustering is topical for the robust control systems [10][11][12][13][14][15] and control of the multiagent systems [16].…”