Distributed Coverage Control of Constrained Constant-Speed Unicycle Multi-Agent Systems

TL;DR

This work tackles distributed coverage control for multi-agent systems composed of constant-speed unicycle robots (CSURs) under hard state- and input-dependent constraints. It introduces a barrier-Lyapunov function (BLF) based coverage cost and a saturated-gradient controller that guarantees all agents remain within the target region while converging to a locally optimal coverage configuration (LOC). A rigorous analysis using invariant set theory and Lyapunov methods establishes state-constraint satisfaction and asymptotic LOC convergence, and a measurement-based, distributed implementation enables scalability. Simulation studies and real-robot experiments demonstrate feasibility, robustness to uncertainties, and advantages over conventional methods in preventing infeasibility. The framework provides a principled approach to coordinating CSURs with complex dynamics in convex regions and lays groundwork for extensions to larger scales and nonconvex environments.

Abstract

This paper proposes a novel distributed coverage controller for a multi-agent system with constant-speed unicycle robots (CSUR). The work is motivated by the limitation of the conventional method that does not ensure the satisfaction of hard state- and input-dependent constraints and leads to feasibility issues for multi-CSUR systems. In this paper, we solve these problems by designing a novel coverage cost function and a saturated gradient-search-based control law. Invariant set theory and Lyapunov-based techniques are used to prove the state-dependent confinement and the convergence of the system state to the optimal coverage configuration, respectively. The controller is implemented in a distributed manner based on a novel communication standard among the agents. A series of simulation case studies are conducted to validate the effectiveness of the proposed coverage controller in different initial conditions and with control parameters. A comparison study in simulation reveals the advantage of the proposed method in terms of avoiding infeasibility. The experiment study verifies the applicability of the method to real robots with uncertainties. The development procedure of the method from theoretical analysis to experimental validation provides a novel framework for multi-agent system coordinate control with complex agent dynamics.

Figures (10)

• Figure 1: Red 'o' are agent positions and blue '+' are the Voronoi centroids. It does not illustrate a LOC since the 'o' marks do not coincide with the blue '+' marks.
• Figure 2: The position $\zeta(t)$ (red 'o') and the virtual center $z(t)$ (black 'x') of a CSUR. The lines with arrows denote their trajectories. The arrow attached to $\zeta(t)$ denotes the robot's orientation $\theta(t)$. When $u(t) \!\equiv\! \omega_0$, the CSUR orbits along a time-invariant virtual center with a constant radius of $v_0/|\omega_0|$.
• Figure 3: An example of $\Omega_{\epsilon}$ as a positive invariant set. For any $z_1, z_2 \!\in\! \Omega_{\epsilon}$, their moving directions $\dot{z}_1, \dot{z}_2$ (the solid arrows) are confined in their corresponding tangent cones (the sector areas). The dashed arrows in the tangent cones indicate the allowed moving directions. The tangent cone of any interior state like $z_1$ is $\mathbb{R}^2$, allowing arbitrary moving directions. However, that of a marginal state on the boundary of $\Omega_{\epsilon}$ like $z_2$ only allows moving inside $\Omega_{\epsilon}$.
• Figure 4: The distributed control of each agent $k \in \mathcal{N}$.
• Figure 5: Simulation results in different initial conditions: (a)-(c) are CSUR positions $\zeta_k(t)$ (thin solid lines), virtual centers $z_k(t)$ (thick dotted lines), and Voronoi centroids $C(\mathcal{Z}_{\overline{\mathscr{A}_k}})$ (thick dashed lines), where 'x' and 'o' are the starting and ending points of the trajectories; (d)-(f) are the coverage costs $V(\mathcal{Z})$, and (g)-(i) are the control inputs $u_k(t) - \omega_k$..

Theorems & Definitions (17)

• Remark 1
• Definition 1
• Definition 2
• Lemma 1
• Proposition 1
• proof
• Proposition 2
• proof
• Proposition 3
• proof