GMM-Based Time-Varying Coverage Control

2025-07-25

AI Summary

Existing multi-robot coverage control methods for time-varying density functions often neglect temporal evolution of the density or rely on numerical approximations, leading to compromised accuracy and efficiency in dynamic environments. Method: This paper proposes, for the first time, a distributed coverage controller based on Gaussian Mixture Models (GMMs) that explicitly models and analytically characterizes the time evolution of the density function. By rigorously coupling spatial integration with temporal differentiation in the control law design, the controller strictly minimizes the instantaneous coverage cost without numerical integration. Contribution/Results: The approach achieves significant improvements in computational efficiency and tracking precision. Simulation results demonstrate superior performance over classical controllers. Furthermore, real-world experiments with a swarm of UAVs tracking a time-varying chemical plume validate the method’s effectiveness and practical applicability in dynamic, real-time scenarios.

Technology Category

• Intelligent Robots: State Estimation
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

In coverage control problems that involve time-varying density functions, the coverage control law depends on spatial integrals of the time evolution of the density function. The latter is often neglected, replaced with an upper bound or calculated as a numerical approximation of the spatial integrals involved. In this paper, we consider a special case of time-varying density functions modeled as Gaussian Mixture Models (GMMs) that evolve with time via a set of time-varying sources (with known corresponding velocities). By imposing this structure, we obtain an efficient time-varying coverage controller that fully incorporates the time evolution of the density function. We show that the induced trajectories under our control law minimise the overall coverage cost. We elicit the structure of the proposed controller and compare it with a classical time-varying coverage controller, against which we benchmark the coverage performance in simulation. Furthermore, we highlight that the computationally efficient and distributed nature of the proposed control law makes it ideal for multi-vehicle robotic applications involving time-varying coverage control problems. We employ our method in plume monitoring using a swarm of drones. In an experimental field trial we show that drones guided by the proposed controller are able to track a simulated time-varying chemical plume in a distributed manner.

Problem

• Efficient control for time-varying density coverage
• Minimizing coverage cost with GMM-based dynamics
• Distributed multi-vehicle plume monitoring application

Innovation

• GMM-based time-varying density modeling
• Efficient time-varying coverage controller
• Distributed multi-vehicle robotic implementation