Constrained Learning for Decentralized Multi-Objective Coverage Control

The multi-objective coverage control problem requires a robot swarm to collaboratively provide sensor coverage to multiple heterogeneous importance density fields (IDFs) simultaneously. We pose this as an optimization problem with constraints and study two different formulations: (1) Fair coverage, where we minimize the maximum coverage cost for any field, promoting equitable resource distribution among all fields; and (2) Constrained coverage, where each field must be covered below a certain cost threshold, ensuring that critical areas receive adequate coverage according to predefined importance levels. We study the decentralized setting where robots have limited communication and local sensing capabilities, making the system more realistic, scalable, and robust. Given the complexity, we propose a novel decentralized constrained learning approach that combines primal-dual optimization with a Learnable Perception-Action-Communication (LPAC) neural network architecture. We show that the Lagrangian of the dual problem can be reformulated as a linear combination of the IDFs, enabling the LPAC policy to serve as a primal solver. We empirically demonstrate that the proposed method (i) significantly outperforms state-of-the-art decentralized controllers by 30% on average in terms of coverage cost, (ii) transfers well to larger environments with more robots, and (iii) is scalable in the number of IDFs and robots in the swarm.

Authors

• Juan Cerviño
• Saurav Agarwal
• Vijay Kumar 0001
• Alejandro Ribeiro

Keywords

• Costs
• Heuristic algorithms
• Robot sensing systems
• Graph neural networks
• Sensors
• Complexity theory
• Resource management
• Optimization
• Coverage Control
• Constrained Learning
• Neural Network
• Scalable
• Optimization Problem
• Multi-objective Optimization
• Limited Communication
• Dual Problem
• Maximum Cost
• Decentralized Control
• Swarm Robotics
• Lagrangian Problem
• Equitable Distribution Of Resources
• Cost Threshold
• Convolutional Neural Network
• Multilayer Perceptron
• Constrained Optimization Problem
• Voronoi Diagram
• Local Perceptions
• Dual Variables
• Primal-dual Algorithm
• Imitation Learning
• Exchange Algorithm
• Clairvoyant
• Environment Size
• Position Of The Robot
• Communication Graph
• Coverage Problem
• Environmental Point