Privacy-preserving formation control for multi-agent systems with collision avoidance

This paper presents a privacy-preserving formation control scheme with collision avoidance for leaderless distributed multi-agent systems. In this scheme, the initial positions and velocities of individual agents are kept confidential from one another. Two efficient privacy-preserving protocols are developed based on homomorphic computation. These protocols enable cooperative determination of the relative direction and spatial relationship of the two agents without revealing the respective input states. On the basis of these two protocols, a sliding-mode-like controller with a chatter attenuation mechanism is proposed. Under privacy-preserving constraints, it dynamically adjusts control gains using local state history, which results in smooth control inputs. Theoretical analysis and numerical simulations demonstrate that formation errors asymptotically converge within a bounded region under undirected communication topology. They also validate the achievement of collision-free trajectories under maximum velocity constraints and the confidentiality of the initial states against semi-honest adversaries.