State Offset Synchronization with Velocity-Dependent Potentials for Collision-Aware Time-Varying Formations

Author preprint of a manuscript submitted to IEEE European Control Conference. This is the author-submitted version, not the version of record. The scientific content is unchanged from the submitted manuscript; the preprint notice and running headers identify this repository version. Abstract: This paper addresses control of time-varying formations with collision and obstacle avoidance for planar point-mass vehicles modeled as second-order linear agents. Formation tracking is cast as state offset synchronization: offsets generated by an auxiliary linear system are subtracted from the agent states, thereby reducing the formation control problem to standard leader--follower synchronization. For physically motivated double-integrator and harmonic-oscillator vehicle models, the admissible offset generators and the associated acceleration feedforward are given explicitly and interpreted as formation maneuvers. The formation tracking law is combined with a velocity-dependent potential field for collision and obstacle avoidance: an elliptical safety region is aligned with the relative velocity and elongated by the closing speed, repulsion acts only while the distance decreases, and a lateral component resolves head-on encounters. The avoidance action enters at the acceleration level, is bounded, and vanishes in steady formation, so that nominal state offset synchronization is ultimately recovered. Simulations of rigid and parallel turns, a follower exchange, and a formation passing obstacles illustrate the proposed approach. Funding acknowledgment: This work was supported by the European Union under the project ROBOPROX, registration no. CZ.02.01.01/00/22_008/0004590. Version: Version 1.0 of the Zenodo preprint, prepared on 5 November 2026. The date identifies preparation of this repository version, not the date of submission to IEEE European Control Conference.