Closed-Form Barrier Functions for Multi-Agent Ellipsoidal Systems With Uncertain Lagrangian Dynamics

In this letter, we design a decentralized control protocol for the collision avoidance of a multi-agent system, which is composed of 3-D ellipsoidal agents that obey second-order uncertain Lagrangian dynamics. More specifically, we derive a novel closed-form smooth barrier function that resembles a distance metric between 3-D ellipsoids and can be used by feedback-based control laws to guarantee inter-agent collision avoidance. Discontinuities and adaptation laws are incorporated in the control protocol to deal with the uncertainties of the dynamic model. The control laws are decentralized, in the sense that each agent uses only local sensing information. Simulation results verify the theoretical findings.