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

Abstract

In this paper, we design a decentralized control protocol for the collision avoidance of a multi-agent system, which is comprised of 3D ellipsoidal agents that obey 2nd-order uncertain Lagrangian dynamics. More specifically, we derive a novel closed-form smooth barrier function that resembles a distance metric between 3D 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.

Asymptotic Stability of Uncertain Lagrangian Systems with Prescribed Transient Response

“…Moreover, many of these works deal with parametric model uncertainties or assume uniform boundedness and/or growth conditions on the unknown dynamical terms. Discontinuous control schemes for system uncertainties are also used in our works [27], [28] that tackle multi-agent problems. The model uncertainties in these works, however, are restricted to uniformly bounded disturbances and terms bounded by the state norm.…”

Adaptive robot navigation with collision avoidance subject to 2nd-order uncertain dynamics

“…Adaptive control for multi-robot coordination was also employed in our previous works . The results in , however, are only existential, since we do not provide an explicit potential function that satisfies the desired properties, while Verginis and Dimarogonas (2019) focus on the multi-agent ellipsoidal collision avoidance, without guaranteeing achievement of the primary task.…”

Distributed Collision-Free Motion Coordination on a Sphere: A Conic Control Barrier Function Approach

“…In the case of a rigid body network on a sphere under the spherical constraint (2), the attitude synchronization (16) also implies the position synchronization defined as…”

“…No matter what motion constrained workspace a multirobot system operates in, effective collision avoidance is an essential requirement to guarantee hardware safety. A potential function based approach is one common collision avoidance strategy for multi-agent systems [11], [16]- [20].…”