Backstepping control design for motion coordination of self‐propelled vehicles in a flowfield

Abstract

Abstract-Motion coordination of autonomous vehicles has applications from target surveillance to climate monitoring. Previous research has yielded stabilizing control laws for a selfpropelled-vehicle model with first-order rotational dynamics; however, this model may not adequately describe the rotational dynamics of vehicles in the atmosphere or ocean. This paper describes the design of backstepping algorithms for the decentralized control of self-propelled vehicles with secondorder rotational dynamics. We design backstepping controls for planar parallel and circular formations in the absence of a flowfield and in the presence of a steady, uniform flowfield. These controls extend prior results to a more realistic vehicle model.

Motion coordination of planar rigid bodies

“…We show that under existing second-order steering control laws provided in [7] and a new speed control, the planar rigid body model achieves comparable closed-loop performance to a particle model. In prior work, the vehicles were each considered to be particles with unit mass and unit speed and the direction of travel was controlled by a force orthogonal to the heading [8].…”

“…An example of a kinematic control for a multiagent system is [6], in which integrator backstepping is used for formation control of non-holonomic agents. A similar approach has been used in [7], in which the authors introduced a vehicle model based on [11] and [8] with secondorder rotational dynamics. We previously used integrator backstepping to adapt controllers designed for first-order rotational dynamics; however, forces and moments were not considered before now.…”

“…Model (1) represents an extension of a selfpropelled particle model with first-order rotational dynamics [7]. In the first-order case, phase and spacing potentials were used to derive control laws for parallel and circular formations in the absence of an external flowfield [11], and in the presence of a spatiotemporal flowfield [10].…”

“…This implies that θ k is constant for all k. Thus, Λ contains the set of parallel formations. Using transformation (4), a backstepping-based secondorder controller for parallel formations in (1) is [7] …”

Observer-Based Feedback Control for Stabilization of Collective Motion

“…In [6], control laws for self-propelled particles were proven to stabilize synchronized, balanced, circular, and symmetric circular formations in the presence of a timeinvariant flowfield. Taking another direction, [5] provided a rotational acceleration controller for a self-propelled particle using backstepping and proportional control. Another method for creating collective motion utilized pursuit dynamics.…”