Global finite-time attitude consensus of leader-following spacecraft systems based on distributed observers

Abstract

This paper addresses the leader-following attitude consensus problem for a group of spacecraft when at least one follower can access the leader's attitude and velocity relative to the inertial space. A nonlinear distributed observer is designed to estimate the leader's states for each follower. The observer possesses one important and novel feature of keeping attitude and angular velocity estimation errors on second-order sliding modes, and thus provides finite-time convergent estimates for each follower. Further, quaternion-based hybrid homogeneous controllers recently developed for single spacecraft are extended and then applied, by establishing a separation principle with the proposed observer, to track the leader's attitude motion. As a result, global finite-time attitude consensus is achieved on the entire attitude manifold, with either full-state measurements or attitude-only measurements, as long as the network topology among the followers is undirected and connected. Numerical simulations are presented to demonstrate the performance of the proposed methods.

Distributed observer‐based leader‐follower attitude consensus control for multiple rigid bodies using rotation matrices

“…Lemma Consider the systems and with , , where , p 1 ∈(0,1), , and ρ 1 , ρ 2 , ρ 3 are constants. If Assumption holds, and ρ 1 >0, ρ 2 > ρ 3 , then x ( t ) and y ( t ) are uniformly bounded and the states converge to x 1 =⋯= x n and y 1 =⋯= y n in a finite time interval t s >0, which can be estimated by the algorithm given in the work of Gui and de Ruiter …”

“…The first‐order sliding mode distributed observer was first proposed for multiple integrators dynamics in the work of Cao et al Since then, the sliding mode distributed observers have been successfully designed to estimate the leader's information including attitude and angular velocity, where the MRP‐based observer is proposed in the works of Meng et al and Zou et al and the quaternion‐based observer is proposed in the work of Zou . Recently, a novel second‐order sliding mode distributed observer is proposed to estimate the leader's trajectory in the work of Gui and de Ruiter . Based on the internal model in output regulation approach, the distributed observer has been designed to estimate the reference's quaternion attitude and angular velocity, wherein the leader's velocity input is generated by an autonomous exosystem that generates various nonvanishing signals including constant and sinusoidal signals.…”

“…First of all, in contrast to the MRPs and quaternion attitude representations, the dynamics of rigid bodies and distributed attitude observer that evolve on nonlinear manifold SO (3) are more meaningful, since the rotational motion can avoid both singularity and unwinding phenomenon. Secondly, the estimated attitude evolves on a vector space instead of the quaternion in the distributed attitude observers . In practice, keeping the estimated attitude always evolving on SO (3) is more expected, so that the existing attitude tracking control for single rigid body can be directly applied to design the consensus control law without modification.…”

“…Based on the above observations and motivated by the literatures, in this paper, the distributed observer‐based attitude consensus control for multiple rigid bodies whose kinematics evolves on SO (3) is developed. The distributed observer is designed on an undirected and connected network topology among the followers, but only a subset of followers has access to the leader's trajectory.…”

“… A distributed attitude observer is developed on the rotation matrices SO (3) directly. Unlike those defined on the vector space , our proposed attitude observer scheme guarantees that the estimated attitude evolves on SO (3) all the time, which provides us a simple way to design the consensus control law that can be converted from the single rigid body's tracking control law . In addition, the dynamics of rigid bodies and observer are both modeled on SO (3) so that the singularity and unwinding phenomenon associated with the parameterization and quaternion attitude representations can be avoided. Following the proposed distributed observer, the biased angular velocity‐based attitude consensus control law is designed.…”