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

Abstract

Summary This paper addresses the distributed observer‐based leader‐follower attitude consensus control problem for multiple rigid bodies. An intrinsic distributed observer is proposed for each follower to estimate the leader's trajectory, which is only available to a subset of followers. The proposed observer can guarantee that the estimated attitude evolves on rotation matrices all the time, and it provides us with a simple way to design the attitude consensus control law. The dynamics of rigid bodies and distributed observer are both modeled directly on rotation matrices, so that the singularity and ambiguity can be avoided. Furthermore, adopting the idea of disturbance observer on vector space, a gyro bias observer on the rotation matrices is proposed. Based on the distributed observer, three types of attitude consensus control law are proposed, which are respectively on the basis of full‐state, biased angular velocity, and external disturbance combined with biased angular velocity. Finally, the SimMechanics experiments are provided to illustrate effectiveness of the proposed theoretical results.

Robust noncooperative attitude tracking control for rigid bodies on rotation matrices subject to input saturation constraint

“…where ||e|| > 𝜅 1 , || η|| > 𝜅 2 , and || ω|| > 𝜅 3 . From (40), one concludes that there exists a small gain 𝜌 1 > max{𝜅 1 , 𝜅 2 , 𝜅 3 } satisfying V ≤ 0. Thus, the saturated time derivative of virtual angular velocity is guaranteed all the time.…”

“…In the SimMechanics experiments, the constructed physical rigid body's mass matrix and moment of inertia matrix depend on the size of rigid body and its density. 40,45 Without loss of generality, the lengths of the first, second, third principal axes are denoted as L = (L 1 , L 2 , L 3 ) T ∈ R 3 , and the density of rigid body is denoted as 𝜚. Thereafter, the mass of rigid body is defined as m = 4 3 𝜋L 1 L 2 L 3 𝜚, and the corresponding mass matrix is denoted as M = diag{m, m, m}.…”

“…The designed four types of noncooperative attitude tracking control laws satisfy the input saturation requirement as well as the active disturbance rejection properties using only relative attitude measurements. Compared with the disturbance observer-based control law, 40 the proposed control law is no longer dependent on the disturbance observer. Since the control laws are subject to the input saturation constraint and the active disturbance rejection, the applicability of the designed control schemes is enhanced.…”

Systematic convergence of nonlinear stochastic estimators on the Special Orthogonal Group SO(3)

“…In addition, nonlinear deterministic estimators consider only constant bias attached to the angular velocity measurements disregarding irregularity of the noise behavior. Therefore, successful maneuvering applications, for instance [16][17][18], might not be achieved without robust attitude estimators.…”

Distributed observers design for a class of nonlinear systems to achieve omniscience asymptotically via differential geometry

“…Due to the extensive research concerning output regulation problem (ORP) of multi‐agent and its several application fields, 1‐11 the distributed state observers, as one of the important basic theories of ORP, has attracted high attention in recent years 12‐16 . Distributed observers mainly inherit the idea of distributed Kalman filter (DKF) 17‐21 and fuses the observed data by constructing a cooperative observer network.…”