Attitude Tracking of a Rotating Rigid Body System

R. Ahmed, D.-w. Gu, and I. Postlethwaite (UK)


Attitude stabilization, Lyapunov function, Output feedback, Tracking, Nonlinear control, Stability.NOMENCLATUREx, y, z : Roll, pitch & yaw axes of rigid bodyφ, θ, ψ : Euler angles of roll, pitch and yaw axesωx, ωy, ωz : Angular velocity about x, y, z axesω = (ωx, ωy, ωz)Tτx, τy, τz : Control torque about x, y, z axesτ = (τx, τy, τz)TJ : Rigid body inertia matrixJ =Jxx Jxy JxzJyx Jyy JyzJzx Jzy Jzzµx, µy, µz : Euler eigenaxis about x, y, z axesµ = (µx, µy


In this paper we address the issue of attitude stabilization and time varying attitude tracking of a rotating rigid body system. The nonlinear plant (attitude model) is defined by Euler’s equation of rotational dynamics and the kinematic differential equation. Modified Rodrigues parameter (MRP) is used for attitude representation. A new globally asymptotically stabilizing output feedback control law is proposed for the attitude motion. The overall stability of the closed loop system is proved by proposing a new candidate Lyapunov function. The proposed scheme does not require angular velocity measurements and the plant output (attitude) is the only measured variable used in the control design. The control law has some robustness as it does not require any information about the plant inertia and the over all system response is not affected by a certain variation in the plant inertia matrix for the same controller effort. Simulation results are included to show the stabilization and time varying attitude acquisition for the plant illustrating the effectiveness of the proposed control law.

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