A coupled nonlinear spacecraft attitude controller and observer with an unknown constant gyro bias and gyro noise

This paper presents a modified Rodrigues parameter (MRP)-based nonlinear observer design to estimate bias, scale factor and misalignment of gyroscope measurements. A Lyapunov stability analysis is carried out for the nonlinear observer. Simulation is performed and results are presented illustrating the performance of the proposed nonlinear observer under the condition of persistent excitation maneuver. In addition, a comparison between the nonlinear observer and alignment Kalman filter (AKF) is made to highlight favorable features of the nonlinear observer.

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“…The kinematic equations of motion in terms of the MRP can be derived in terms of spacecraft angular velocity 7) such that…”

Section: Mrp-based Equations Of Motionmentioning

confidence: 99%

A Modified Rodrigues Parameter-based Nonlinear Observer Design for Spacecraft Gyroscope Parameters Estimation

Yong

Bang

2012

Trans. Japan Soc. Aero. S Sci.

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“…In this paper, the problem in question is revisited under the assumption that measurements of the rotation matrix R(t) are available, while measurements of ω(t) obtained by means of rate gyros are corrupted by additive harmonic noise. The considered setup arises frequently in the control of aerospace vehicles with significant aeroelastic effects [3], where structural vibrations are transmitted to the rate gyros through the coupling with the airframe, or in the attitude control of rigid of flexible satellites, where harmonic disturbance in the angular velocity measurements are produced by imbalance or mechanical defects in gyroscopes [4]- [6]. Dealing with uncertainties on the natural frequencies is a fundamental issue in applications to control of hypersonic vehicles, where the vibrational modes change in response to mass variation and unsteady heating effects [7].…”

Section: Problem Definitionmentioning

confidence: 99%

“…By using a technique similar to the one proposed in [11], the disturbance models (4) and (5) can be modified to include a constant bias in the signal d, thus incorporating the setup considered in [6]. Since such an extension does not lead to a substantial modification of the control algorithm, it has been omitted for simplicity.…”

Section: Disturbance Modelmentioning

confidence: 99%

“…The role of (8) is to reconstruct the disturbance d, and to provide asymptotic convergence ofR(t) to the identity matrix. While the structure of the observer is conceptually similar to the one employed in [6], the higher complexity of (8) is required to handle the uncertainty on the frequencies of the harmonic components of the disturbance.…”

Section: Disturbance Modelmentioning

confidence: 99%

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Attitude tracking with adaptive rejection of rate gyro disturbances

Pisu

Serrani

2008

2008 American Control Conference

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Abstract-The classical attitude control problem for a rigid body is revisited under the assumption that measurements of the angular rates obtained by means of rate gyros are corrupted by harmonic disturbances, a setup of importance in several aerospace applications. The paper extends previous methods developed to compensate bias in angular rate measurements by accounting for a more general class of disturbances, and by allowing uncertainty in the inertial parameters. By resorting to adaptive observers designed on the basis of the internal model principle, it is shown how converging estimates of the angular velocity can be obtained, and used effectively in a passivity-based certainty-equivalence controller yielding global convergence within the chosen parametrization of the group of rotations. Since a persistence of excitation condition is not required for the convergence of the state estimates, only an upper bound on the number of distinct harmonic components of the disturbance is needed for the applicability of the method. I. PROBLEM DEFINITIONConsider the rotational dynamics of a rigid bodẏwith state (R, ω) ∈ SO(3) × R 3 , representing the orientation and angular velocity of a body-fixed frame with respect to an inertial frame, and control input u ∈ R 3 . The matrix S(·) denotes the skew-symmetric operator S(v)w := v×w, where v, w ∈ R 3 . The inertia matrix J(µ) ∈ R 3×3 is assumed to depend continuously on a vector of unknown parameters µ ranging over a given compact setfor the orientation and angular velocity of the body-fixed frame of (1) is provided by a smooth autonomous system of the form̟with state of importance in aerospace applications [1], and greatly simplify the analysis. The rotation matrix for the attitude error R e := R T d R ∈ SO(3) satisfies the kinematic equatioṅ R e = R e S(ω e ), where ω e := ω−R e T ω d denotes the angular velocity error resolved in the body frame.The classic attitude control problem [2] is loosely defined as that of finding a feedback control law such that all trajectories of the closed-loop system are bounded, and the tracking error satisfies (R e (t), ω e (t)) → (I 3 , 0) as t → ∞, for any given reference trajectory in the considered family of solutions of (2), and for all µ ∈ K µ . In this paper, the problem in question is revisited under the assumption that measurements of the rotation matrix R(t) are available, while measurements of ω(t) obtained by means of rate gyros are corrupted by additive harmonic noise. The considered setup arises frequently in the control of aerospace vehicles with significant aeroelastic effects [3], where structural vibrations are transmitted to the rate gyros through the coupling with the airframe, or in the attitude control of rigid of flexible satellites, where harmonic disturbance in the angular velocity measurements are produced by imbalance or mechanical defects in gyroscopes [4]- [6]. Dealing with uncertainties on the natural frequencies is a fundamental issue in applications to control of hypersonic vehicles, where the vibrational mo...

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“…In contrast, nonlinear observers exploit the underlying geometry in order to account for the highly nonlinear nature of the problem. As a result, they appear to be more robust and have provable almost global stability properties (see, e.g., [3], [4], [5], [6], [7]). For the attitude problem, Mahony et al [4] derived a complementary nonlinear attitude observer exploiting the underlying Lie group structure of the Special Orthogonal group SO(3) of all rotations, and proved almost global stability of the error system.…”

Section: Introductionmentioning

confidence: 99%

Observer design on the Special Euclidean group SE(3)

Hua

Zamani

Trumpf

et al. 2011

IEEE Conference on Decision and Control and European Control Conference

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Abstract-This paper proposes a nonlinear pose observer designed directly on the Lie group structure of the Special Euclidean group SE(3). We use a gradient-based observer design approach and ensure that the derived observer innovation can be implemented from position measurements. We prove local exponential stability of the error and instability of the non-zero critical points. Simulations indicate that the observer is indeed almost globally stable as would be expected.

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A coupled nonlinear spacecraft attitude controller and observer with an unknown constant gyro bias and gyro noise

Cited by 245 publications

References 9 publications

A Modified Rodrigues Parameter-based Nonlinear Observer Design for Spacecraft Gyroscope Parameters Estimation

A Modified Rodrigues Parameter-based Nonlinear Observer Design for Spacecraft Gyroscope Parameters Estimation

Attitude tracking with adaptive rejection of rate gyro disturbances

Observer design on the Special Euclidean group SE(3)

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