Control on the Sphere and Reduced Attitude Stabilization

Bullo, Francesco; Murray, Richard M.; Sarti, Augusto

doi:10.1016/s1474-6670(17)46878-9

Cited by 78 publications

(91 citation statements)

References 6 publications

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“…Almost global reduced attitude stabilizing controllers on S 2 have been studied in [4], [8], [9], [10], [11]. In [4], [8] a control system that stabilizes a rigid body to a fixed reference direction q d ∈S 2 is summarized, where the error function used in [8] is,…”

Section: A Error Functionmentioning

confidence: 99%

Attitude and angular velocity tracking for a rigid body using geometric methods on the two-sphere

Ramp¹,

Papadopoulos²

2015

2015 European Control Conference (ECC)

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The control task of tracking a reference pointing direction (the attitude about the pointing direction is irrelevant) while obtaining a desired angular velocity (PDAV) around the pointing direction using geometric techniques is addressed here. Existing geometric controllers developed on the two-sphere only address the tracking of a reference pointing direction while driving the angular velocity about the pointing direction to zero. In this paper a tracking controller on the two-sphere, able to address the PDAV control task, is developed globally in a geometric frame work, to avoid problems related to other attitude representations such as unwinding (quaternions) or singularities (Euler angles). An attitude error function is constructed resulting in a control system with desired tracking performance for rotational maneuvers with large initial attitude/angular velocity errors and the ability to negotiate bounded modeling inaccuracies. The tracking ability of the developed control system is evaluated by comparing its performance with an existing geometric controller on the two-sphere and by numerical simulations, showing improved performance for large initial attitude errors, smooth transitions between desired angular velocities and the ability to negotiate bounded modeling inaccuracies.

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Section: A Error Functionmentioning

confidence: 99%

Attitude and angular velocity tracking for a rigid body using geometric methods on the two-sphere

Ramp¹,

Papadopoulos²

2015

2015 European Control Conference (ECC)

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“…Stemming from the seminal work of [1] about control theory on general Lie groups, much of the literature has been devoted to the control of systems defined on SO(3) and SE (3). Although it is usual to design controllers for these systems using matrices to represent elements of these Lie groups [2], [3], it has been noted by some authors that controllers designed using another type of representation, namely, the unit quaternions for SO (3) and the unit dual quaternions for SE (3), may have advantages regarding computational time and storage requirements [4], [5].…”

Section: Introductionmentioning

confidence: 99%

Dual quaternion-based bimodal global control for robust rigid body pose kinematic stabilization

Magro

Kussaba

Figueredo

et al. 2017

2017 American Control Conference (ACC)

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“…This work is a contribution in the area of nonlinear control theory for mechanical systems (Murray 1995) and it is the completion of our previous works and (Bullo, Murray and Sarti 1995). Given a fully actuated control system, that is a system with as many inputs as degrees of freedom, our control objective is to track a trajectory with exponential convergence rates and to guarantee performance and robustness.…”

Section: Introductionmentioning

confidence: 99%

Trajectory tracking for fully actuated mechanical systems

Bullo

Murray

1997

1997 European Control Conference (ECC)

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This paper presents a general framework for the control of mechanical systems with as many inputs as degrees of freedom. The notions of error function and transport map are introduced to properly de ne a con guration and a velocity error. These are the crucial ingredients in designing a proportional derivative feedback and feedforward control. The proposed approach includes various results on control of manipulators, autonomous vehicles and pointing devices.

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Control on the Sphere and Reduced Attitude Stabilization

Cited by 78 publications

References 6 publications

Attitude and angular velocity tracking for a rigid body using geometric methods on the two-sphere

Attitude and angular velocity tracking for a rigid body using geometric methods on the two-sphere

Dual quaternion-based bimodal global control for robust rigid body pose kinematic stabilization

Trajectory tracking for fully actuated mechanical systems

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