Almost-Global Tracking of Simple Mechanical Systems on a General Class of Lie Groups

Maithripala, D. H. S.; Berg, Jordan M.; Dayawansa, W.P.

doi:10.1109/tac.2005.862219

Cited by 121 publications

(97 citation statements)

References 34 publications

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“…Proposition 2: (Exponential Stability of the Complete Dynamics) Consider the control force f and moment M defined in (15), (16). Suppose that the initial condition satisfies…”

Section: Exponential Asymptotic Stabilitymentioning

confidence: 99%

“…By characterizing geometric properties of nonlinear manifolds intrinsically, geometric control techniques provide unique insights to control theory that cannot be obtained from dynamic models represented using local coordinates [15]. This approach has been applied to fully actuated rigid body dynamics on Lie groups to achieve almost global asymptotic stability [14], [16], [17], [18].…”

Section: Introductionmentioning

confidence: 99%

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Geometric tracking control of a quadrotor UAV on SE(3)

Lee

Leoky

McClamroch

2010

49th IEEE Conference on Decision and Control (CDC)

1,003

825

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Abstract-This paper provides new results for the tracking control of a quadrotor unmanned aerial vehicle (UAV). The UAV has four input degrees of freedom, namely the magnitudes of the four rotor thrusts, that are used to control the six translational and rotational degrees of freedom, and to achieve asymptotic tracking of four outputs, namely, three position variables for the vehicle center of mass and the direction of one vehicle body-fixed axis. A globally defined model of the quadrotor UAV rigid body dynamics is introduced as a basis for the analysis. A nonlinear tracking controller is developed on the special Euclidean group SE(3) and it is shown to have desirable closed loop properties that are almost global. Several numerical examples, including an example in which the quadrotor recovers from being initially upside down, illustrate the versatility of the controller.

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“…Proposition 2: (Exponential Stability of the Complete Dynamics) Consider the control force f and moment M defined in (15), (16). Suppose that the initial condition satisfies…”

Section: Exponential Asymptotic Stabilitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Geometric tracking control of a quadrotor UAV on SE(3)

Lee

Leoky

McClamroch

2010

49th IEEE Conference on Decision and Control (CDC)

1,003

825

View full text Add to dashboard Cite

show abstract

“…whether the separation principle holds. Maithripala et al [34,35] proved that the separation principle also holds in the general case of compact Lie Groups and therefore also for SO (3). For the reader's convenience this general result is restated in terms of SO (3) in the Appendix B.…”

Section: Attitude Stabilization Via the Separation Principlementioning

confidence: 93%

“…For the reader's convenience this general result is restated in terms of SO (3) in the Appendix B. In this section, results from [34,35] are specialized to SO(3), the Lie Groups of rigid body rotations, and traditional state feedback control is combined with the dynamic attitude observer presented in [33].…”

Section: Attitude Stabilization Via the Separation Principlementioning

confidence: 99%

Attitude Stabilization of a Biologically Inspired Robotic Housefly via Dynamic Multimodal Attitude Estimation

et al. 2009

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In this paper, we study sensor fusion for the attitude stabilization of Micro Aerial Vehicles (MAVs), in particular mechanical flying insects. Following a geometric approach, a dynamic observer is proposed which estimates attitude based on kinematic data available from different and redundant bio-inspired sensors such as halteres, ocelli, gravitometers, magnetic compass and light polarization compass. In particular, the traditional structure of complementary filters, suitable for multiple sensor fusion, is specialized to the Lie group of rigid body rotations SO(3). The filter performance based on a 3-axis accelerometer and a 3-axis gyroscope is experimentally tested on a 2 degreesof-freedom support showing its effectiveness. Finally, attitude stabilization is proposed based on a feedback scheme with dynamic estimation of the state, namely the orientation and the angular velocity. Almost-global stability of the proposed controller in the case of dynamic state estimation is demonstrated via the separation principle, and realistic numerical simulations with noisy sensors and external disturbances are provided to validate the proposed control scheme.keywords: attitude control on SO(3), separation principle, geometric control, complementary filtering, biologically inspired robots.

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“…The configuration error was described with geodesics on Lie group and exponential convergence of the energy function was obtained. Maithripala designed an intrinsic Luenberger observer on Lie group with intrinsic information and provide a coordinate-free tracking controller for mechanical systems on Lie group [7][8][9]. He also introduced an intrinsic geometric PID method with covariant differentiation for left-invariant or right-invariant system [3,10].…”

Section: Introductionmentioning

confidence: 99%

Intrinsic Optimal Control for Mechanical Systems on Lie Group

Liu

Tang

Guo

2017

Advances in Mathematical Physics

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The intrinsic infinite horizon optimal control problem of mechanical systems on Lie group is investigated. The geometric optimal control problem is built on the intrinsic coordinate-free model, which is provided with Levi-Civita connection. In order to obtain an analytical solution of the optimal problem in the geometric viewpoint, a simplified nominal system on Lie group with an extra feedback loop is presented. With geodesic distance and Riemann metric on Lie group integrated into the cost function, a dynamic programming approach is employed and an analytical solution of the optimal problem on Lie group is obtained via the HamiltonJacobi-Bellman equation. For a special case on SO(3), the intrinsic optimal control method is used for a quadrotor rotation control problem and simulation results are provided to show the control performance.

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Almost-Global Tracking of Simple Mechanical Systems on a General Class of Lie Groups

Cited by 121 publications

References 34 publications

Geometric tracking control of a quadrotor UAV on SE(3)

Geometric tracking control of a quadrotor UAV on SE(3)

Attitude Stabilization of a Biologically Inspired Robotic Housefly via Dynamic Multimodal Attitude Estimation

Intrinsic Optimal Control for Mechanical Systems on Lie Group

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