Robust hybrid controllers for continuous-time systems with applications to obstacle avoidance and regulation to disconnected set of points

Sanfelice, Ricardo G.; Messina, Michael J.; Tuna, S. Emre; Teel, Andrew R.

doi:10.1109/acc.2006.1657236

Cited by 73 publications

(57 citation statements)

References 13 publications

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“…The corresponding stability analysis would need to carefully consider the fact that convergence to a single attitude implies convergence to either of the two disconnected, antipodal points on S 3 [22]. This requires a continuous selection of the sign of quaternions or a discontinuous control system, which are shown to be sensitive to small measurement noise [23]. Without these considerations, a quaternion-based controller can exhibit an unwinding phenomenon, where the controller unnecessarily rotates the attitude through large angles [15].…”

Section: E Properties and Extensionsmentioning

confidence: 99%

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

Lee

Leoky

McClamroch

2010

49th IEEE Conference on Decision and Control (CDC)

1,074

846

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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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Section: E Properties and Extensionsmentioning

confidence: 99%

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

Lee

Leoky

McClamroch

2010

49th IEEE Conference on Decision and Control (CDC)

1,074

846

View full text Add to dashboard Cite

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“…Albeit this control law avoids unwinding, a careful look reveals a strong sensitivity around attitudes that are up to π away from the desired attitude about some axis-that is, η = 0. In view of Theorem 2.6 of [33], one can see that such control law isn't robust in the sense that arbitrarily small measurement noises can force η to stay near to 0 for initial conditions within its neighborhood. Indeed, similar to Theorem 3.2 of [11], one can even exhibit an explicit noise signal to persistently trap the system about a fixed pose, thus preventing its stability.…”

Section: Prior Work On Pose Stabilizationmentioning

confidence: 99%

Hybrid kinematic control for rigid body pose stabilization using dual quaternions

Kussaba

Figueredo

Ishihara

et al. 2017

Journal of the Franklin Institute

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In this paper, we address the rigid body pose stabilization problem using dual quaternion formalism. We propose a hybrid control strategy to design a switching control law with hysteresis in such a way that the global asymptotic stability of the closed-loop system is guaranteed and such that the global attractivity of the stabilization pose does not exhibit chattering, a problem that is present in all discontinuous-based feedback controllers. Using numerical simulations, we illustrate the problems that arise from existing results in the literature-as unwinding and chattering-and verify the effectiveness of the proposed controller to solve the robust global pose stability problem.

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“…Lastly, even using a (memoryless) discontinuous state feedback, it is impossible to achieve robust global asymptotic stabilization of a disconnected set of points resulted from the double covering of the SE(3) [9], [10].…”

Section: Hybrid Pose Controlmentioning

confidence: 99%

“…As noted in [9], however, nonhybrid strategies are prone to chattering and are not robust to arbitrarily small measurement noise since it is impossible to use pure discontinuous state feedback to achieve robust global asymptotic stabilization of a disconnected set of points [10].…”

Section: Introductionmentioning

confidence: 99%