Feedback Control of Impact Dynamics: the Bouncing Ball Revisited

Abstract-The paper considers the feedback stabilization of periodic orbits in a planar juggler. The juggler is "blind," i.e, he has no other sensing capabilities than the detection of impact times. The robustness analysis of the proposed control suggests that the arms acceleration at impact is a crucial design parameter even though it plays no role in the stability analysis. Analytical results and convergence proofs are provided for a simplified model of the juggler. The control law is then adapted to a more accurate model and validated in an experimental setup.

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“…The optimal acceleration for static performance, as identified in (30), has also been derived from the original nonlinear equations [33].…”

Section: ) Static Errormentioning

confidence: 99%

Rhythmic Feedback Control of a Blind Planar Juggler

2007

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“…In [11], [12], Ronsse also addressed robustness of the bouncing ball system to static and dynamic errors in the ball's coefficient of restitution (CR). The authors first derived the transfer function of the errors in the CR to the postimpact velocity perturbations.…”

Section: A Related Workmentioning

confidence: 99%

Bouncing an Unconstrained Ball in Three Dimensions with a Blind Juggling Robot

Reist

D’Andrea

2009

2009 IEEE International Conference on Robotics and Automation

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We describe the design of a juggling robot that is able to vertically bounce a completely unconstrained ball without any sensing. The robot consists of a linear motor actuating a machined aluminum paddle. The curvature of this paddle keeps the ball from falling off while the apex height of the ball is stabilized by decelerating the paddle at impact. We analyze the mapping of perturbations of the nominal trajectory over a single bounce to determine the design parameters that stabilize the system. The first robot prototype confirms the results from the stability analysis and exhibits substantial robustness to perturbations in the horizontal degree of freedoms. We then measure the performance of the robot and characterize the noise introduced into the system as white noise. This allows us to refine the design parameters by minimizing the H2 norm of an input-output representation of the system. Finally, we design an H2 optimal controller for the apex height using impact time measurements as feedback and show that the closed-loop performance is only marginally better than what is achieved with open-loop control.

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“…Ronsse and Sepulchre [19] showed that the acceleration of the table with a bouncing ball at impact is an important parameter for the robustness of the feedback system to model uncertainty, in particular to the uncertainty on the coefficient of restitution. Figure 13 shows the dependence of the coefficient of restitution on the velocity of the model just before impact.…”

Section: Identification Of Model Parameters and Modeling The Coefficimentioning

confidence: 99%

Inelastic impact dynamics of ships with one-sided barriers. Part II: experimental validation

2011

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This paper is the second part of a twopart study of impact interaction of a ship roll motion with one-sided ice barrier. The first part was devoted to analytical and numerical simulations for the case of inelastic impact. The analytical approach was based on Zhuravlev and Ivanov non-smooth coordinate transformations. Extensive numerical simulations were carried out for all initial conditions covered by the ship grazing orbit for different values of excitation amplitude and frequency of external waveinduced roll moment. The basins of attraction of safe operation revealed the coexistence of different response regimes such as non-impact periodic oscillations, modulated impact motion, period added impact oscillations, chaotic impact motion and roll-over dynamics. This part presents an experimental investigation conducted on a small ship model in a tow tank. In particular, the experimental tests reveal complex dynamic response characteristics such as multifrequency wave motion caused by the wave reflection from the tank end wall. Measured results show a good agreement with the predicted results by for small angles of the barrier relative to the ship unbiased position. However, deviation becomes significant as the angle increases. This deviation is mainly attributed to the uncertainty of the coefficient of restitution, which I.M. Grace · R.A. Ibrahim ( ) · V.N. Pilipchuk is found to depend on the velocity of impact in addition to the geometry and material properties of the model and barrier.

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Feedback Control of Impact Dynamics: the Bouncing Ball Revisited

Cited by 10 publications

References 23 publications

Rhythmic Feedback Control of a Blind Planar Juggler

Rhythmic Feedback Control of a Blind Planar Juggler

Bouncing an Unconstrained Ball in Three Dimensions with a Blind Juggling Robot

Inelastic impact dynamics of ships with one-sided barriers. Part II: experimental validation

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