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A. F. Vakakis and J. W. Burdick. Chaotic motions of a simplified hopping robot. In Proc. IEEE Int. Conf. Robotics and Automation, pages 1464--1469, Cincinnati, OH, 1990.

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Design, Control, and Energetics of an Electrically.. - Gregorio, Ahmadi.. (1997)   (Correct)

....leg spring compression. The ensuing additional leg spring compression injects energy into the system. The vertical oscillation stabilises around an operating point, where the losses during a complete cycle are balanced by the added energy. The stability of this approach has been investigated in [10, 11, 12]. Since the ground force against the leg actuator at maximum compression is approximately 500N , a position step is an impractical strategy with low power electric actuators. Instead, we adopted a new open loop controller, 1 Gamma ) which specifies a scaled version of the ....

A. F. Vakakis and J. W. Burdick, "Chaotic motions of a simplified hopping robot", in Proc. IEEE Int. Conf. Robotics and Automation, Cincinnati, OH, 1990, pp. 1464--1469.


Vertical Motion Control of a Hopping Robot - Michalska, Ahmadi, Buehler (1996)   (Correct)

....different mathematical descriptions in non overlapping regions of the state space. The analysis of such systems has long been recognized as complex; interesting dynamical behaviour including possible existence of higher order limit cycles, bifurcations and strange attractors has been demonstrated [5, 3, 9], based on simplified models of Raibert s [8] one legged robots and his control laws. Research supported NSERC of Canada under grants OGPO 138352 and OGPO 138117 Due to the enormous success of Raibert s pioneering experimental work, his models have become a standard for most of the past ....

....applied, and the vertical hopper dynamics are essentially second order, the analytical integration of the stance phase dynamics is possible. This in turn permits the derivation of a scalar Poincar e map, for which a bounty of analytical techniques have been developed. This approach is followed in [3, 4, 5, 9]. Analysis of the continuous dynamics is difficult, even for second order systems, since most of the standard mathematical results from nonlinear systems theory do not apply, due to the variable structure of the system. The approaches have been varied but apply some form of perturbation theory, as ....

A. F. Vakakis and J. W. Burdick. Chaotic motions of a simplified hopping robot. In Proc. IEEE Int. Conf. Robotics and Automation, Cincinnati, OH, 1990.


Stable Control Of A One-Legged Robot - Exploiting Passive Dynamics   (Correct)

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A. F. Vakakis and J. W. Burdick. Chaotic motions of a simplified hopping robot. In Proc. IEEE Int. Conf. Robotics and Automation, pages 1464--1469, Cincinnati, OH, 1990.


Analysis of a Simplified Hopping Robot - Daniel Koditschek And   (Correct)

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A. F. Vakakis and J. W. Burdick. Chaotic motions of a simplified hopping robot. In Proc. IEEE Int. Conf. Robotics and Automation, pages 1464--1469, Cincinnati, OH, 1990.

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