In recent years, researchers have been dedicated to the study of underactuated manipulators which have more joints than control actuators. In previous works, one always assumes that there is enough dynamic coupling between the active and the passive joints of the manipulator, for it to be possible to control the position of the passive joints via the dynamic coupling. In this work, the authors ...

This article studies the dynamics and control of a novel underactuated system, wherein a plate suspended by cables and with a freely moving mass on top, whose other ends are attached to three quadrotors, is sought to be horizontally stabilized at a certain height, with the ball positioned at the center of mass of the plate. The freely moving mass introduces a 2-degree of underactuation into the...

This paper describes a systematic procedure to exponentially stabilize relative equilibria of mechanical systems. We review the notion of relative equilibria and their stability in a Riemannian geometry context. Potential shaping and damping control are employed to obtain full exponential stabilization of the desired trajectory. Two necessary conditions are that the effective potential be posit...

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In this paper, we address the tracking problem for an underactuated ship using two controls, namely surge force and yaw moment. A simple state-feedback control law is developed and proved to render the tracking error dynamics globally -exponentially stable. Experimental results are presented where the controller is implemented on a scale model of an offshore supply vessel.

Designing and analyzing controllers for underactuated systems with underactuation degree greater than one is still an open and challenging problem. In this paper, we study an unsolved problem of analyzing energy based swing-up control for a double pendulum on a cart, which has three degrees of freedom and only one control input. We present an original analysis of the convergence of the energy o...

This paper uses a recently developed generalized averaging theory [18] to develop stabilizing control laws for a large class of nonlinear systems with drift. These control laws exponentially stabilize in the average.