An impulse-momentum approach to control of a class of underactuated mechanical systems.

Underactuated mechanical systems pose challenging control problems because they have fewer control inputs than degrees of freedom. The dynamics of these systems are such that they cannot be always controlled by traditional nonlinear control methods. In this dissertation we present a new and general methodology to control underactuated mechanical systems, and we apply this methodology to the control problems of systems with two and three generalized coordinates with a single underactuated joint. We first consider the swing-up control problems of the Pendubot and the Acrobot, which are benchmark problems. A comparison of our methodology with other controllers previously applied to these problems shows that the systems are stabilized in a settling time comparable to the best results available in the literature, using the same actuators. However, a significant advantage of our methodology is that it can be applied to both the Pendubot and the Acrobot alike, and only two of the many previously developed control methodologies share this feature. Our methodology is based on rest-to-rest maneuvers of the actuated link using impulse-like control inputs. These inputs are designed to make the energy of the system converge to a level corresponding to that at the desired equilibrium point while restricting the movement of the actuated link. In order to show the generality of this methodology we show in this dissertation that it can be used for posture control of a synthetic-wheel biped robot. The biped robot, which is introduced for the first time in this dissertation, has two legs and a torso; and we consider stabilization of its standing configuration after the application of disturbances. Specifically, we consider the case of small disturbances in which we require the robot to maintain its posture using only the torso and keeping its feet on the ground. The torso will use impulsive torques to bring the energy of the system to the desired level. This problem is similar to a person who is trying to balance and stand without taking any steps. However, not all disturbances can be handled this way; therefore, we consider the stabilization problem for this biped after the application of a large disturbance. This time the biped is going to use both legs during the stabilization process. The biped will walk the necessary steps before stopping and finally stabilize around the standing configuration. The torso again is responsible for bringing the energy to the desired level while the legs' role are to keep the biped from falling. The algorithms are provided for solving each control problem mentioned above. Simulation results are also presented to demonstrate the efficacy of the approaches.