Computed torque control and utilization of parametric excitation for underactuated dynamical systems

Dynamical systems with less independent control input than degrees of freedom are called underactuated systems. They form a special group of robotic systems, because they are more energy efficient and agile compared to the classical industrial robots having heavy mechanical structure and robust actuators at each joint. Cranes are typical underactuated systems because there is no direct actuation on the swinging payload. The present work is motivated by a newly designed domestic robot called Acroboter, which moves on a specially designed ceiling and the working unit of the robot hangs down and operates in the 3D workspace like a crane. Since the robot has a complex multibody structure, the dynamic modeling requires a special approach, where non-minimum set of redundant coordinates describes the system instead of the classical minimum set of generalized coordinates. Geometric constraints are introduced to represent the relations among the redundant coordinates. The corresponding dynamical model is a system of differential algebraic equations. The present work addresses the developement of model based motion control algorithms for underactuated multibody systems, in general. As an application of the results, the proposed control algorithms are applied for varying topology systems, like fully actuated systems in the presence of actuator saturation. Actuator saturation is a relevant nonlinearity, which is treated here as a decrement in the number of independent control inputs. Another group of varying topology underactuated systems in focus belong to the limbless locomotion. One of the most intricate problems is when certain tasks are prescribed for the passive DoF of an underactuated system. By augmenting the actuator forces with some periodic excitation for the active DoF, the tasks could be approached even for the passive DoF. Since this periodic excitation at the actuators usually presents some time-periodic parameters in the equations of motion, this kind of forcing is called parametric excitation in classical mechanics. In this sense, parametric excitation could succesfully be used for the control of certain underactuated systems. Case studies of stabilization of water vessels and the control of pendulum-like robots via parametric excitation are presented. Finally, the motion control of the Acroboter is accomplished, which is partially based on closed form formulae derived from simplified pendulum-like models of the robot. The simplified control appoaches are combined with the general methods derived in the first part of the dissertation. The control approaches are tested and applied in laboratory experiments for the Acroboter prototype.