Dynamics and Control of Underactuated Manipulators

Abstract

The class of underactuated systems is composed of a variety of mechanical as well as biological systems. The term underactuation refers to the fact that not all joints or dcgrees-of-freedom (DOFs) of the system are equipped with actuators, or are directly controllable. The DOFs of an underactuated system are dynamically coupled, and their dynamic equations are nonlinear and are constrained by nonholonomic differential equations. In this dissertation, it is our goal to study these fundamental characteristics toward the aim of developing modeling and control methods for underactuated systems, with focus on the class of serial chain underactuated manipulators with joints connected by rigid links. Although an underactuated manipulator can be structurally identical to a fully actuated one, their dexterities differ because of the presence of unactuated joints. We quantify the dexterity of underactuated manipulators, and propose an optimization index to determine the positions of the unactuated joints which maximize the dexterity. Also differently from a conventional manipuIator, the unactuated joints of underactuated manipulator can be driven only indirectly through their coupling with the actuated ones. We present the dynamic characteristics of underactuated manipuIators , and propose the coupling index concept to measure the dynamic coupling between the joints. The coupling index is utilized for the analysis, design, and optimal control of underactuated manipulators. Parameter uncertainty and external disturbances interfere with the control of manipulators. We propose a robust control method to control all joints of an underactuated manipulator to an equilibrium point. We investigate the controllability of the system, and demonstrate that controllability and the coupling index are related concepts. We also propose the optimal control sequence of the unactuated joints to account for underactuated manipulators with more unactuated than actuated joints. In practice, manipulators operate in workspaces populated with obstacles. We propose a high-level motion planning method that generates collision-free trajectories to be followed by the manipulator. The methods proposed are implemented on a planar manipulator designed and built at the Space Robotics Laboratory at Carnegie Mellon University.