Carnegie Mellon University Dynamics and Control of Underactuated Manipulators

ivThe class of underactuated systems is composed of a variety of mechanical as well asbiological systems. The term underactuation refers to the fact that not all joints or degrees-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 dynamicequations are nonlinear and are constrained by nonholonomic differential equations. In thisdissertation, it is our goal to study these fundamental characteristics toward the aim ofdeveloping modeling and control methods for underactuated systems, with focus on theclass 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 thedexterity of underactuated manipulators, and propose an optimization index to determinethe positions of the unactuated joints which maximize the dexterity. Also differently froma conventional manipulator, the unactuated joints of an underactuated manipulator can bedriven only indirectly through their coupling with the actuated ones. We present thedynamic characteristics of underactuated manipulators, and propose the coupling indexconcept to measure the dynamic coupling between the joints. The coupling index is utilizedfor 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 manipulatorto an equilibrium point. We investigate the controllability of the system, and demonstratethat controllability and the coupling index are related concepts. We also propose theoptimal control sequence of the unactuated joints to account for underactuatedmanipulators with more unactuated than actuated joints. In practice, manipulators operatein workspaces populated with obstacles. We propose a high-level motion planning methodthat generates collision-free trajectories to be followed by the manipulator. The methodsproposed are implemented on a planar manipulator designed and built at the SpaceRobotics Laboratory at Carnegie Mellon University.