Inverse kinematics and dynamic control methods for robotic systems
Deo, Arati Suresh
Walker, Ian D.
Doctor of Philosophy
This dissertation presents new algorithms for inverse kinematic computations of robotic manipulators and for the control of multiple cooperating manipulator systems. The results presented in this thesis can be classified into three parts. The first part is an extension of our earlier work in computing inverse kinematic solutions using the damped least squares method. An adaptive algorithm is presented, which switches from the damped least-squares model to a second-order model, in situations where the former is unable to converge to the desired configuration. This algorithm is insensitive to the reachability of the desired end-effector position. The second part introduces minimum-effort inverse kinematics for redundant robotic manipulators. The Euclidean norm has been universally used in optimizing various criteria for computing the joint velocities of a redundant arm. Here, the use of the infinity norm for defining these criteria is investigated. It is shown that in various applications, better physical representation of the performance criteria is obtained by using this norm instead of the Euclidean norm. The third section of the thesis deals with the formulation of dynamic equations and control law for a multiple cooperating manipulator system handling a common object, when the surfaces of the end-effectors and the object maintain rolling contact with each other. A new unified dynamic formulation for such a robotic system is derived, by modeling the rolling contacts as unactuated joints of the manipulators. This enables the formulation of trajectory planning methods that can be used to perform an additional subtask such as collision avoidance. In addition, a computed-torque type control law is designed, which explicitly controls the object trajectory, object internal forces and the contact trajectories.
Electronics; Electrical engineering; Mechanical engineering