| Kinematically redundant manipulators composed of a rigid-link, rigid-joint robot and a structurally flexible arm on top of which the former is located constitute a new paradigm of long-reach manipulation systems. In order to have the end-effector of such a system faithfully follow a preplanned path, one should be able to reliably monitor the motions of the flexible submanipulator due to its elastic deformations. To this end, it is proposed that redundant point-acceleration measurements made on the rigid-robot base be used in an extended Kalman filter to estimate the flexural states of the flexible submanipulator. More specifically, this is done by processing the above-mentioned acceleration data in a novel pose and twist estimation technique, formulated in this thesis, to obtain those of the tip of the flexible arm; the pose and the twist data are then utilized as the measured outputs for the observer. Of course, the state-output relations should be linearized; the linearization is performed in closed-form.;The mathematical models of the flexible and the rigid submanipulators are derived separately, each through the premultiplication of the transpose of the kinematic-constraint matrix by the assembled set of the link Lagrange equations; this matrix is the natural orthogonal complement of the kinematic-constraint wrench. Obviously, the reaction wrench acting between the rigid-robot base and the end-effector of the flexible submanipulator couples the two sets of dynamics equations. This wrench can be determined by substituting the twist-rate of the base, i.e., its angular and translational accelerations, into the dynamics equations of the rigid submanipulator and, subsequently, solving them. Then, considering the wrench as a time-dependent input for the flexible arm, we take the flexible-arm dynamics as the modelled dynamics in the observer. The reduced-order dynamics helps dramatically reduce the required floating-point operations within the observer.;Two redundancy-resolution techniques, namely, rigid-link redundancy resolution and flexible-link redundancy resolution, are discussed. Whereas the former assumes all the links to be rigid, the latter takes the flexibility effects into account. In both approaches, the self-motion of the system is computed so as to minimize the forces exciting its lowest "modal coordinates" while imposing a proportional damping on the flexural dynamics. |
