Redundant Manipulators

A manipulator is termed kinematically redundant when it possesses more degrees of freedom than it is needed to execute a given task. Redundancy can be conveniently exploited to achieve more dexterous robot motions. The inverse kinematic problem is of particular interest in this case since it admits infinite solutions. The above inverse kinematic algorithms have been suitably extended to redundant manipulators by adopting a task space augmentation technique. Formally, a functional constraint task is imposed to be satisfied along with the end-effector task; typical constraints include obstacle avoidance, limited joint range, manipulability measures and singularity avoidance. A reformulation of dynamic manipulability ellipsoid for both redundant and non-redundant manipulators has been established. An augmented Jacobian is obtained which is formed by the usual end-effector Jacobian and by the Jacobian relative to the constraint task. In order to avoid the problem of feasible constraint task specification, a task priority strategy has been applied, according to which the task with lower priority is executed only if it does not conflict with the higher priority task. This is accomplished by projecting the constraint Jacobian onto the null space of the end-effector Jacobian; the order of priority being invertible. The technique has been applied to redundancy resolution for space manipulators mounted on a free-floating spacecraft. The task-priority strategy has been revisited with the aim of eliminating the occurrence of algorithmic singularities arising from conflicts between the two tasks. A user-defined accuracy inverse kinematics algorithm based on task priority has been developed for redundant manipulators. The extension of such schemes to derive accelerations for task space control purposes has been investigated. In particular, a scheme for stabilization of internal null-space motion has been proposed; its performance has been compared with that of local optimization and second-order extended Jacobian schemes. Also, a general recursive algorithm that computes joint velocities and accelerations for model-based controllers has been derived. The above algorithms have been experimentally tested on the industrial robot manipulator with a non-spherical wrist in the laboratory. A solution to the minimum-time control problem for redundant manipulators has been proposed.