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.