Robot control actions are naturally executed in the joint space while robot motions are specified in the task space. It is then
necessary to solve an inverse kinematics problem; namely, given the end-effector trajectory, find the corresponding joint
trajectories. Only simple manipulator geometries allow analytical inverse kinematics solutions to be computed. Closed-loop
inverse kinematics algorithms have been developed which are based on the computation of the direct kinematic function
and Jacobian transpose; the solution is obtained in terms of joint displacements and velocities. The problem of orientation
parameter specification has been solved by specifying the desired trajectory in terms of Euler angles and the actual
trajectory in terms of normal, sliding, and approach unit vectors. These algorithms have been derived first for spherical
wrist manipulators, then for non-solvable structures such as a manipulator with two-by-two intersecting axes at the wrist.
Experimental results have been obtained for the non-spherical wrist industrial robot in the laboratory. The problem of
kinematic singularities has been addressed and algorithm performance in such occurrences has been characterized. The
basic algorithm has been properly applied for the determination of the manipulator reachable workspace. The extension of
the technique to incorporate joint acceleration solution has also been proposed. Different representations of end-effector
orientation have been used, and a comparison among the classical Euler angles feedback, an alternative Euler angles
feedback, an angle/axis feedback, and a quaternion feedback has been carried out. The usual inverse kinematics algorithm
based on the Jacobian pseudo-inverse has been improved to allow robot control through singularities. Further, a damped
least-squares solution has been derived with varying damping factor and/or user-defined accuracy; this permits kinematic
control of the manipulator along feasible task space directions. A numerical technique to estimate the two smallest singular
values of the Jacobian matrix has been proposed. The inclusion of velocity limits for general inverse kinematics algorithms
has been proposed and its effectiveness has been experimentally tested on a two-joint direct-drive manipulator.
Experimental tests have been conducted on both five-joint and six-joint manipulators. The closed-loop algorithm has been
applied to solve the direct kinematics problem for a class of parallel manipulators.