Redundant robots that are kinematically controlled by using Jacobian pseudoinverses may not have repeatable joint motions. This problem was initially observed and analyzed by C.A. Klein and C.H. Huang (1983). T. Shamir and Y. Yomdin (1988) analyzed this problem using a differential geometric approach. Both studies arrived at conditions under which a cyclic path in the work space does not result in a cyclic path in the joint space. It is shown that these criteria are equivalent. A measure for the drift motion of planar kinematically redundant manipulators is presented. A mathematical analysis that determines the predictable properties of drift motion for planar manipulators operating under pseudoinverse control is presented. In fact, it is shown that the Lyapunov stability analysis and phase portrait techniques can be used to predict the stability behavior of drift utilizing the drift density measure. The information-such as how much drift will occur and which configurations are drift stable-can be obtained from the analysis.>

Redundant robots which are kinematically controlled by using Jacobian pseudo-inverses may not have repeatable joint motions. This problem was initially observed and analyzed by C.A. Klein and C.H. Huang (1983). T. Shamir and Y. Yomdin (1988) recently analyzed this problem using a differential geometric approach. The above papers arrived at conditions under which a cyclic path in the work space does not result in a cyclic path in the joint space. However, it was not clear that these conditions were equivalent. It is presently shown that these two criteria are indeed equivalent. A measure for the drift motion is presented. The mathematical analysis given in the present paper can determine these predictable properties of drift motion. It is shown that the Lyapunov analysis and phase portrait techniques can be used to predict the stability behavior of drift utilizing the drift density measure described here. Information about how much drift will occur and which configurations are stable can be obtained from the analysis.>

The problem of coordinating a positioning table and a seven-axis manipulator is examined. The method described is based on subdivision of tasks. The welding table is coordinated to align the weld point surface normal antiparallel to the direction of gravity. The seven-axis robot (a six-axis Cybotech WV 15 robot and a track) is constrained to move the weld torch along the weld trajectory. The robot coordination is achieved by keeping the six-axis arm in good maneuverability position, i.e. far from its singular configurations and far from the motion limits of the six-axis arm and the track. The singularity configurations of the Cybotech WV 15 are expressed in terms of Cartesian coordinates. As a result, the redundancy coordination is expressed as an optimization of the maneuverability in Cartesian coordinates. An analytic solution to the optimization is found; it gives the Cartesian positions of the track and the robot end-effector. These positions are used to generate the joint angles of the arm by inverse kinematics.>

The authors analyze the singularity states of robot manipulators; only the manipulator inverse kinematic relationships are considered. In such relationships, three types of triangular equations arise for the kinematically general manipulator with the nominal decoupling conditions as found in conventional robots. These equations reveal the manipulator structural properties and the Cartesian configurations of the end effector in which the manipulator is singular; they may be used to determine the singularity states of a given trajectory. The method of singularity analysis presented is applicable to robots with six or less degrees of freedom.>

The authors consider the problem of coordinating multiple motion devices for welding purposes. They focus on the problem of controlling a positioning table and a seven-axis manipulator, given the parametric definition of a trajectory on a weld piece. The problem is complex as there are more than nine axes involved and a number of permutations are possible which achieve the same motions of the weld torch. The system is redundant and the robot has singular configurations. As a result, manual programming of the robot system is rather complex. The authors illustrate an approach to redundancy control and coordination of a multiple-robotic-device arc welding system that does not require manual teaching of the intermediate trajectory points. The system requires only the start and end points of the trajectory for setting up and calibration. The redundancy coordination scheme is based on constrained optimization of the maneuverability of the manipulator in Cartesian space. To bypass accuracy issues related to joint rate control, inverse kinematics is directly used in the kinematic control of the manipulator.>