It is proved that if the manipulator Jacobian is properly scaled, the largest singular value is bounded within a small interval close to unity. In this case, the inverse of the smallest singular value is a good estimate of the condition number. This is useful in singularity analysis. Bounds are derived for a general six-joint manipulator and for the ABB IRb 2000 industrial robot in a case study.>

Singularity robust redundancy resolution with task priority can be implemented using the extended Jacobian technique with weighted damped least-squares. The resulting scheme is simple to implement and involves less computation than the task priority scheme. The minimum singular value of the Jacobian can be estimated reliably and accurately with little computation, and this estimate was used to calculate an appropriate damping factor. A constant damping factor was also used with good results. The scheme was successfully implemented in a simulation study with a seven-joint manipulator with a kinematic design derived from the PUMA geometry.>

A control scheme for the coordination of motion in a macro-micro manipulator system is presented. The motion of the end-effector is decoupled from the rest of the system using resolved acceleration control, while a slow gross positioning is used for the macro part. To avoid saturated inputs and excessive use of energy for systems with limited fuel, the end-effector is not decoupled from macro part motion, but from selected directions of the linear momentum of the total system. For the vehicle-manipulator case, the end-effector is decoupled also from the angular momentum. This leads to lower force and torque peaks in the actuators, and control force is used on the macro part only when it is necessary to reposition this to keep the micro part inside its workspace.>

A control system for a 7-joint manipulator with three intersecting shoulder axes is presented. A singularity avoidance scheme is developed, where the redundancy is resolved through a position transformation. The internal and external motions are decoupled using nonlinear feedback linearization in an augmented task space. It is then possible to use linear controllers both for the internal nullspace and for the end-effector coordinates. It is shown how optimal control theory can be applied to coordinate the motion in the arm, and how to do this so that the input generalized forces are minimized. This gives a coordination of internal and external motion which resembles the motion of the human arm; this is demonstrated by simulating a throwing motion with the manipulator.>