A singularities avoidance approach for the optimal local path generation of redundant manipulators

A singularities-avoidance approach suitable for the optimal local path generation of redundant robot manipulators is presented. It is based on establishing proper bounds for the rate of change of the Jacobian matrix representing the transformation between the joints speeds and the end-effector Cartesian speed. These bounds become an additional constraint for an optimization problem which is formulated locally to obtain the optimal path of the considered robot manipulator. The problem is considered as a minimization of energy with given robot kinematics (and dynamics) and subject to the robot requirements and singularities-avoidance constraint. From this formulation, a closed-form solution is derived which allows online interaction with sensors