A global approach for the path generation of redundant manipulators

A singularities avoidance approach suitable for the optimal path planning of redundant robot manipulators is presented. The approach is based on establishing proper bounds for the rate of change of the Jacobian matrix of the transformation between the joint speeds and the end effector Cartesian speed. These bounds become an additional constraint for an optimization problem that is formulated to obtain the optimal path of the robot manipulator. Here, the optimization problem is formulated globally as a state-constrained continuous optimal control problem which can consider joint (speeds) constraints and/or manipulator dynamics, and be solved by an efficient iterative numerical technique. This approach is particularly exemplified for the optimal path generation of a simulated planar redundant manipulator, and its results are compared with the results yielded by a local approach. The results obtained (although not adequate for present real-time implementation) confirm the superiority of the global approach