A singularities avoidance method for the trajectory planning of redundant and nonredundant robot manipulators

In this paper, a singularities avoidance method suitable for the trajectory planning of redundant and nonredundant robot manipulators is presented. This method is based on establishing proper bounds for the rate of change of the Jacobian matrix of the transformation between the joints speed and end effector Cartesian speed These bounds are computationally inexpensive and easy to deal with by their conversion into additional constraints for any optimization problem which may be formulated to obtain the local or global optimal control of the robot manipulator. Here, this approach is exemplified for the trajectory planning problem of a particular type of redundant and nonredundant robot manipulators studied under an optimal control problem formulation. For each case, this problem is treated as a minimum energy problem with given kinematics and dynamics and subject to the robot requirements, tasks, and the additional singularities avoidance constraints; resulting in a state constrained continuous optimal control which is solved numerically.