A predictive algorithm for rate control of mechanisms near singularities

A new kinematic algorithm for the control of mechanisms is described, which produces smoother and more accurate control near kinematic singularities than the usual damped least-squares method. The new method predicts the occurrence of singularities, evaluates the singular terms of the inverse kinematic function using a nonsingular expression, and smoothly interpolates between the singular and nonsingular forms. The desingularized expression makes use of the rates of change of the singular vectors and values of the Jacobian matrix; formulas for these derivatives are presented. Simulations of the control of two and six joint serial manipulators moving through and near singular configurations are given to illustrate the method.