Inverse kinematic algorithms for redundant systems

An iterative method of computing the solution of the inverse kinematic problem is developed for redundant systems using the transpose of the Jacobian matrix instead of the pseudoinverse. The solutions may be optimized on a criterion function or on physical constraints, such as obstacle avoidance. Stability and convergence of the method are shown. Although its convergence rate is only about half that of Newton´s method, the advantage of the method is that it remains easily tractable close to the singular configurations of the manipulator. A hybrid method combining the Jacobian transpose and Newton´s methods is proposed. Results of the application of the method on a 10-link manipulator in 2-D space are shown