A solution of the inverse kinematics problem using the sliding mode

A closed-loop algorithm for solving the inverse kinematics problem is presented. An easy-to-implement method achieves coordinate transformation using the sliding-mode principle and a Lyapunov-like concept. An attractive feature of this algorithm over the Newton-Raphson method is that its computational burden is reduced. Furthermore, it requires no Jacobian matrix inversion and thus avoids the numerical instabilities associated with matrix singularities. Simulation results demonstrate the performance of the proposed algorithm for a robot that has no analytical solution to the inverse kinematics problem.