This study investigates the application of Newton method to the problems of collision avoidance and path planning for robotic manipulators, especially robots with high Degrees of Freedom (DOF). The proposed algorithm applies to the potential fields method, where the Newton technique is used for performing the optimization. As compared to classical gradient descent method this implementation is mathematically elegant, enhances the performance of motion generation, eliminates oscillations, does not require gains tuning, and gives a faster convergence to the solution. In addition, the paper presents a computationally efficient symbolic formula for calculating the Hessian with respect to joint angles, which is essential for achieving realtime performance of the algorithm in high DOF configuration spaces. The method is validated successfully in simulation environment. Results for different methods (Newton, gradient descent and gradient descent with momentum) are compared in terms of quality of the path generated, oscillations, minimum distance to obstacles and convergence rate.