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This paper investigates the inherent oscillation problem of potential field methods (PFMs) in the presence of obstacles and in narrow passages. These problems can cause slow progress and system instability in implementation. To overcome these two problems, in this paper, we propose a modification of Newton's method. The use of the modified Newton's method, which applies anywhere C2 continuous navigation functions are defined, greatly improves system performance when compared to the standard gradient descent approach. To the best of our knowledge, ours is the first systematic approach to the oscillation problems in PFMs. We have validated this technique by comparing its performance with the gradient descent method in obstacle-avoidance tasks with different potential models and parameter changes.