One of the approaches to collision-free nonholonomic motion planning is the "approximation method". The corresponding planners compute first a holonomic path among obstacles before approximating it by a concatenation of feasible collision-free paths. These methods are one of the rare ones which can lead to exact and complete planners. However, the performance of these planners (in terms of computation time and the complexity of the solution) is highly influenced by the "quality" of the first geometric path. We suggest a way to estimate this quality and present the first general approach leading to an improvement of the quality of the geometric path. This approach is based on local deformations of a holonomic potential field with respect to the nonholonomic constraints of the system.