A General Approach for Planning a Smooth Planar Path Within a Channel Using NURBS

This letter presents a new and comprehensive approach to planning a smooth and optimal path in a planar channel. The algorithm generates a NURBS that traverses the channel, in turn defined by two bounding rational splines, and stays inside. A nonlinearly constrained problem is solved to model the shape of the two-sided bounded path to optimise the objective function. The user can choose the degree of the curve that defines the resulting path and optionally add the interpolation of waypoints and orientations. The presented method expands the domain of feasible solutions compared to previous approaches based on nonrational splines, leading to improvements in terms of the objective function. Various examples are provided to illustrate and clarify the method.