The channel problem solution, as initially formulated by Lutterkort and Peters, has found a large number of engineering applications. Some of these are collision-free path planning of autonomous vehicles, polylines smoothing algorithms with guaranteed error bound for machining, and isogeometric segmentation of 3D models. The traditional approach uses a non-rational spline to parameterise the unknown curve. This choice has the advantage of defining non-interference constraints through linear relationships using a SLEVE (Subdividable Linear Efficient Function Enclosure) definition based on a tight envelope of the spline. Therefore the problem can be mathematically formulated as a linearly constrained optimisation. The aim of this study is to investigate a possible extension of this approach that parameterises the unknown curve with a NURBS. The proposed algorithm is based on a new envelope definition of rational splines with few pieces using the perspective map function. While rational splines offer significant advantages in terms of geometric representation, the complexity of the problem increases considerably due to nonlinear relationships in the constraints’ formulation. In these cases it is necessary to determine whether the problem is a local or global optimisation. This work summarises the analysis of the proposed method, explores its robustness and evaluates its advantages over the established approach based on non-rational splines.