Real-time Approximation of Clothoids With Bounded Error for Path Planning Applications

We present a method for real-time computation of clothoid coordinates that guarantees bounded approximation error over a wide range of clothoid parameters provided that the clothoid's orientation change and length are bounded. It is shown that coordinates of clothoid with any parameters can be computed from those of a single clothoid (with fixed parameters), using appropriate geometrical transformations. A comprehensive analysis is given on how to determine a required set of clothoids and, based on this, how to sample a clothoid in a lookup table in order to achieve required approximation precision. The algorithm is computationally very efficient and therefore suitable for real-time path planning, as well as for other applications that benefit from fast clothoid computation.