Clothoid-based model predictive control for autonomous driving

This paper presents a novel linear time-varying model predictive controller (LTV-MPC) using a sparse clothoid-based path description: a LTV-MPCC. Clothoids are used world-wide in road design since they allow smooth driving associated with low jerk values. The formulation of the MPC controller is based on the fact that the path of a vehicle traveling at low speeds defines a segment of clothoids if the steering angle is chosen to vary piecewise linearly. Therefore, we can compute the vehicle motion as clothoid parameters and translate them to vehicle inputs. We present simulation results that demonstrate the ability of the controller to produce a very comfortable and smooth driving while maintaining a tracking accuracy comparable to that of a regular LTV-MPC. While the regular MPC controllers use path descriptions where waypoints are close to each other, our LTV-MPCC has the ability of using paths described by very sparse waypoints. In this case, each pair of waypoints describes a clothoid segment and the cost function minimization is performed in a more efficient way allowing larger prediction distances to be used. This paper also presents a novel algorithm that addresses the problem of path sparsification using a reduced number of clothoid segments. The path sparsification enables a path description using few waypoints with almost no loss of detail. The detail of the reconstruction is an adjustable parameter of the algorithm. The higher the required detail, the more clothoid segments are used.