Application of Sigmoidal Gompertz Curves in Reverse Parallel Parking for Autonomous Vehicles

Abstract

A new method for the planning and autonomous execution of a single-trajectory, velocity-independent, parallel parking manoeuvre for autonomous vehicles is presented. The procedure commences with the identification and pre-selection of a smooth sigmoidal trajectory known as the Gompertz curve in parametric format. Trajectory parameters are determined in real-time during the path-planning phase using an optimization scheme in order to generate a candidate path. The optimization scheme takes into account the maximum steering angles that can be physically realized and checks the generated candidate trajectory for collisions. Thereafter, the trajectory is reparametrized to arc-length format using the cubic interpolation method and the vehicle orientation at every point of the trajectory is deduced. Following that, values of the steering angle(s) are determined. In the final step, the vehicle uses dead-reckoning to follows the arc-length parametrized path in reverse in order to park itself in a single-manoeuvre. The proposed method is substantiated through both extensive simulations and real sensor data.