Motion Planning for Autonomous Vehicles Based on Sequential Optimization

This study presents the development and analysis of a technique for planning the autonomous vehicle (AV) motion references using sequential optimization. The method determines the trajectory plan, speed and acceleration distributions, and other AV kinematic parameters. The approach combines the basics of the finite element method (FEM) and nonlinear optimization with nonlinear constraints. First, we briefly described the generalization of representing an arbitrary function by finite elements (FE) within a road segment. We chose a one-dimensional FE with two nodes and three degrees of freedom (DOF) in a node corresponding to the 5th-degree polynomial. Next, we presented a method for defining the motion trajectory. The following are considered: the formation of a restricted space for the AV's allowable maneuvering, the motion trajectory geometry and its relation with vehicle steerability parameters, cost functions and their influences on the desirable trajectory's nature, and the compliance of nonlinear restrictions of the node parameters with the motion area boundaries. In the second stage, we derived a technique for optimizing the AV's speed and acceleration redistributions. The model considers possible combinations of objective functions, limiting the kinematic parameters by the tire slip critical speed, maximum speed level, maximum longitudinal acceleration, and critical lateral acceleration. In the simulation section, we compared several variants of trajectories and versions of distributing the longitudinal speed and acceleration curves. The advantages, drawbacks, and conclusions regarding the proposed technique are presented.