Technical Paper
Development and Validation of an Optimized Emergency Lane-Change Trajectory
1998-02-23
980231
In this paper, functional analysis is employed to develop an ideal path of a vehicle undergoing a limit lane-change maneuver. Inputs to the problem are the lane width, tire-road coefficient of friction and either vehicle velocity or total longitudinal lane-change distance. Vehicle velocity is assumed to be constant. The problem is formulated using the calculus of variations. The solution technique relies on elliptic functions to achieve a closed-form solution. The synthesis of an ideal lane-change trajectory is treated as a minimal-energy-curve optimization problem with prescribed continuity and boundary conditions. The concept of critical speed is employed to limit the maximum curvature of any specified lane-change, thereby ensuring that the synthesized trajectory function describes a path that can be traversed under realistic road conditions. The analytical solution is confirmed by comparison to a numerical solution and a validated 8 degree-of-freedom vehicle model simulation.