Time-Optimal Trajectory Planning along Parametric Polynomial Lane-Change Curves with Bounded Velocity and Acceleration: Simulations for a Unicycle Based on Numerical Integration

lane-change path imposes symmetric conditions on the path geometric properties. This paper presents the comparative study of time-optimal velocities to minimize the time needed for traversal of three planar symmetric parametric polynomial lane-change paths followed by an autonomous vehicle, assuming that the neighboring lane is free. A simulated model based on unicycle that accounts for the acceleration and velocity bounds and is particularly simple for generating the time-optimal path parameterization of each lane-change path is adopted. We base the time-optimal trajectory simulations on numerical integration on a path basis under two different end conditions representing sufficient and restricted steering spaces with remarkable difference in allowable maximum curvature. The rest-to-rest lane-change maneuvering simulations highlight the effect of the most relevant path geometric properties on minimal travel time: a faster lane-change curve such as a quintic Bezier curve followed by a unicycle tends to be shorter in route length and lower in maximum curvature to have achievable highest speed at the maximum curvature points. The results have implications to path selection for parallel parking and allow the design of continuous acceleration profile via time scaling for smooth, faster motion along a given path. This could provide a reference for on-road lane-change trajectory planning along a given path other than parametric polynomials for significantly more complex, complete higher-dimensional highly nonlinear dynamic model of autonomous ground vehicle considering aerodynamic forces, tire and friction forces of tire-ground interaction, and terrain topology in real-world.