G2 lane-change path imposes symmetric conditions on the path geometric properties. This paper presents the comparative study\nof time-optimal velocities to minimize the time needed for traversal of three planar symmetric parametric polynomial lane-change\npaths followed by an autonomous vehicle, assuming that the neighboring lane is free. A simulated model based on unicycle that\naccounts for the acceleration and velocity bounds and is particularly simple for generating the time-optimal path parameterization\nof each lane-change path is adopted. We base the time-optimal trajectory simulations on numerical integration on a path basis\nunder two different end conditions representing sufficient and restricted steering spaces with remarkable difference in allowable\nmaximum curvature. The rest-to-rest lane-change maneuvering simulations highlight the effect of the most relevant path\ngeometric properties on minimal travel time: a faster lane-change curve such as a quintic Bezier curve followed by a unicycle tends\nto be shorter in route length and lower in maximum curvature to have achievable highest speed at the maximum curvature points.\nThe results have implications to path selection for parallel parking and allow the design of continuous acceleration profile via time\nscaling for smooth, faster motion along a given path. This could provide a reference for on-road lane-change trajectory planning\nalong a given path other than parametric polynomials for significantly more complex, complete higher-dimensional highly\nnonlinear dynamic model of autonomous ground vehicle considering aerodynamic forces, tire and friction forces of tire-ground\ninteraction, and terrain topology in real-world.
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