G² lane-change path imposes symmetry boundary conditions on the path geometry for autonomous point-to-point movement. This paper presents the comparative study of three planar parametric polynomial curves as lane-change paths followed by an autonomous vehicle, assuming that the neighboring lane is free. A simulated model based on unicycle that accounts for acceleration constraints, velocity bounds and the time-optimal parameterization of each path is adopted. We base the timeoptimal trajectory simulations on numerical integration for each family of lane-change curves under two different end conditions representing loose and hard curvature scenarios to highlight the effect of path curvature on achievable speed or minimal travel time. Simulations show that the dominating factor for travel time of following a lane change curve is different for loose and hard curvature condition. Conclusions for fastest lane-change performed by unicycle could provide a reference for more complex and complete dynamic model of autonomous vehicle considering tire and friction forces.