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A horizontal waypoint guidance algorithm is proposed by applying line-following guidance to waypoint line segments in sequence. The line-following guidance is designed using an LQR (linear quadratic regulator). Then, the optimal waypoint changing points are derived by minimizing the accelerations required for changing the waypoint line segments. Also derived is a sufficient condition for the stability bound of ground speed changes based on the Lyapunov stability theorem. Simulation results show that the proposed algorithm can effectively guide a vehicle along the sequence of waypoint line segments.