In this paper, we propose a method for a two-wheeled rover, which generates a trajectory whose curvature is sparse, that is, the desired trajectory is mostly linear. Such a trajectory can be obtained by sparse control minimizing the L¹ -norm of the angular velocity input. We call this trajectory a hands-off trajectory. The proposed method is based on L¹/L²- optimal control. In the method, we use the cost function consisting of the L¹ -norm of the angular velocity input and the L² -norm of all the inputs of the system. Minimizing it leads to a sparse control on a rover angle, which means that the generated trajectory is mostly linear. Then, a rover can track it easily. For obtaining the optimal control input in a numerically stable manner, we propose an algorithm based on the continuation method. The effectiveness of the proposed method is demonstrated by numerical simulations.