The growing trend of onboard computational autonomy has increased the need for self-reliant rovers (SRRs) with high efficiency for unmanned rover activities. Mobility is directly associated with a successful execution mission, thus fault response for actuator failures is highly crucial for planetary exploration rovers in such a trend. However, most of the existing mobility health management systems for rovers have focused on fault diagnosis and protection sequences that are determined by human operators through ground-in-the-loop solutions. This paper presents a special four-wheeled two-steering lunar rover with a modified explicit steering mechanism, where each left and right wheel is controlled by only two actuators. Under these constraints, a new motion planning method that combines reinforcement learning with the rover’s kinematic model without the need for dynamics modeling is devised. A failure-safe algorithm is proposed to address the critical loss of mobility in the case of steering motor failure, by expanding the devised motion planning method, which is designed to ensure mobility for mission execution in a four-wheeled rover. The algorithm’s performance and applicability are validated through simulations on high-slip terrain scenarios caused by steering motor failure and compared with a conventional control method in terms of reliability. This simulation validation serves as a preliminary study toward future works on deformable terrain such as rough or soft areas and optimization of the deep neural network’s weight factor for fine-tuning in real experiments. The failure-safe motion planning provides valuable insights as a first-step approach toward developing autonomous recovery strategies for rover mobility.