This paper describes obstacle avoidance control for planetary exploration rover based on a novel potential function method. Planetary exploration rovers are crucial for investigating environments that are inaccessible to humans, such as the surfaces of Mars or the Moon. These rovers must autonomously navigate unstructured terrain filled with rocks and other obstacles. The potential function (PF) method has been widely adopted for real-time path planning due to its algorithmic simplicity and low computational cost. However, its inherent limitation, specifically the tendency to become trapped in local minima, remains a major challenge, especially in complex environments. In this study, we propose the PF with an adaptive rotated velocity field (ARVF) to enhance rover navigation. Our PF with ARVF improves upon the conventional PF with a rotated VF by adaptively determining the direction of repulsive velocity field rotation, based on the angular relationship among the rover, target, and obstacles. Furthermore, it introduces virtual obstacles by grouping clusters of obstacles, enabling the rover to avoid dense and trap-like regions. Numerical simulations compare the PF with ARVF against traditional PF and PF with rotated VF. We confirm that the proposed method allows the rover to reach the target position while avoiding local minima and suppressing abrupt changes in control inputs. ©2025 IEEE.