Tracked robots operating on rough terrain are often equipped with controllable flippers to help themselves overcome large obstacles or gaps. How to automate the control of these auxiliary flippers to achieve autonomous traversal remains an open question, which still necessitates inefficient manual teleoperation in practice. To tackle this problem, this article presents a geometry‐based motion planning method for an articulated tracked robot to self‐control its flippers during autonomous or semiautonomous traversal over rough terrain in urban search and rescue environments. The proposed method is developed by combining dynamic programming with a novel geometry‐based pose prediction method of high computational efficiency, which is applicable for typical challenging rescue terrains, such as stairs, Stepfields, and rails. The efficient pose prediction method allows us to make thousands of predictions about the robot poses at future locations for given flipper configurations within the onboard sensor range. On the basis of such predictions, our method evaluates the entire discretized configuration space and thereby determines the optimal flipper motion online for a smooth traversal over the terrain. The overall planning algorithm is tested with both simulated and real‐world robots and compared with a reinforcement‐learning‐based method using the RoboCup Rescue Robot League standard testing scenarios. The experimental results show that our method enables the robots to automatically control the flippers, successfully go over challenging terrains, and outperform the baseline method in passing smoothness and robustness to different terrains.