Heavy-duty legged robots often have robust legs to effectively bear the load. The considerable mass of these robust legs makes agile movements challenging for heavy-duty robots because the legs need to remain as agile as possible without exceeding the actuators’ capacity. Animals with robust legs tend to minimize changes in body momentum and leg momentum during rapid running to achieve higher movement efficiency and effectively prevent joint damage. Inspired by this biological locomotion characteristic, we adopted a motion generation criterion based on minimizing leg momentum changes to further optimize the movement of heavy-duty legged robots. This criterion is formulated as a cost function of leg center of mass momentum and incorporated into an optimal control problem (OCP) based on full-kinematics and centroidal dynamics. We derive the Leg Centroidal Momentum Matrix (LCMM) and validate our method through simulations, demonstrating effectiveness across various gaits. Results indicate that using leg centroidal momentum as a cost function reduces the drive forces required for diverse movements.