Trajectory-Level Design-Space Exploration and Performance Mapping of a 1-DoF Transformable Wheel for Obstacle Climbing

This paper proposes a trajectory-level design framework for a one-degree-of-freedom (1-DoF) transformable wheel capable of overcoming structured obstacles. The framework enables systematic quantitative evaluation of acceleration-based motion smoothness, actuator load, and energy consumption at the trajectory level while supporting systematic design space exploration. First, a kinematic mapping is constructed to determine feasible wheel postures corresponding to given obstacle geometry. Trajectories are then parameterized using transformation start (TS), transformation end (TE), and pivoting angle (α), and generated with cubic Hermite splines to ensure second-order continuity. A kinematic model and quasi-static model are employed to analyze force and moment equilibrium, from which six performance indices—average and maximum acceleration, motor torque, and mechanical power—are derived to assess motion smoothness, actuator load, and energy. A full factorial design is conducted to evaluate the feasible design space. The resulting performance maps reveal global trade-offs among stability, torque, and energy, together with distinct trajectory design strategies. Finally, a 1-DoF transformable wheel prototype and obstacle testbed are developed for experimental validation. The experiments confirm that trajectories with different performance characteristics are clearly distinguished byTS–TE–α combinations, consistent with simulation predictions. These results demonstrate that the proposed framework provides practical quantitative guidelines for designing obstacle-overcoming trajectories and selecting actuator capacities for transformable wheels.