Hip motor state-optimized jump trajectory planning algorithm for bipedal wheeled robots

To address the limitation of maximum jump height constrained by the maximum torque of hip joint motors in bipedal wheeled robots during trajectory planning using the dual-mass linear spring model (DMLSM), this study aims to reduce the maximum required hip joint torque for achieving equivalent jump heights. Concurrently, reducing the maximum rotational speed of hip joint demanded by equivalent jumps is essential to minimize motor wear and enhance system stability. Building upon the dual-mass model, we propose a trajectory planning method based on hip joint motor state optimization (TPM-HJMSO). This method integrates a nonlinear spring model, cubic polynomial interpolation, and a min–max optimization approach with nonlinear constraints. Simulation results demonstrate two critical advances: TPM-HJMSO achieves 163.16% higher jump heights than the DMLSM under identical maximum hip torque constraints, while reducing maximum hip motor speed by 37.17% when attaining equivalent jump heights. These outcomes validate the method’s superior performance. Precise trajectory tracking is demonstrated through feedforward-plus-PD control in both Webots simulations and physical prototype experiments, verifying TPM-HJMSO’s effectiveness.