Jump Control Based on Nonlinear Wheel-Spring-Loaded Inverted Pendulum Model: Validation of a Wheeled-Bipedal Robot with Single-Degree-of-Freedom Legs

Jumping is a fundamental capability for wheeled-bipedal robots (WBRs) navigating unstructured terrains, with jump height and stability serving as indicators of the robot's environmental adaptability. However, existing trajectory planning methods demand high output capacity from the joints and fail to balance computational load with trajectory tracking performance. This limitation hinders most robots from experimental validation. To address these challenges, this study presents an optimized virtual model, trajectory planning strategy, and control method. These solutions enhance both the height and stability of jumps while ensuring real-time execution on physical robots. Firstly, inspired by the human jumping mechanism, a Nonlinear Wheel-Spring-Loaded Inverted Pendulum (NW-SLIP) model was originally proposed as the virtual model for trajectory planning. The jump height is increased by 3.4 times compared to the linear spring model. Then, cost functions are established based on this virtual model, and the trajectory for each stage is iteratively optimized using Quadratic Programming (QP) and a bisection method. This leads to a 21.5% increase in the maximum jump height while reducing the peak joint torque by 14% at the same height. This significantly eases execution and enhances the robot's trajectory-tracking ability. Subsequently, a leg statics model is introduced alongside the kinematics model to map the relationship between the virtual model and joint space. This approach improves trajectory tracking performance while circumventing the intricate calculation of the dynamics model, thereby enhancing jump consistency and stability. Finally, the proposed trajectory planning and jump control method is validated through both simulations and real-world experiments, demonstrating its feasibility and effectiveness in practical robotic applications.