Bio-Inspired Compliant Joints and Economic MPC Co-Design for Energy-Efficient, High-Speed Locomotion in Snake-like Robots

Snake-like robots face critical challenges in energy-efficient locomotion and smooth gait transitions, limiting their real-world deployment. This study introduces a bio-inspired compliant joint design integrated with a hierarchical neural oscillator network and an energy-optimized control framework. The joint mimics biological skeletal flexibility using specialized wheeled mechanisms and adaptive parallel linkages, while the control network enables adaptive gait generation and seamless transitions through a phase-smoothing algorithm. Critically, this work adopts a synergistic design philosophy where mechanical components and control parameters are co-optimized through shared dynamic modeling. The proposed predictive control strategy optimizes locomotion speed while minimizing energy consumption. Experimental simulations demonstrate that the method achieves an 18% higher average forward speed (0.0563 m/s vs. 0.0478 m/s) with 7% lower energy use (0.1952 J vs. 0.2107 J) compared to conventional approaches. Physical prototype testing confirms these improvements under real-world conditions, showing a 12.9% speed increase (0.0531 m/s vs. 0.0470 m/s) and 7.3% energy reduction (0.2147 J vs. 0.2317 J). By unifying mechanical flexibility and adaptive control parameter tuning, this work bridges dynamic performance and energy efficiency, offering a robust solution for unstructured environments.