Optimal spine morphology for high-speed bounding in quadruped robots

Quadrupedal animals leverage flexible spines to achieve agile locomotion, yet most robotic counterparts, like the Kemba robot, retain rigid or revolute spinal joints, limiting dynamic performance. While prior studies suggest that prismatic spines enhance acceleration in quadruped robots, these often neglect physical actuator constraints inherent in real-world systems. This study investigates spine morphology—rigid, revolute, and prismatic—on the steady-state bounding of Kemba using a dynamics-driven framework. Planar models for each spine configuration integrate actuator torque, velocity, and piston force constraints, alongside complementarity conditions for ground and valve contact interactions. A second-order Radau contact-implicit direct collocation method optimises trajectories using a bio-inspired contact sequence derived from cheetah and greyhound gaits. Results demonstrate the prismatic spine’s superiority in stride length and velocity over rigid and revolute designs, attributed to enhanced leg extension and ground reaction force alignment. The prismatic spine also exhibits energy storage potential through linear actuation, suggesting efficiency gains. These findings underscore the importance of co-optimising spine morphology and actuator constraints in bio-inspired robots. This work bridges simulation-based biomechanics with practical robotic design, advancing Kemba’s capabilities. Future efforts will experimentally validate these models through the physical integration of a prismatic spine.