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This paper presents a novel methodology to model and optimize trajectories ofa quadrupedal robot with spinal compliance to improve standing jump performancecompared to quadrupeds with a rigid spine. We introduce an elastic model for aprismatic robotic spine that is actively preloaded and mechanicallylock-enabled at initial and maximum length, and develop a constrainedtrajectory optimization method to co-optimize the elastic parameters and motiontrajectories toward enhanced jumping distance. Results reveal that a less stiffspring is likely to facilitate jumping performance not as a direct propellingsource but as a means to unleash more motor power for propelling by trading-offoverall energy efficiency. We also visualize the impact of spring coefficientson the overall optimization routine from energetic perspectives to identify thesuitable parameter region.

Modeling and Trajectory Optimization for Standing Long Jumping of a Quadruped with A Preloaded Elastic Prismatic Spine