Tunable Leg Stiffness in a Monopedal Hopper for Energy-Efficient Vertical Hopping Across Varying Ground Profiles

Although aerial-legged robots offer combined agility and efficiency, controlling high-speed hopping under complex hybrid dynamics is challenging. Reinforcement Learning (RL) is promising but prone to energy-inefficient "reward hacking". We propose a Dynamics-Informed RL framework for a monopedal hopping quadcopter. By embedding a target Specific Energy into the reward, we constrain the optimization to a physically viable energy manifold, ensuring stable hopping behaviour. By rewarding the phase-consistent behavior, it can encourage bio-inspired stance-phase impulse. Furthermore, penalizing the electro-mechanical power waste induces the motors generate an efficient impulse. This enables the policy to inject energy strictly during spring restitution without heuristic state machines. MuJoCo simulations validate robust height regulation and forward velocity tracking up to 2.0 m/s despite severe attitude-contact coupling. Ultimately, our approach yields a highly agile hopping gait, reducing energy consumption by 82% and 73% compared to hovering baselines and inefficiency baseline, respectively.

Quadruped robots are often designed with rigid feet to simplify control and maintain stable contact during locomotion. While this approach is straightforward, it limits the ability of the legs to absorb impact forces and reuse stored elastic energy, leading to higher energy expenditure during locomotion. To explore whether compliant feet can provide an advantage, we integrate foot compliance into a reinforcement learning (RL) locomotion controller and study its effect on walking efficiency. In simulation, we train eight policies corresponding to eight different spring stiffness values and then cross-evaluate their performance by measuring mechanical energy consumed per meter traveled. In experiments done on a developed quadruped, the energy consumption for the intermediate stiffness spring is lower by ~ 17% when compared to a very stiff or a very flexible spring incorporated in the feet, with similar trends appearing in the simulation results. These results indicate that selecting an appropriate foot compliance can improve locomotion efficiency without destabilizing the robot during motion.

We present a novel stepping strategy for pitch unlocked planar monopeds where the reaction torques from stabilizing pitch with a conventional PD + feedfoward controller are recruited to counteract energetic losses from damping. By moving the location of the mass center, our controller increases the pitch stabilization torque, thereby adding energy to the gait. A new stepping policy adjusts the distribution of energy between the radial and angular degrees of freedom to counteract dissipative losses and achieve a user specified balance between steady state fore-aft speed and apex height. Hybrid averaging analysis yields closed form expressions for the fixed points and eigenvalues of the resulting gait, lending insight into the interplay between the physical and control parameters' influence on performance. Simulation studies on a generic 5 link biped and a careful model of the Penn Jerboa reveal a useful correspondence to these analytical predictions. Physical experiments on the Penn Jerboa exhibit stable locomotion with speeds ranging from 1.02 m/s to 1.77 m/s (5.10 leg lengths/s to 8.85 leg lengths/s) in a manner effectively approximated by the mathematical analysis.