Improved hopping control on slopes for small robots using spring mass modeling

Planetary bodies characterized by low gravitational acceleration, such as the Moon and near-Earth asteroids, impose unique locomotion constraints due to diminished contact forces and extended airborne intervals. Among traversal strategies, hopping locomotion offers high energy efficiency but is prone to mid-flight attitude instability caused by asymmetric thrust generation and uneven terrain interactions. This paper presents an underactuated bipedal hopping robot that employs an internal reaction wheel to regulate body posture during the ballistic flight phase. The system is modeled as a gyrostat, enabling analysis of the dynamic coupling between torso rotation and reaction wheel momentum. The locomotion cycle comprises three phases: a leg-driven propulsive jump, mid-air attitude stabilization via an active momentum exchange controller, and a shock-absorbing landing. A reduced-order model is developed to capture the critical coupling between torso rotation and reaction wheel dynamics. The proposed framework is evaluated in MuJoCo-based simulations under lunar gravity conditions (g = 1.625 m/s^2). Results demonstrate that activation of the reaction wheel controller reduces peak mid-air angular deviation by more than 65% and constrains landing attitude error to within 3.5 degrees at touchdown. Additionally, actuator saturation per hop cycle is reduced, ensuring sufficient control authority. Overall, the approach significantly mitigates in-flight attitude excursions and enables consistent upright landings, providing a practical and control-efficient solution for locomotion on irregular extraterrestrial terrains.

Robotic jumping is pivotal in applications such as search and rescue and logistics, where crossing obstacles and enhancing mobility efficiency are critical. The Spring-Loaded Inverted Pendulum (SLIP) model leverages simplified spring-mass dynamics that naturally encode biologically plausible hopping motions, yet its performance degrades on irregular terrain due to idealized assumptions regarding contact and joint dynamics. Meanwhile, Reinforcement Learning (RL) can adapt to diverse and complex environments but often requires extensive data from unguided exploration. The complementary strengths of SLIP's physically grounded baseline and RL's adaptive capabilities motivate a hybrid framework that overcomes these individual limitations. We therefore propose Spring-loaded Reinforcement Learning (SRL), which integrates SLIP-based feedforward control signals with RL-driven real-time feedback, enabling continuous optimization of robotic jumping. Experimental results demonstrate that SRL can achieve more stable jumps with much less training time than the baseline method, maintaining an average position tracking error below 0.1 m and velocity tracking errors within +/-3% of the target values. Through bipedal and quadrupedal simulations of ground and stair jumping, as well as sim-to-sim and sim-to-real validations, SRL exhibits robust adaptability to various task requirements and environmental complexities, underscoring its potential for real-world deployment.

Monopedal hopping robots are conceptually simple but highly dynamic and inherently unstable. Achieving robust 3D hopping is still difficult because ground reaction forces are available only during the short stance phase, while the robot is underactuated in flight. A key unresolved issue is how to improve flight-phase control authority. Propeller assistance provides a promising solution, but it requires careful coordination of leg-generated contact forces and propeller thrusts across stance and flight. This paper presents Pro-OMEGA2, a propeller-assisted 3D monopedal hopping robot with an active 3-RSR parallel leg and a trunk-mounted tri-rotor for auxiliary attitude regulation. To address the force coordination challenge, we propose a Hierarchical Force Allocation (HFA) framework based on a single rigid body (SRB) model. The leg generates the main stance contact wrench, while the tri-rotor provides auxiliary attitude regulation, compensating the residual attitude moment in stance and maintaining attitude during flight. Real-robot experiments in indoor and outdoor scenarios demonstrate sustained 3D hopping, including terrain transitions and impulsive push recovery, validating robustness under unmodeled contact and external disturbances.