Dynamic Modeling and Attitude Control of a Reaction-Wheel-Based Low-Gravity Bipedal Hopper

Abstract

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.

Figures (6)

• Figure 1: Overview of the reaction-wheel based bipedal hopper operating on procedurally generated low-gravity terrain.
• Figure 2: Planar dynamic model of the reaction-wheel hopper illustrating the torso-mounted reaction wheel (RW), wheel rotation $\Phi_w$, hip and knee joint angles ($q_{hL}, q_{hR}, q_{kL}, q_{kR}$), and the ground reference frame used for system modeling.
• Figure 3: Representative time instants of a single hopping cycle illustrating touchdown, propulsion, mid-air stabilization, and landing phases.
• Figure 4: Continuous spatial trajectories across successive hops. The changing vertical baseline indicates successful adaptation to the uneven lunar heightmap, while forward progression remains consistent.
• Figure 5: Reaction wheel dynamic response. The wheel accelerates dynamically to absorb liftoff-induced angular momentum, with torque impulses aligning strictly with physical push-off and landing disturbances.