A Bi-level Co-design Framework for Lunar Monoped with 2D Jump and Landing Control

Legged robots can extend planetary exploration to rugged and discontinuous terrain that is inaccessible to conventional rovers. In lunar gravity, jumping further expands this mobility by enabling robots to cross obstacles and gaps that cannot be traversed by walking alone. We present a multistage reinforcement-learning approach that produces a single end-to-end control policy for commanded point-to-point jumping under lunar gravity. The resulting policy has a simple architecture and relies exclusively on mission-compatible onboard sensing, making its deployment on a real lunar mission plausible. In simulation, the learned policy performs accurate point-to-point jumps with landing errors smaller than the robot's body size. We analyze the torque and power demands of lunar jumping and characterize performance degradation under extreme outlier events, including control-update freezes of up to \SI{1}{s} during flight. Hardware transfer demonstrates that the policy can successfully execute a vertical jump under lunar-gravity offloading. Furthermore, the measured torque and power profiles are consistent with the simulation results and remain within the robot's hardware limits.

We present a rolling and jumping underactuated monopedal robot designed to explore multimodal locomotion on low-gravity bodies. It uses only two reaction wheels to control its spatial orientation with two controllers: a balancing controller which can aim the robot's jump direction on the ground, and an aerial reorientation controller which can aim the robot's leg for landing after flight. We demonstrate rolling, targeted jumping and landing, and self-righting using only three actuators total, keeping system size to 0.33m and 1.25kg. Simple switching between locomotion modes enables the system to deal with differing landscapes and environmental conditions.

Locomotion under reduced gravity is commonly realized through jumping, yet continuous pronking in lunar gravity remains challenging due to prolonged flight phases and sparse ground contact. The extended aerial duration increases landing impact sensitivity and makes stable attitude regulation over rough planetary terrain difficult. Existing approaches primarily address single jumps on flat surfaces and lack both continuous-terrain solutions and realistic hardware validation. This work presents a Dual-Horizon Hybrid Internal Model for continuous quadrupedal jumping under lunar gravity using proprioceptive sensing only. Two temporal encoders capture complementary time scales: a short-horizon branch models rapid vertical dynamics with explicit vertical velocity estimation, while a long-horizon branch models horizontal motion trends and center-of-mass height evolution across the jump cycle. The fused representation enables stable and continuous jumping under extended aerial phases characteristic of lunar gravity. To provide hardware-in-the-loop validation, we develop the MATRIX (Mixed-reality Adaptive Testbed for Robotic Integrated eXploration) platform, a digital-twin-driven system that offloads gravity through a pulley-counterweight mechanism and maps Unreal Engine lunar terrain to a motion platform and treadmill in real time. Using MATRIX, we demonstrate continuous jumping of a quadruped robot under lunar-gravity emulation across cratered lunar-like terrain.