Dual-Horizon Hybrid Internal Model for Low-Gravity Quadrupedal Jumping with Hardware-in-the-Loop Validation

TL;DR

This paper introduces a dual-horizon internal model for continuous quadrupedal jumping in lunar gravity, validated with a novel hardware-in-the-loop system that emulates lunar terrain and gravity conditions.

Contribution

It presents a hybrid internal model with dual temporal encoders for stable continuous jumping under lunar gravity, and a real-time hardware-in-the-loop validation platform called MATRIX.

Findings

Successful continuous jumping under lunar gravity emulation.

Effective modeling of vertical and horizontal dynamics across jump cycles.

Hardware validation on lunar-like terrain demonstrates practical applicability.

Abstract

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.