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

2026-03-09

AI Summary

This work addresses the challenges of prolonged flight phases, impact sensitivity upon landing, and posture instability on rugged terrain that hinder continuous hopping of quadrupedal robots in lunar low-gravity environments. While existing approaches are largely confined to single hops on flat terrain and lack real hardware validation, this study proposes a dual-timescale hybrid internal model control method that integrates short-horizon vertical dynamics modeling with long-horizon horizontal motion prediction, enabling stable continuous hopping using only proprioceptive sensing. Validation is performed on the MATRIX mixed-reality testbed, which combines pulley-based gravity offloading, real-time Unreal Engine rendering, and a motion platform to create a digital-twin-driven hardware-in-the-loop system. Experiments on simulated lunar crater terrain demonstrate the method’s stability and environmental adaptability under lunar gravity conditions.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

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.

Problem

• low-gravity locomotion
• quadrupedal jumping
• continuous pronking
• lunar terrain
• hardware-in-the-loop validation

Innovation

• Dual-Horizon Hybrid Internal Model
• low-gravity locomotion
• hardware-in-the-loop validation
• quadrupedal jumping
• proprioceptive sensing