End-to-End Reinforcement Learning for Quadrupedal Jumping in Lunar Gravity

This paper presents reinforcement learning (RL) policies for dynamic quadrupedal locomotion in planetary exploration scenarios. Building on a taskoptimized quadruped with a 5-bar leg design, we develop RL policies for walking, vertical jumping, forward jumping, and in-flight attitude control, explicitly tailored to the reduced gravity on Mars. These policies jointly enable such robots to overcome obstacles larger than themselves through coordinated jumping and precise in-flight reorientation for safe landings. We demonstrate Sim2Real transfer of the attitude control policy on the Olympus quadruped through single-axis reorientation tests, while all locomotion policies are validated in simulation. A complete Mars exploration mission scenario demonstrates coordinated policy deployment across challenging terrain. Experimental results show 90° attitude reorientation in 2.6 seconds, with simulations demonstrating 3.1 meter vertical jumps and 3.9 meter forward jumps under Martian gravity conditions. - Supplementary video: https://www.youtube.com/watch?v=qlSJ3P87A4A

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.

Deploying legged robots in extra-terrestrial environments includes many challenges due to complex terrain interactions, energy, and thermal constraints. For effective mechanical design of a lunar exploration quadrupedal robot, careful consideration of motor torques, energy expenditure, and cost of transport is required. The lunar surface is composed of granular regolith, which impacts the locomotion of legged robots and their performance. Locomotion algorithms trained with rigid contact assumptions are also ineffective when applied to environments with soft contacts, such as granular surfaces, which can result in instability and poor tracking. In this report, the physical modelling of the granular lunar surface-robot foot contacts is applied to a simulation environment with locomotion trained using Reinforcement Learning. A comparison is conducted between the policy trained on rigid contact and soft contact environments, analysing the gait and locomotion performance metrics. The analysis demonstrates that soft contacts simulating regolith surfaces pose additional challenges for Reinforcement Learning based training, result in a qualitatively different gait, and increase the overall energy expenditure.