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

Levin Müller; Oliver Fischer; Marco Trentini; Yusuke Tanaka; Marco Hutter

cs.ROOct 21, 2026

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

Authors: Levin Müller, Oliver Fischer, Marco Trentini, Yusuke Tanaka, Marco Hutter

Organizations: ETH Zurich, Robotics Systems Lab; Leonhardstrasse 21, 8092 Zurich, Switzerland.

Abstract

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.

Figures & tables

Fig. 1 : The Magnecko robot mid-flight under gravity offloading during hardware deployment of the jumping controller.

Fig. 2 : Illustration of the five-stage control scheme used during training and its transition logic. The control policy does not observe the current stage.

Category	Parameter	Value
Command Sampling	Jump distance $d$	$\mathcal{U}(0,5)\,\mathrm{m}$
	Heading $\phi$	$\mathcal{U}(-45^{\circ},45^{\circ})$
	Launch elevation $\vartheta$	$\geq 45^{\circ}$
	Launch speed	$\leq 3\,\mathrm{m/s}$
	Apex height $z_{A}$	$\geq 0.8\,\mathrm{m}$
Terrain	Flat terrain friction	$\mu_{s}=\mu_{d}=1.0$

TABLE I : Simulation and training parameters.

Transition	Condition	Param.	Value
STANCE $\to$ LAUNCH	$(s{=}0)\wedge(t_{ep}\!\geq\!\tilde{t}_{\mathrm{pre}})$	$\tilde{t}_{\mathrm{pre}}$	$2\,$ s
LAUNCH $\to$ FLIGHT	$(s{=}1)\wedge(h\!\geq\!\tilde{h}_{LF})$	$\tilde{h}_{LF}$	$0.75\,$ m
FLIGHT $\to$ LANDING	$(s{=}2)\wedge(h\!\leq\!\tilde{h}_{FL})$	$\tilde{h}_{FL}$	$0.75\,$ m
LANDING $\to$ RECOVERY	$(s{=}3)\wedge(b_{TD})$	$\tilde{t}_{\mathrm{rec}}$	$2\,$ s

TABLE II : Stage transition conditions and parameters.

b_{TD}

is set once at least three feet are simultaneously in contact after takeoff.

Term	Expression	Stage (weight)	Parameters
Task rewards & penalties
Start Base Pos.	$e^{-(e/\sigma)^{2}},\hskip 8.50012pte=\lVert\bm{p}_{B,xy}-\bm{p}^{\mathrm{init}}_{B,xy}\rVert$	STA $0.5$	$\sigma{=}0.2$
Start Base Head.	$e^{-(e/\sigma)^{2}},\hskip 8.50012pte=\bar{\psi}_{B}-\bar{\psi}^{\mathrm{init}}_{B}$	STA $0.5$	$\sigma{=}0.7$
Launch Speed	$\gamma_{t}\,\big(\lambda~r_{\mathrm{speed}}(\sigma_{1})+(1-\lambda)~r_{\mathrm{speed}}(\sigma_{2})\big)$ , ( 5 ) ( 8 )	LAU $25.0$	$\lambda=0.5,\sigma_{1}=0.6,\sigma_{2}=0.08$
Launch Direction	$\gamma_{t}\,\big(\lambda~r_{\mathrm{dir}}(\sigma_{1})+(1-\lambda)~r_{dir}(\sigma_{2})\big)$ , ( 6 ) ( 8 )	LAU $15.0$	$\lambda=0.3,\sigma_{1}=0.35,\sigma_{2}=0.06$
Bad Launch	$\mathbb{I}\{c_{NL}\lor c_{BL}\}$ ( 10 ) ( 9 )	LAU $-10.0$	$\tilde{\delta}_{v,mag}=$ 0.15\text{,}\mathrm{m}\text{/}\mathrm{s} $, $\tilde{\delta}_{v,dir}=$15\text{\,}\mathrm{\SIUnitSymbolDegree}$

TABLE III : Reward terms, expressions, active stages with weights, and parameters. Stages: STA = STANCE, LAU = LAUNCH, FLI = FLIGHT, LAN = LANDING, REC = RECOVERY; “ALL” denotes a term active in every stage. The LAUNCH task rewards

r_{\mathrm{speed}}

and

r_{\mathrm{dir}}

, modulated by the temporal kernel

\gamma_{t}

, are defined in ( 5 )–( 8 ).

Fig. 3 : Landing accuracies corresponding to $10{,}000$ commands covering the full command workspace. Top: Flat Terrain. Bottom: Sloped Terrain.

Fig. 4 : Mid-air recovery behavior of the controller.

Failure duration	Flat Crashes	Sloped Crashes
$0.0\text{\,}\mathrm{s}$ (nominal)	7.5%	11.9%
$0.2\text{\,}\mathrm{s}$	7.8%	12.5%
$0.5\text{\,}\mathrm{s}$	11.3%	15.6%
$1.0\text{\,}\mathrm{s}$	16.7%	20.3%

TABLE IV : Failure rates under fixed-duration control freeze.

Fig. 5 : Simulated torque and power demands of the robot around takeoff; dashed line and black triangle mark takeoff time.

Fig. 6 : Sim-to-real joint value transfer. Left: per joint group torque distributions during the launch for simulation and hardware deployment. Right: total actuator input power demand during the launch for simulation and hardware deployment.

Fig. 7 : Example of the jumping sequence deployed on Magnecko .

Robotics

Robotics studies the design and control of machines that perceive, move, and act in physical environments.

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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

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