ETH Zurich Quadruped Solves a Giant Rubik's Cube With Its Feet
A quadruped robot from ETH Zurich's Robotic Systems Lab has solved a giant Rubik's Cube with its feet alone, without an arm or a gripper. The machine is ANYmal-D, the cube measures 0.4 m along each edge and weighs 4.6 kg, and the team reports three autonomous solves on hardware, each about thirty steps and between eight and nine minutes long.
The slowness is the substance of the result rather than a footnote. A layer turn needs one foot pinning the bottom layer while the other rotates the upper two, and an unintended quarter turn corrupts the cube state the planner has been working from, so every step has to land cleanly enough for the next one to stay valid. The system is deliberate because the task punishes anything else.
Nothing in the perception stack is specialised to cubes beyond a single text prompt. A ZED X Mini camera feeds SAM 3, which segments the cube from the words "rubik's cube" with no fine tuning, and the masked depth then gives a first pose that iterative closest point fitting refines. And a silhouette gate rejects any fit whose intersection over union with the segmentation mask falls below 0.90, which keeps a plausible looking pose out of the state estimate.
Colours are classified in CIE-LAB space by a nearest neighbour model trained on 5819 hand labelled facelet patches, and the uniquely coloured centre facelets resolve the cube's twenty four rotational symmetries. Out to 2 m the pipeline holds a median position error of about 2 cm and a median rotation error below 3 degrees. Facelet classification reached 100 per cent indoors and 98.7 per cent outdoors, and the whole pipeline runs on an NVIDIA Jetson AGX Orin carried by the robot.
The robot first walks a 270 degree arc around the cube, flips it once to expose the sixth face, and passes the assembled cube net to Kociemba's solver, whose face turns are then compiled into skills the body can actually perform. Repositioning moves it along a 90 degree arc, flip forward and flip backward tip the cube away from and toward the robot, and rotate anticlockwise turns the upper two layers while the right front foot pins the base. Clockwise rotation was never trained separately; it is the anticlockwise policy mirrored about the sagittal plane at inference.
Training ran in Isaac Lab, where a teacher policy with privileged sight of the cube state and contact forces was distilled into a student that sees only what the robot sees. But the student receives 45 proprioceptive values and two depth images from the front RealSense cameras at 30 by 53 pixels and 10 Hz, and it outputs joint position targets at 50 Hz. A wrench assisted curriculum held the cube steady early in training and faded as success improved, while randomisation covered placement, masses, layer friction, and external pushes.
Recovery is the part that reads as engineering rather than as demonstration. The skills kept working from misaligned starts, on a low friction floor, on cobblestones, and on mossy cobblestones, and they reached again after a leg was pulled with a rope or the cube was shoved away with a stick. A heavy box blocking a flip drew two or three further attempts before the robot either finished the flip or settled back into a stable stance, and the authors note that recovery is limited once the policy has committed to the press.
The same flips were also run on a small light box and on a cylindrical container. Those were flips rather than solves, and the paper reports no solved puzzle beyond the three Rubik's Cube runs.
The commercial relevance sits with machines that already walk into plants and substations without a manipulator. Unitree's B2 and DEEP Robotics' X20 are both advertised for industrial and power inspection, and neither product page presents a fitted arm as standard equipment. And the authors point in that direction themselves, suggesting a robot could steady a toolbox while closing its lid, or brace a collapsible crate while folding its sides, with one foot stabilising the object while the other moves the part.
Three solves is a small sample. The preprint states that all three attempted solves completed without human intervention, and it gives no success rate beyond that, no comparison of completion time against an arm based system, and no indication of how the approach holds up on heavier or less cooperative objects. The work is a preprint, posted to arXiv, and it has not been through peer review.
ETH Zurich's ANYmal-D solved a 0.4 m, 4.6 kg Rubik's Cube using only its feet, three times, at about thirty steps and eight to nine minutes per solve.
Perception runs onboard on a Jetson AGX Orin, with median pose error of about 2 cm and below 3 degrees out to 2 m, and 98.7 per cent facelet accuracy outdoors.
Four skills carry the solve, and clockwise rotation is the anticlockwise policy mirrored at inference rather than trained.
The team reports no failed attempts across the three solves, and the work has not been peer reviewed.
Source: arXiv
