ANYmal solved a Rubik's Cube with its feet. Hello ... pedipulation?

Here's what the ANYmal-D quadruped's Rubik's Cube solve reveals about pedipulation: the hard part was not the cube. It was the full perception-planning-execution loop with no external aids, no fixed camera, and no second chance if a foot slip corrupted an early layer. 

Solving a 3x3x3 cube requires a precise sequence of steps where one error propagates through every move that follows. The ETH Zurich and NVIDIA researchers built a test case for whether a walking robot can perform multi-step dexterous manipulation using only the contact surfaces it already has.

Apparently, the answer is yes.

The paper, titled "Solving a Giant Rubik's Cube", was submitted to arXiv on October 17 by ETH Zurich's Legged Robotics group and NVIDIA researchers including Mayank Mittal.

The cube and the robot

The researchers did not use a standard Rubik's Cube.

The cube they used is a bit bigger: 0.4 meters on each edge. It weighs 4.6 kilograms, and was placed freestanding on flat ground. T

he oversized scale is, of course, deliberate: a standard-size cube is too small for foot-based manipulation. At 0.4 meters, each face is large enough for a foot to make reliable contact and apply torque, while still requiring precise alignment. 

The robot was an ANYmal-D, a legged platform developed at ETH Zurich, operating with no additional end-effectors: just four legs, four feet, onboard compute, and an onboard RGB-D camera.

Scan, plan, solve

The solve ran in 3 phases. 

1. In the scan phase, the robot walked a 270-degree arc around the cube and performs 1 controlled flip, building a complete color map of all 6 faces using its onboard RGB-D pipeline.
2. In the plan phase, an off-the-shelf Rubik's Cube solver processed the color map and generated a move sequence, which is converted into robot-executable pedipulation primitives.
3. Finally, in the solve phase, the robot executed 4 types of foot moves: flip backward, flip forward, rotate counterclockwise, and a pin-and-turn where 1 foot holds the lower layers stable while the other rotates the upper 2 layers independently.

Each complete solve requires approximately 30 pedipulation and repositioning steps and takes 8 to 9 minutes, and the robot demonstrated 3 autonomous hardware solves. 

Fairly impressive for a robot with no hands!

How the policies were trained

The pedipulation skills were trained with reinforcement learning using privileged training observations during learning, then distilled into policies that use only onboard depth perception and proprioception at deployment. 

Privileged training gave the policy access to ground-truth state information it cannot have on hardware, such as exact cube pose and face color from every angle, which accelerates learning. 

Distillation transfers the learned behavior into a deployable policy that works with the limited sensing available on the physical robot.

The policies are designed to be robust to variations in cube placement and to recover from external disturbances mid-solve. This is meaningful because the real world is messy: multi-step manipulation with a physical object in the real world involves slip, drift, and contact uncertainty that simulation cannot fully model. 

The distillation approach is one way to bridge that gap without requiring exhaustive hardware data collection.

Why pedipulation matters

Most legged robots are designed for locomotion, with any manipulation capability added via a separate arm mounted on the body. That architecture adds weight, power consumption, and mechanical complexity. 

Pedipulation is the alternative hypothesis: that a sufficiently capable RL-trained locomotion system can extend its contact surfaces into manipulation tasks without dedicated end-effectors.

Prior work in pedipulation addressed simpler tasks: pushing objects, making contact with buttons, performing coarse manipulation. The Rubik's Cube result is the most complex multi-step sequential manipulation task demonstrated with foot contact alone. 

The practical application is not Rubik's Cube solving, of course. 

It is an answer -- in the affirmative -- to the question of whether quadruped and humanoid robots can use their locomotion hardware for manipulation without adding a separate arm. A humanoid with capable hands and feet has more manipulation options than one that relies exclusively on its hands.

Sources

• arXiv — Solving a Giant Rubik's Cube with a Quadruped Robot
• ETH Zurich — Rubik's cube skills project page
• IEEE Spectrum — Video Friday feature