A four-legged ANYmal-D robot has autonomously solved a giant Rubik’s Cube using only its feet, researchers at ETH Zurich and NVIDIA report. Across three completed solutions on physical hardware, each attempt required approximately 30 steps and eight to nine minutes.
The robot circles and flips the freestanding cube, using an onboard depth camera to identify its colored squares. A standard solver calculates the solution, while a separate planner translates it into repositioning, flips and layer turns. Camera updates between movements track the cube’s location; color recognition reached 100% indoors and 98.7% outdoors in the researchers’ tests.
The manipulation skills include 90-degree flips toward and away from the robot. For a counterclockwise turn, the right foot stabilizes the cube while the left rotates its upper two layers by a quarter turn; the clockwise skill mirrors this movement. Unintended rotation of the remaining layers must be prevented to preserve the solution.
Training used reinforcement learning in simulation, with virtual rewards for accurate foot placement, clean turns and balance. A teacher system with full access to the simulated environment trained a student controller relying on front-camera depth images and joint sensors. An assisting force initially steadied the cube, then was gradually withdrawn.
Tests challenged the skills on slippery floors, cobblestones and moss-covered paving, as well as through leg pulls, cube pushes and an obstructed flip. The robot recovered from disturbances, and its flipping skills also transferred to a small, lightweight box and a cylindrical container. The team says the work demonstrates how onboard perception and coordinated feet can enable extended physical tasks without additional arms or grippers.
