This cube-shaped robot can balance with only a single reaction wheel

The development has the potential for application in space.


Underactuated robotics is an area of growing interest in robotics. While presenting many advantages in application, the loss of actuators also brings about great challenges to the control of underactuated systems.

In many cases, the degrees of freedom that are actuated indirectly are stable. More challenging and arguably more interesting systems arise when these degrees of freedom are unstable.

Almost ten years ago, robotic researchers led by ETH professor Raffaello D’Andrea made a splash with Cubli, a cube-shaped robot that can jump up and balance on its pivot. As reaction wheels (mounted on three faces of the cube) spin at high speeds, a brake can be applied to make the robot jump up and move around. Each wheel’s torque is adjusted to make it balance or achieve a controlled fall in any arbitrary direction. All these abilities can be combined to make the robot ‘walk.’

Now, Cubli has received a major simplification to create the One-Wheel Cubli, which only requires a single reaction wheel – as the name implies – for its balancing act.

Like its predecessor, One-Wheel Cubli has the reaction wheel mounted inside the housing. Instead of additional wheels, it is equipped with a balancing pole. When the wheel is accelerated by the electric motor, a reaction torque acts on the housing that is used to stabilize the system.

The system is carefully designed in such a way that the inertia in one direction is higher than in the other direction by attaching two masses far away from the center. As a result, the system moves faster in the direction with the lower inertia and slower in the direction with the higher inertia. This allows the One-Wheel Cubli to stabilize both directions simultaneously with only a single reaction wheel, researchers explain.

The One-Wheel Cubli has two main degrees of freedom, tilting front to back or side to side. In addition, the engineers say that even if the One-Wheel Cubli is disturbed, it can recover and reliably balance on its pivot.

Now, the team is working on further improving the system and also investigating its potential application in the attitude control of satellites. Additionally, the inverted pendulum system represents a simple yet challenging testbed for research and education in the field of control.

Journal reference:

  1. Matthias Hofer, Michael Muehlebach, Raffaello D’Andrea. The One-Wheel Cubli: A 3D inverted pendulum that can balance with a single reaction wheel. Mechatronics, 2023; DOI: 10.1016/j.mechatronics.2023.102965


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