http://www.youtube.com/watch?v=pp89tTDxXuI[/video]
(Don’t miss the shock absorber blowing up in smoke at 1:34!)
Freaking AMAZING.Two of the most challenging problems tackled with quadrocopters so far are balancing an inverted pendulum and juggling balls. My colleagues at ETH Zurich’s Flying Machine Arena have now combined the two.
As part of his Master thesis Dario Brescianini, student at ETH Zurich’s Institute for Dynamic Systems and Control, has developed algorithms that allow quadrocopters to juggle an inverted pendulum. If you are not sure what that means (or how that is even possible), have a look at his video “Quadrocopter Pole Acrobatics”:
The Math
A quadrocopter with a plate for balancing the pole. The cross-shaped cut-outs are used for easy attachment to the vehicle and have no influence on the pendulum’s stability.
To achieve this feat, Dario and his supervisors Markus Hehn and Raffaello D’Andrea started with a 2D mathematical model. The goal of the model was to understand what motion a quadrocopter would need to perform to throw the pendulum. In other words, what is required for the pendulum to lift off from the quadrocopter and become airborne?
This first step allowed to determine (theoretical) feasibility. In addition, it showed the ideal trajectory in terms of positions, speeds, and angles the quadrocopter needed to follow to throw a pendulum. And it offered an insight into the throwing process, including identification of its key design parameters.
Reality Checks
The main goal of the next step was to determine how well the theoretic model described reality: How well does the thrown pendulum’s motion match the mathematical prediction? Does the pendulum really leave the quadrocopter at the pre-computed time? How does the pendulum behave while airborne? How well do assumptions for catching the pendulum (e.g., completely inelastic collisions, completely rigid pendulum, infinite friction between quadrocopter and pendulum when balancing) hold?
This second step involved multiple tests with the physical system, including throwing the pendulum by hand to study its aerodynamic properties and precisely timing the quadrocopters’ and pendulum’s motions during the maneuver.
Analyze, Experiment, Repeat
The shock absorber at the end of the pendulum is a balloon filled with flour and attached to a sliding metal cap with zip ties.
Armed with a good theoretical model and knowledge of its strengths and limitations, the researchers set out on a process of engineering the complete system of balancing, throwing, catching, and re-balancing the pendulum. This involved leveraging the theoretic insights on the problem’s key design parameters to adapt the physical system. For example, they equipped both quadrocopters with a 12cm plate that could hold the pendulum while balancing and developed shock absorbers to add at the pendulum’s tips.
This also involved bringing the insights gained from their initial and many subsequent experiments to bear on their overall system design. For example, a learning algorithm was added to account for model inaccuracies.
