Differential Flatness in Quadcopters

Previous post explains Differential Flatness for Nonlinear Systems. In this post, let's look at differential flatness in quadcopters.

The earliest references to differential flatness I came across are by Michel Fliess, Jean Lévine, Philippe Martin, Pierre Rouchon.

Differential Flatness References
  • Fliess, Michel, Jean Lévine, Philippe Martin, and Pierre Rouchon. "On differentially flat nonlinear systems." In Nonlinear Control Systems Design 1992, pp. 159-163. Pergamon, 1993.
  • Pomet, J. B., C. H. Moog, and E. Aranda. "A non-exact Brunovsky form and dynamic feedback linearization." In [1992] Proceedings of the 31st IEEE Conference on Decision and Control, pp. 2012-2017. IEEE, 1992.
  • Fliess, Michel, Jean Lévine, Philippe Martin, and Pierre Rouchon. "Flatness and defect of non-linear systems: introductory theory and examples." International journal of control 61, no. 6 (1995): 1327-1361.
  • van Nieuwstadt, Michiel, Muruhan Rathinam, and Richard M. Murray. "Differential flatness and absolute equivalence." In Proceedings of 1994 33rd IEEE Conference on Decision and Control, vol. 1, pp. 326-332. IEEE, 1994.
  • Murray, Richard M., Muruhan Rathinam, and Willem Sluis. "Differential flatness of mechanical control systems: A catalog of prototype systems." In ASME international mechanical engineering congress and exposition. 1995.

I might have digressed a bit, but I hope you got the idea of using differential flatness for planning. The two earlier examples are a bit abstract; let's look at a more tangible example next, differential flatness in quadrotors and how the states are computed from the flat variables.