References

[1]

Tom M. Apostol. Calculus, Volume I: One-Variable Calculus, with an Introduction to Linear Algebra. Wiley, 2nd edition, 1967. General Leibniz rule for the $n$-th derivative of a product, §6.17.

[2]

Francesco Bullo and Andrew D. Lewis. Geometric Control of Mechanical Systems. Springer, 2004.

[3]

Michel Fliess, Jean Lévine, Philippe Martin, and Pierre Rouchon. Flatness and defect of non-linear systems: introductory theory and examples. International Journal of Control, 61(6):1327–1361, 1995.

[4]

Prasanth Kotaru, Guofan Wu, and Koushil Sreenath. Differential-flatness and control of quadrotor(s) with a payload suspended through flexible cable(s). In Indian Control Conference (ICC), 352–357. 2018.

[5]

Taeyoung Lee, Melvin Leok, and N. Harris McClamroch. Geometric tracking control of a quadrotor UAV on SE(3). In IEEE Conference on Decision and Control (CDC), 5420–5425. 2010.

[6]

Jean Lévine. Analysis and Control of Nonlinear Systems: A Flatness-based Approach. Springer, 2009.

[7]

Daniel Mellinger and Vijay Kumar. Minimum snap trajectory generation and control for quadrotors. IEEE International Conference on Robotics and Automation (ICRA), pages 2520–2525, 2011.

[8]

Richard M. Murray, Zexiang Li, and S. Shankar Sastry. A Mathematical Introduction to Robotic Manipulation. CRC Press, 2017.

[9]

Koushil Sreenath, Taeyoung Lee, and Vijay Kumar. Geometric control and differential flatness of a quadrotor UAV with a cable-suspended load. In IEEE Conference on Decision and Control (CDC), 2269–2274. 2013.

[10]

Koushil Sreenath, Nathan Michael, and Vijay Kumar. Trajectory generation and control of a quadrotor with a cable-suspended load — a differentially-flat hybrid system. In IEEE International Conference on Robotics and Automation (ICRA), 4888–4895. 2013.