References¶
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.
Francesco Bullo and Andrew D. Lewis. Geometric Control of Mechanical Systems. Springer, 2004.
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.
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.
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.
Jean Lévine. Analysis and Control of Nonlinear Systems: A Flatness-based Approach. Springer, 2009.
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.
Richard M. Murray, Zexiang Li, and S. Shankar Sastry. A Mathematical Introduction to Robotic Manipulation. CRC Press, 2017.
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.
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.