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Mathematical Problems in Engineering
Volume 2014, Article ID 464056, 8 pages
Research Article

Trajectory Evaluation of Rotor-Flying Robots Using Accurate Inverse Computation Based on Algorithm Differentiation

State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China

Received 26 March 2014; Revised 9 June 2014; Accepted 11 June 2014; Published 13 August 2014

Academic Editor: Fatih Yaman

Copyright © 2014 Yuqing He et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Autonomous maneuvering flight control of rotor-flying robots (RFR) is a challenging problem due to the highly complicated structure of its model and significant uncertainties regarding many aspects of the field. As a consequence, it is difficult in many cases to decide whether or not a flight maneuver trajectory is feasible. It is necessary to conduct an analysis of the flight maneuvering ability of an RFR prior to test flight. Our aim in this paper is to use a numerical method called algorithm differentiation (AD) to solve this problem. The basic idea is to compute the internal state (i.e., attitude angles and angular rates) and input profiles based on predetermined maneuvering trajectory information denoted by the outputs (i.e., positions and yaw angle) and their higher-order derivatives. For this purpose, we first present a model of the RFR system and show that it is flat. We then cast the procedure for obtaining the required state/input based on the desired outputs as a static optimization problem, which is solved using AD and a derivative based optimization algorithm. Finally, we test our proposed method using a flight maneuver trajectory to verify its performance.