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Unmanned aerial–aquatic vehicles are a new type of aircraft that can navigate in air and underwater. An unmanned aerial–aquatic rotorcraft (UAAR) is introduced to complete the task of navigating between air and underwater, and the trajectory optimization problem for this task is focused on in this study. The dynamics of a four-axle rotorcraft with eight rotors operating in air and underwater is described. On this basis, the trajectory optimization model is established, wherein the constraints on control variables and states in different media are included. The optimization index is denoted as the weighted sum of the terminal states. In view of the weakness of the teaching- and learning-based optimization (TLBO) algorithm, the formula for updating the individual grade in the teaching process is modified. Thus, this ensures that the algorithm avoids converging at the local optimum and improves the solution quality. Finally, an improved TLBO (ITLBO)-based trajectory optimization method for UAAR navigating between air and water is developed. The control variables are discretized with respect to height at a set of Chebyshev collocation points to reduce the terminal error of states, and the values of control variables at other heights are obtained via interpolation. In the simulation studies, the ITLBO-based method exhibits better performance in terms of optimizing the index when compared to the other two algorithms. Furthermore, the effects of the distribution and number of collocation points on the results are analyzed.

Trajectory optimization of an unmanned aerial–aquatic rotorcraft navigating between air and water