Multi-phase trajectory optimization for an aerial-aquatic vehicle considering the influence of navigation error

The environment-induced multi-phase trajectory optimization problem is studied in this paper, and the underwater target tracking task is focused on. The task is finished by an aerial-aquatic coaxial eight-rotor vehicle and is divided into two phases, i.e., the diving phase and the underwater navigation phase. The dynamic model and constraints on angular velocity of rotor in each phase are established to understand the motion characteristic. Then the model of navigation information and terrain matching are contained in the trajectory optimization model to reflect the influence of underwater navigation error on the quality of trajectory. Correspondingly, the forms of collision detection and cost function are changed to adapt to the inaccurate navigation information. To obtain the trajectory with the minimum terminal position error, an improved teach & learn-based optimization (ITLBO) algorithm is developed to strengthen the influence of individual historical optimal solution. Besides, Chebyshev collocation points are applied to determine the locations of control variables. Simulation results demonstrate that the established navigation error-based trajectory optimization model can reflect the real situation of multi-phase task. Especially, it is able to calculate the collision probability between the vehicle and the obstacle when GPS is unavailable underwater, thus ensuring the safety of underwater navigation. Compare to other common effective algorithms, the proposed ITLBO algorithm is in general more suitable for solving this problem because it is swarm-based and can obtain good solution without worrying about the inappropriate values of user-defined parameters.