Abstract
This paper describes a novel algorithm for solving flight trajectory optimization problems subject to avoidance constraints of turbulent regions detected by an airborne Doppler lidar. The algorithm adopts a second-order cone programming (SOCP) relaxation of an original non-convex problem so as to obtain the estimate of global optimum, and subsequently applies a convex quadratic programming (CQP) based on the estimate. Moreover, by adopting a travel distance as the independent variable of the dynamics, the linearization of nonlinear state equations and the reduction of the number of constraints are achieved. The algorithm is well-suited to real-time applications due to its guaranteed convergence in polynomial computational time, and is expected to provide practically useful trajectories. Through some numerical simulations of the turbulence avoidance, the fast computational speed of the algorithm as well as the reasonableness of the calculated trajectories is demonstrated.
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