Optimal Control Problem Based On Convex Programming Algorithm And Its Application In Trajectory Planning Model

The main task of trajectory planning is to plan a flight path for the aircraft from the launch point to the target point in the planning space,satisfying various constraints,and therefore make a certain performance index reach the optimal or nearly optimal flight path.The quality of the planned trajectory and the speed of the planning work directly affects the flight mission,thus the study of the trajectory planning algorithm is important in application.This thesis studies the application of the convex optimization algorithm in the trajectory planning problem of unmanned aerial vehicle(UAV).The main works are as follows:Aiming at the problem of UAV obstacle avoidance trajectory planning in no-fly threatened areas,the threat is regarded as a cylindrical obstacle,and it is only considered to bypass from the side instead of flying from the top.Since the UAV obstacle avoidance trajectory planning problem is mathematically a nonlinear optimal control problem with non-convex constraints,a non-convex control problem model consists of time-invariant nonlinear system,non-affine equality constraint and non-convex inequality constrain is established,along with an algorithm designed for solving the aforementioned model.First of all,based on iterative optimization solution,a convex optimization iterative solution method is proposed,the non-convex inequality constraint function in the model is converted to the sum of the convex function and the concave function through the concave-convex process(CCCP).The Taylor function is used to convert the obtained concave function and nonlinear equality constraint function into linear functions,therefore obtained a convex optimization model that is easy to solve and suitable for the CVX toolbox.The convergence analysis of the obtained convex optimization model proves that the convex optimization process converges strictly to a Karush-Kuhn-Tucker(KKT)point of the original problem.Secondly,in order to solve the situation that the infeasible initial solution cannot be converged due to the linearization process of Taylor formula where the second-order term rejection of constraint function,especially the equation constraint function,a penalty function optimization strategy is proposed.The processing item of the convex optimization process is applied as a penalty term to the objective function,by imposing penalties on infeasible iteration points.The iteration points are forced to approach the feasible region,thereby it can reduce the initial point feasibility limit.The convergence analysis of the resulting penalty function optimization model proves that the convergence point of the penalty function optimization process converges to a KKT point of the original problem.Finally,a penalty function convex optimization iterative algorithm is proposed,a UAV obstacle avoidance trajectory planning model is established and the feasibility and superiority of the proposed algorithm are verified through simulation experiments.Through the two-dimensional and three-dimensional simulation experiments in a complex environment,it is verified that the proposed algorithm can converge on an obstacle-avoiding flight path that meets the requirements.Compared with genetic algorithm,ant colony algorithm,and dynamic programming algorithm,the results show that the proposed algorithm has a shorter planning path length,and the planned flight path is smoother and more stable.