罚函数凸优化迭代算法及在无人机路径规划中的应用  

Penalty function convex optimization iterative algorithm and its application in UAV path planning

作　　者：胡锟 张亮[1] Hu Kun;Zhang Liang(School of Science,Wuhan University of Technology,Wuhan 430070,China)

机构地区：[1]武汉理工大学理学院,武汉430070

出　　处：《计算机应用研究》2021年第3期725-728,共4页Application Research of Computers

基　　金：国家自然科学基金面上项目(61573012)。

摘　　要：针对无人机路径规划问题,建立了具有定常非线性系统、非仿射等式约束、非凸不等式约束的非凸控制问题模型,并对该模型进行了算法设计和求解。基于迭代寻优的求解思路,提出了凸优化迭代求解方法和罚函数优化策略。前者利用凹凸过程(CCCP)和泰勒公式对模型进行凸化处理,后者将经处理项作为惩罚项施加到目标函数中以解决初始点可行性限制。经证明该方法严格收敛到原问题的Karush-Kuhn-Tucker(KKT)点。仿真实验验证了罚函数凸优化迭代算法的可行性和优越性,表明该算法能够为无人机规划出一条满足条件的飞行路径。This paper established a non-convex control model consists of time-invariant nonlinear system,non-affine equality constraint and non-convex inequality constrain aiming at the path planning problem of unmanned aerial vehicle,along with an algorithm designed for solving the aforementioned model.Based on iterative optimization,it proposed the convex optimization iteration method and penalty function optimization strategy.The former used the concave-convex process(CCCP)and Taylor formula to convexity the model,while the latter added the processed term to the objective function as a penalty term to solve the feasibility limit of the initial point.It is proved that the proposed method strictly converges to a Karush-Kuhn-Tucker(KKT)point of the original problem.Simulation experimental results verify the feasibility and superiority of the penalty function convex optimization iteration algorithm,and it indicates that the proposed algorithm can provide a flight path satisfying the conditions for the unmanned aerial vehicle.

关 键 词：无人机 路径规划 线性化 凸优化 迭代 罚函数 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]