SUMMARYQuadrotors are unmanned aerial vehicles with many potential applications ranging from mapping to supporting rescue operations. A key feature required for the use of these vehicles under complex conditions is a technique to analytically solve the problem of trajectory planning. Hence, this paper presents a heuristic approach for optimal path planning that the optimization strategy is based on the indirect solution of the open-loop optimal control problem. Firstly, an adequate dynamic system modeling is considered with respect to a configuration of a commercial quadrotor helicopter. The model predicts the effect of the thrust and torques induced by the four propellers on the quadrotor motion. Quadcopter dynamics is described by differential equations that have been derived by using the Newton–Euler method. Then, a path planning algorithm is developed to find the optimal trajectories that meet various objective functions, such as fuel efficiency, and guarantee the flight stability and high-speed operation. Typically, the necessary condition of optimality for a constrained optimal control problem is formulated as a standard form of a two-point boundary-value problem using Pontryagin’s minimum principle. One advantage of the proposed method can solve a wide range of optimal maneuvers for arbitrary initial and final states relevant to every considered cost function. In order to verify the effectiveness of the presented algorithm, several simulation and experiment studies are carried out for finding the optimal path between two points with different objective functions by using MATLAB software. The results clearly show the effect of the proposed approach on the quadrotor systems.

中文翻译：

---

各种目标函数的四旋翼系统轨迹规划

摘要四旋翼飞行器是一种无人驾驶飞行器，具有从测绘到支持救援行动的许多潜在应用。在复杂条件下使用这些车辆所需的一个关键特征是分析解决轨迹规划问题的技术。因此，本文提出了一种基于开环最优控制问题的间接解的最优路径规划的启发式方法。首先，针对商用四旋翼直升机的配置考虑了充分的动态系统建模。该模型预测了四个螺旋桨引起的推力和扭矩对四旋翼运动的影响。Quadcopter 动力学由使用 Newton-Euler 方法导出的微分方程描述。然后，开发了路径规划算法，以找到满足燃油效率等各种目标函数的最优轨迹，并保证飞行稳定性和高速运行。通常，约束最优控制问题的最优必要条件被表述为使用 Pontryagin 最小原理的两点边值问题的标准形式。所提出的方法的一个优点可以解决与每个考虑的成本函数相关的任意初始和最终状态的各种最佳操作。为了验证所提出算法的有效性，利用MATLAB软件进行了多次仿真和实验研究，以寻找具有不同目标函数的两点之间的最优路径。