基于蒙特卡洛法的小型无人机飞行轨迹控制方法

Flight trajectory control method of small UAV based on Monte Carlo method

摘要:

小型无人机在复杂低空环境受障碍物随机分布和风速扰动不确定影响,而传统确定性模型难以量化动态风险场,使得候选轨迹易陷局部最优,不利于无人机状态、环境模型和控制策略实时更新,导致实际飞行与候选轨迹出现偏差。因此,提出基于蒙特卡洛法的小型无人机飞行轨迹控制方法研究。构建环境风险场模型(障碍物位置子模型与风速扰动子模型),通过状态向量概率密度函数初始化实现动态风险的量化表征。基于马尔科夫链蒙特卡洛方法生成候选轨迹,通过动态调节采样密度策略平衡探索效率与计算成本,构建符合动力学约束的轨迹解集。引入贝叶斯优化框架,利用高斯过程代理模型与蒙特卡洛积分评估轨迹综合代价,实现多目标优化下的最优轨迹筛选。结合滑动窗口优化技术、卡尔曼滤波与蒙特卡洛方法,对无人机状态、环境模型和控制策略进行实时更新,应对不确定性因素的变化,从而实现小型无人机飞行轨迹的有效控制。实验结果显示:设计方法应用后生成的四旋翼小型无人机候选轨迹与实际候选轨迹趋于一致,确定的四旋翼小型无人机最优轨迹与实际最优轨迹相同,控制扰动方差与期望代价最小值分别为0.2与10。

Abstract:

Small unmanned aerial vehicles are affected by the random distribution of obstacles and uncertain wind speed disturbances in complex low altitude environments. Traditional deterministic models are difficult to quantify dynamic risk fields, making candidate trajectories prone to local optima, which is not conducive to real-time updates of drone status, environmental models, and control strategies, resulting in deviations between actual flight and candidate trajectories. Therefore, a research on small unmanned aerial vehicle flight trajectory control method based on Monte Carlo method is proposed. Construct an environmental risk field model (obstacle position sub model and wind speed disturbance sub model), and achieve quantitative representation of dynamic risks through initialization of state vector probability density function. Generate candidate trajectories based on Markov chain Monte Carlo method, balance exploration efficiency and computational cost by dynamically adjusting sampling density strategy, and construct trajectory solution set that conforms to dynamic constraints. Introducing Bayesian optimization framework, utilizing Gaussian process surrogate model and Monte Carlo integration to evaluate the comprehensive cost of trajectory, achieving optimal trajectory screening under multi-objective optimization. By combining sliding window optimization technology, Kalman filtering, and Monte Carlo methods, real-time updates are made to the state, environmental model, and control strategy of unmanned aerial vehicles to cope with changes in uncertain factors, thereby achieving effective control of the flight trajectory of small unmanned aerial vehicles. The experimental results show that the candidate trajectories generated by the application of the design method for quadcopter small unmanned aerial vehicles tend to be consistent with the actual candidate trajectories, and the determined optimal trajectory for quadcopter small unmanned aerial vehicles is the same as the actual optimal trajectory. The minimum values of control disturbance variance and expected cost are 0.2 and 10, respectively.