论文标题
具有随机效应的最佳人类导航模型
A Model for Optimal Human Navigation with Stochastic Effects
论文作者
论文摘要
我们提出了一种使用控制理论公式和汉密尔顿 - 雅各比 - 贝尔曼方程的山区人体步行路径最佳路径规划的方法。以前的人类导航模型是完全确定性的，假设对环境高程数据和人类步行速度的完美知识是地形当地斜率的函数。我们的模型包括一个随机组件，可以说明问题中的不确定性，因此包括带有粘度的汉密尔顿 - 雅各比 - 贝尔曼方程。我们在存在和不存在随机效应的情况下讨论了该模型，并提出了模拟模型的数值方法。当问题存在不确定性时，我们讨论了最佳路径的两个不同概念。最后，我们比较模型在不同级别的不确定性水平上提出的最佳路径，并观察到，随着不确定性的大小趋于零（因此，方程式中的粘度趋于零），最佳路径倾向于确定性最佳路径。
We present a method for optimal path planning of human walking paths in mountainous terrain, using a control theoretic formulation and a Hamilton-Jacobi-Bellman equation. Previous models for human navigation were entirely deterministic, assuming perfect knowledge of the ambient elevation data and human walking velocity as a function of local slope of the terrain. Our model includes a stochastic component which can account for uncertainty in the problem, and thus includes a Hamilton-Jacobi-Bellman equation with viscosity. We discuss the model in the presence and absence of stochastic effects, and suggest numerical methods for simulating the model. We discuss two different notions of an optimal path when there is uncertainty in the problem. Finally, we compare the optimal paths suggested by the model at different levels of uncertainty, and observe that as the size of the uncertainty tends to zero (and thus the viscosity in the equation tends to zero), the optimal path tends toward the deterministic optimal path.
