Stochastic Artificial Potentials for Online Safe Navigation
Stochastic Artificial Potentials for Online Safe Navigation
复制标题
在线安全导航的随机人工势
DOI：
10.1109/tac.2019.2927714
复制
发表时间：
2016
影响因子：
6.8
通讯作者：
Alejandro Ribeiro
中科院分区：
文献类型：
--
作者：
Santiago Paternain;Alejandro Ribeiro
考虑一个凸集，我们删除了任意数量的不相交凸集-障碍-和凸函数，其最小值是代理的目标。我们考虑的Rimon-Koditschek导航函数的梯度的本地和随机近似的吸引力的潜力是凸函数，代理是最小化。特别是，我们表明，如果估计提供给代理是无偏的，收敛到所需的位置，同时避免的障碍物是保证在相同的几何条件下，在确定性的情况下的概率1。定性地说，这些条件是目标函数的Hessian的最大和最小特征值之间的比率不是太大，并且障碍物不是太平坦或太接近期望的目的地。此外，我们表明，有偏估计收敛到一个点任意接近的目标是实现概率为1。假设的偏见的结果举行的动机是研究的梯度的Rimon-Koditschek导航功能的传感器模型，适合周围的障碍物的圆圈。数值算例探讨了这些理论结果的实用价值。
Consider a convex set of which we remove an arbitrary number of disjoints convex sets—the obstacles—and a convex function whose minimum is the agent's goal. We consider a local and stochastic approximation of the gradient of a Rimon–Koditschek navigation function where the attractive potential is the convex function that the agent is minimizing. In particular, we show that if the estimate available to the agent is unbiased, convergence to the desired location while avoiding the obstacles is guaranteed with probability one under the same geometrical conditions as in the deterministic case. Qualitatively these conditions are that the ratio between the maximum and minimum eigenvalue of the Hessian of the objective function is not too large and that the obstacles are not too flat or too close to the desired destination. Moreover, we show that for biased estimates convergence to a point arbitrarily close to the goal is achieved with probability one. The assumptions on the bias for the result to hold are motivated by the study of the estimate of the gradient of a Rimon–Koditschek navigation function for sensor models that fit circles around the obstacles. Numerical examples explore the practical value of these theoretical results.