论文标题
具有控制屏障功能的基于自适应抽样的运动计划
Adaptive Sampling-based Motion Planning with Control Barrier Functions
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
Sampling-based algorithms, such as Rapidly Exploring Random Trees (RRT) and its variants, have been used extensively for motion planning. Control barrier functions (CBFs) have been recently proposed to synthesize controllers for safety-critical systems. In this paper, we combine the effectiveness of RRT-based algorithms with the safety guarantees provided by CBFs in a method called CBF-RRT$^\ast$. CBFs are used for local trajectory planning for RRT$^\ast$, avoiding explicit collision checking of the extended paths. We prove that CBF-RRT$^\ast$ preserves the probabilistic completeness of RRT$^\ast$. Furthermore, in order to improve the sampling efficiency of the algorithm, we equip the algorithm with an adaptive sampling procedure, which is based on the cross-entropy method (CEM) for importance sampling (IS). The procedure exploits the tree of samples to focus the sampling in promising regions of the configuration space. We demonstrate the efficacy of the proposed algorithms through simulation examples.
