Collision-free navigation is a critical issue in robotic systems as the environment is often dynamic and uncertain. This paper investigates a data-stream-driven motion control problem for mobile robots to avoid randomly moving obstacles when the probability distribution of the obstacle’s movement is partially observable through data and can be even time-varying. A data-stream-driven ambiguity set is firstly constructed from movement data by leveraging a Dirichlet process mixture model and is updated online using real-time data. Then we propose an Online-Learning-based Distributionally Robust Nonlinear Model Predictive Control (OL-DR-NMPC) approach for limiting the risk of collision through considering the worst-case distribution within the ambiguity set. To facilitate solving the OL-DR-NMPC problem, we reformulate it as a finite-dimensional nonlinear optimization problem. To cope with the bilinear matrix inequality constraints in the nonlinear problem, we develop a parabolic relaxation and a sequential algorithm, by which the problem is further transformed into polynomial-time solvable surrogates. The simulations using a quadrotor model are employed to demonstrate the effectiveness and advantages of the proposed method.

The hydrogen-based multimicrogrid (HMMG) has emerged as a game changer for energy transition. However, it encounters new challenges in tackling uncertainty data streams stemming from intermittent renewable energy and load. This article presents a multiple-time-scale HMMG energy management framework. In the day-ahead stage, the optimal scheduling is determined. The deviations of day-ahead predictions are redressed by intraday rescheduling. To accommodate the uncertainty data streams, a novel data-stream-driven distributionally robust model predictive control is proposed for the HMMG real-time operation. Specifically, a Dirichlet process mixture model is leveraged to construct an online-updated ambiguity set, which adequately characterizes the multimodality and local moment information of uncertainties. Based upon this ambiguity set, the data-stream-driven distributionally robust model predictive control enhances the real-time tracking performance of energy storage references. Its salient feature is the capability of greatly reducing conservatism while ensuring probabilistic operational constraints even under time-varying uncertainty distributions. Since this real-time operation is an intractable infinite-dimensional optimization problem, a novel constraint-tightening technique is proposed to address the computational challenge. Case studies demonstrate that the proposed approach offers advantages over state-of-the-art methods in out-of-sample performance.