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We propose a diffusion approximation method to the continuous-state Markov decision processes that can be utilized to address autonomous navigation and control in unstructured off-road environments. In contrast to most decision-theoretic planning frameworks that assume fully known state transition models, we design a method that eliminates such a strong assumption that is often extremely difficult to engineer in reality. We first take the second-order Taylor expansion of the value function. The Bellman optimality equation is then approximated by a partial differential equation, which only relies on the first and second moments of the transition model. By combining the kernel representation of the value function, we design an efficient policy iteration algorithm whose policy evaluation step can be represented as a linear system of equations characterized by a finite set of supporting states. We first validate the proposed method through extensive simulations in 2 D obstacle avoidance and 2.5 D terrain navigation problems. The results show that the proposed approach leads to a much superior performance over several baselines. We then develop a system that integrates our decision-making framework with onboard perception and conduct real-world experiments in both cluttered indoor and unstructured outdoor environments. The results from the physical systems further demonstrate the applicability of our method in challenging real-world environments.

Arid ecosystems are known to be sensitive to climate change. The Jornada Basin in the USA, as one representative of arid land, has suffered from land degradation in recent decades. In order to disentangle the climate–vegetation feedback, we analyzed the vegetation dynamics under the effects of climate change via a mathematical model based on the reaction–diffusion mechanism. Using this model, we conducted a sensitive analysis of climate factors and concluded that the ecosystem might experience a catastrophic shift with the climatic deterioration. We considered the non-local interaction term to explain the competition among plants. Additionally, the PLR (power law range) metric was used to quantify the extent of the degradation and to compare the results of the vegetation patterns from the remote sensing data and the simulations. From the results, this model could simulate the trends of land degradation in this area. We found that the land degradation could be mainly attributed to climate changes in recent years. This approach suggests that vegetation patterns can provide hints as to whether the ecosystem is approaching desertification. These results can help with mapping vulnerable arid areas around the world through model simulation and satellite images.

Metal–organic frameworks (MOFs) have played a crucial role in recent advancements in developing lithium‐based battery electrolytes, electrodes, and separators. Although many MOF‐based battery components rely on their well‐defined porosity and controllable functionality, they also boast a myriad of other significant properties relevant to battery applications. In this mini‐review, the distinct advantages of MOFs in battery applications are discussed, including using MOFs to 1) scavenge impurities to increase cycling stability, 2) widen the operation temperature range of conventional electrolytes, 3) widen the operation voltage range of common electrolytes, and 4) employ as artificial solid‐electrolyte interphases to prevent lithium dendrite growth. Furthermore, subsisting challenges of developing these emerging MOF‐based battery technologies are discussed and guidance for shaping the future of this field is given.