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Prolonged operations close to small solar system bodies require a sophisticated control logic to minimize propellant mass and maximize operational efficiency. A control logic based on Discrete Mechanics and Optimal Control (DMOC) is proposed and applied to both conventionally propelled and solar sail spacecraft operating at an arbitrarily shaped asteroid in the class of Itokawa. As an example, stand-off inertial hovering is considered, recently identified as a challenging part of the Marco Polo mission. The approach is easily extended to stand-off orbits. We show that DMOC is applicable to spacecraft control at small objects, in particular with regard to the fact that the changes in gravity are exploited by the algorithm to optimally control the spacecraft position. Furthermore, we provide some remarks on promising developments.
Unravelling the factors determining the allocation of carbon to various plant organs is one of the great challenges of modern plant biology. Studying allocation under close to natural conditions requires non-invasive methods, which are now becoming available for measuring plants on a par with those developed for humans. By combining magnetic resonance imaging (MRI) and positron emission tomography (PET), we investigated three contrasting root/shoot systems growing in sand or soil, with respect to their structures, transport routes and the translocation dynamics of recently fixed photoassimilates labelled with the short-lived radioactive carbon isotope 11C. Storage organs of sugar beet (Beta vulgaris) and radish plants (Raphanus sativus) were assessed using MRI, providing images of the internal structures of the organs with high spatial resolution, and while species-specific transport sectoralities, properties of assimilate allocation and unloading characteristics were measured using PET. Growth and carbon allocation within complex root systems were monitored in maize plants (Zea mays), and the results may be used to identify factors affecting root growth in natural substrates or in competition with roots of other plants. MRI–PET co-registration opens the door for non-invasive analysis of plant structures and transport processes that may change in response to genomic, developmental or environmental challenges. It is our aim to make the methods applicable for quantitative analyses of plant traits in phenotyping as well as in understanding the dynamics of key processes that are essential to plant performance.