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We reduce the embedding problem for hypo SU (2) and SU (3)-structures to the embedding problem for hypo G 2 -structures into parallel Spin(7)-manifolds. The latter will be described in terms of gauge deformations. This description involves the intrinsic torsion of the initial G 2 -structure and allows us to prove that the evolution equations, for all of the above embedding problems, do not admit non-trivial longtime solutions.

This paper reports on the aims, the approach, and the results of the European project RACE. The project aim was to enhance the behavior of an autonomous robot by having the robot learn from conceptualized experiences of previous performance, based on initial models of the domain and its own actions in it. This paper introduces the general system architecture; it then sketches some results in detail regarding hybrid reasoning and planning used in RACE, and instances of learning from the experiences of real robot task execution. Enhancement of robot competence is operationalized in terms of performance quality and description length of the robot instructions, and such enhancement is shown to result from the RACE system.

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Planning with diverse knowledge, i.e., hybrid planning, is essential for robotic applications. However, powerful heuristics are needed to reason efficiently in the resulting large search spaces. HTN planning provides a means to reduce the search space; furthermore, meta-CSP search has shown promise in hybrid domains, both wrt. search and online plan adaptation. In this paper we combine the two approaches by implementing HTN-style task decomposition as a meta-constraint in a meta-CSP search, resulting in an HTN planner able to handle very rich domain knowledge. The planner produces partial-order plans and if several goal tasks are given, subtasks can be shared, leading to shorter plans. We demonstrate the straightforward integration of different kinds of knowledge for causal, temporal and resource knowledge as well as knowledge provided by an external path planner. The resulting online planner, CHIMP, is integrated in a plan-based robot control system and is demonstrated to physically guide a PR2 robot. 4