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We consider the synthesis of motion primitives with a primary focus on how to efficiently generate robust motion plans that fulfill internal and external constraints while achieving high-level temporal logic specifications.
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Using sampling based motion planning, we will devise reachable phase-space volumes where we can search trajectories in the reduced task spaces with guarantees of internal and external constraints. Once we have found admissible trajectories, we will linearize the dynamics along them, e.g. via Linear Quadratic Regulators, and compute robust regions of attraction. Our efforts will then be targeted towards employing differential dynamic logic to model the previous motion primitives with safety specifications. It is through this formalization that we will be able to connect motion primitives to high-level mission specifications. Indeed, by using model satisfiability modulo theory checkers we will search for paths of complex motion primitives that satisfy our global mission specifications with robustness and high agility.
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Robot learning from demonstration (LfD) explores techniques for learning a task policy from examples provided by a human teacher. Our proposed work with respect to LfD algorithms will be based on preliminary work that leverages the goal-oriented nature of human teachers by learning an action model and a goal model simultaneously from the same set of demonstrations. We will develop algorithms to use the high-level skill objective represented in the temporal model and express this as constraints for the planning framework (i.e., the LTL, STL approaches described previously). We will use the learned model to generate the sequence of desired keyframe poses, and leverage our motion planning framework to plan the best path between them. We will develop new algorithms for adaptive sampling to efficiently and safely perform this sampling-based exploration, providing verification and guarantees during the process.