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Alexander Shkolnik- Sample-Based Motion Planning for High-Dimensional and Differentially-Constrained Systems
State of the art sample-based path planning algorithms, such as the Rapidly-exploring Randomized Tree (RRT), have proven to be effective in path planning for systems subject to complex kinematic and geometric constraints. The performance of these algorithms, however, degrade as the dimension of the system increases. Furthermore, sample-based planners rely on distance metrics which do not work well when the system has differential constraints. Such constraints are particularly challenging in systems with non-holonomic and underactuated dynamics. This thesis develops two intelligent sampling strategies to help guide the search process. To reduce sensitivity to dimension, sampling can be done in a low-dimensional task space rather than in the high-dimensional state space. Altering the sampling strategy in this way creates a Voronoi Bias in task space, which helps to guide the search, while the RRT continues to verify trajectory feasibility in the full state space. Fast path planning is demonstrated using this approach on a 1500-link manipulator. To enable task-space-biasing for underactuated systems, a hierarchical task space controller is developed by utilizing partial feedback linearization. Another sampling strategy is also presented, where the local reachability of the tree is approximated, and used to bias the search, for systems subject to differential constraints. Reachability-guidance is shown to improve search performance of the RRT by an order of magnitude when planning on a pendulum and non-holonomic car. The ideas of task-space-biasing and reachability-guidance are then combined for demonstration of a motion planning algorithm implemented on LittleDog, a quadruped robot. The motion planning algorithm successfully planned bounding trajectories over extremely rough terrain.