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About: This dissertation focuses on motion planning algorithms for hybrid dynamical systems, which feature continuous (flow) and discrete (jump) state variables. Recognizing the limited research in this area compared to pure continuous-time or discrete-time systems, this work introduces novel, provably correct, and efficient methodologies.

Initially, the thesis establishes a foundational theory for motion planning for hybrid systems, using a hybrid equation framework to encapsulate most hybrid systems' dynamics. This includes formalizing and theoretically validating essential operations like propagation, reversal, concatenation, and truncation, which are crucial for motion planning algorithms. A general algorithm template for bidirectional propagation, termed HyRRT, is proposed, illustrating how these operations coalesce to address motion planning challenges. The work progresses by implementing a rapidly-exploring random trees (RRT) approach within this framework. Named HyRRT, this method extends a search tree through a random selection of state samples and propagation (either flow or jump), ensuring probabilistic completeness under mild conditions. Additionally, a bidirectional version, HyRRT-Connect, enhances search efficiency by connecting forward and backward paths in hybrid time, thereby speeding up the solution finding. Further innovations include the stable sparse RRT (SST) algorithm, HySST, which optimizes motion planning by selecting vertices with minimal cost from a neighborhood around a random sample and pruning suboptimal vertices. This approach is shown to be asymptotically near-optimal.

The contributions of this dissertation extend beyond specific algorithms. It proposes a new motion planning problem for hybrid systems and provides a theoretical toolkit that enables researchers to design their solutions with completeness guarantees. This positions hybrid dynamical systems as a general modeling tool for complex motion planning tasks, supporting efficient problem-solving with minimal modeling effort.

Event Host: Nan Wang, Ph.D Candidate, Computer Engineering

Advisor: Ricardo Sanfelice

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Zoom: https://ucsc.zoom.us/j/3051852364?pwd=UFl5eWJNeWJjZ0txWEs2b05RSkp4dz09
Meeting ID: 305 185 2364
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