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A quadratic regulator-based heuristic for rapidly exploring state space

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dc.contributor.advisor Russ Tedrake. en_US
dc.contributor.author Glassman, Elena Leah en_US
dc.contributor.other Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science. en_US
dc.date.accessioned 2011-02-23T14:41:56Z
dc.date.available 2011-02-23T14:41:56Z
dc.date.copyright 2010 en_US
dc.date.issued 2010 en_US
dc.identifier.uri http://hdl.handle.net/1721.1/61286
dc.description Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010. en_US
dc.description Cataloged from PDF version of thesis. en_US
dc.description Includes bibliographical references (p. 53-55). en_US
dc.description.abstract Kinodynamic planning algorithms like Rapidly-Exploring Randomized Trees (RRTs) hold the promise of finding feasible trajectories for rich dynamical systems with complex, non-convex constraints. In practice, these algorithms perform very well on configuration space planning, but struggle to grow efficiently in systems with dynamics or differential constraints. This is due in part to the fact that the conventional proximity metric, Euclidean distance, does not take into account system dynamics and constraints when identifying which node in the existing tree is capable of producing children closest to a given point in state space. Here we argue that the RRTs' coverage of state space is maximized by using a proximity psuedometric proportional to the length, in time, of the quickest possible trajectory between two points in state space. We derive this minimum-time metric for the double integrator and show that an affine quadratic regulator (AQR) design can be used to approximate the exact minimum-time proximity pseudometric at a reasonable computational cost. We demonstrate improved exploration of the state spaces of the double integrator and simple pendulum when using this pseudometric within the RRT framework. However, for more complex nonlinear systems, experiments thus far suggest that the AQR-based proximity pseudometric and the conventional metric produce equivalent coverage of the state space, on average. This drop-off in benefit as system complexity and nonlinearity increase may be due to the linearization of system dynamics that is required to calculate the AQR-based pseudometric. Future work includes exploring methods for approximating the exact minimum-time proximity pseudometric that can reason about dynamics with higher-order terms. en_US
dc.description.statementofresponsibility by Elena Leah Glassman. en_US
dc.format.extent 55 p. en_US
dc.language.iso eng en_US
dc.publisher Massachusetts Institute of Technology en_US
dc.rights M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. en_US
dc.rights.uri http://dspace.mit.edu/handle/1721.1/7582 en_US
dc.subject Electrical Engineering and Computer Science. en_US
dc.title A quadratic regulator-based heuristic for rapidly exploring state space en_US
dc.type Thesis en_US
dc.description.degree M.Eng. en_US
dc.contributor.department Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science. en_US
dc.identifier.oclc 702639081 en_US


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