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The Center for Control, Dynamical Systems, and Computation University of California at Santa Barbara

Summary: The Center for Control, Dynamical Systems, and Computation
University of California at Santa Barbara
Winter 2010 Seminar Series
Incremental Sampling Algorithms for Motion Planning:
Asymptotic Optimality and Complex Tasks
Emilio Frazzoli - MIT
Friday, February 19, 2010, 3:00 4:00pm CHEM 1171
Abstract: During the last decade, incremental sampling-based motion planning algorithms such as Rapidly-exploring
Random Trees (RRTs) have been widely used for robotic applications. For example, the MIT entry to the 2007 DARPA Ur-
ban Challenge, which finished the competition in 4th place, used an RRT-like planning and control algorithm that performed
flawlessly throughout the 60-mile race. While very effective, both in theory and in practice, at finding feasible paths for a
dynamical systems through a complicated environment, RRTs have a number of limitations, among which (i) no character-
ization of the "quality" of the solution provided, and (ii) no ability to deal with tasks other than reaching a point while avoid-
ing obstacles. The subject of the talk will be recent advances in the above directions. First, a negative result is given: it is
proven that the cost of the best path in a RRT converges almost surely to a sub-optimal value, as the number of samples
n increases. Based on the insight gained through the proof of this result, a new algorithm, called RRT* is proposed, which
provably yields paths whose cost converges almost surely to the optimum. The computational overhead of RRT* is shown to
be O (log n) with respect to the standard algorithm. Finally, we consider the problem of computing plans that satisfy a class
of temporal logic specifications, describing, e.g., rules of the road or mission objectives. The proposed algorithms, general-


Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara


Collections: Mathematics