 
Summary: The Center for Control, Dynamical Systems, and Computation
University of California at Santa Barbara
Winter 2010 Seminar Series
Presents
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 samplingbased motion planning algorithms such as Rapidlyexploring
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 RRTlike planning and control algorithm that performed
flawlessly throughout the 60mile 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 suboptimal 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
