64,650 research outputs found
Batch Informed Trees (BIT*): Sampling-based Optimal Planning via the Heuristically Guided Search of Implicit Random Geometric Graphs
In this paper, we present Batch Informed Trees (BIT*), a planning algorithm
based on unifying graph- and sampling-based planning techniques. By recognizing
that a set of samples describes an implicit random geometric graph (RGG), we
are able to combine the efficient ordered nature of graph-based techniques,
such as A*, with the anytime scalability of sampling-based algorithms, such as
Rapidly-exploring Random Trees (RRT).
BIT* uses a heuristic to efficiently search a series of increasingly dense
implicit RGGs while reusing previous information. It can be viewed as an
extension of incremental graph-search techniques, such as Lifelong Planning A*
(LPA*), to continuous problem domains as well as a generalization of existing
sampling-based optimal planners. It is shown that it is probabilistically
complete and asymptotically optimal.
We demonstrate the utility of BIT* on simulated random worlds in
and and manipulation problems on CMU's HERB, a
14-DOF two-armed robot. On these problems, BIT* finds better solutions faster
than RRT, RRT*, Informed RRT*, and Fast Marching Trees (FMT*) with faster
anytime convergence towards the optimum, especially in high dimensions.Comment: 8 Pages. 6 Figures. Video available at
http://www.youtube.com/watch?v=TQIoCC48gp
Recognizing Partial Cubes in Quadratic Time
We show how to test whether a graph with n vertices and m edges is a partial
cube, and if so how to find a distance-preserving embedding of the graph into a
hypercube, in the near-optimal time bound O(n^2), improving previous O(nm)-time
solutions.Comment: 25 pages, five figures. This version significantly expands previous
versions, including a new report on an implementation of the algorithm and
experiments with i
Real-time Planning as Decision-making Under Uncertainty
In real-time planning, an agent must select the next action to take within a fixed time bound.
Many popular real-time heuristic search methods approach this by expanding nodes using time-limited A* and selecting the action leading toward the frontier node with the lowest f value. In this thesis, we reconsider real-time planning as a problem of decision-making under uncertainty. We treat heuristic values as uncertain evidence and we explore several backup methods for aggregating this evidence. We then propose a novel lookahead strategy that expands nodes to minimize risk, the expected regret in case a non-optimal action is chosen. We evaluate these methods in a simple synthetic benchmark and the sliding tile puzzle and find that they outperform previous methods. This work illustrates how uncertainty can arise even when solving deterministic planning problems, due to the inherent ignorance of time-limited search algorithms about those portions of the state space that they have not computed, and how an agent can benefit from explicitly meta-reasoning about this uncertainty
Covering Partial Cubes with Zones
A partial cube is a graph having an isometric embedding in a hypercube.
Partial cubes are characterized by a natural equivalence relation on the edges,
whose classes are called zones. The number of zones determines the minimal
dimension of a hypercube in which the graph can be embedded. We consider the
problem of covering the vertices of a partial cube with the minimum number of
zones. The problem admits several special cases, among which are the problem of
covering the cells of a line arrangement with a minimum number of lines, and
the problem of finding a minimum-size fibre in a bipartite poset. For several
such special cases, we give upper and lower bounds on the minimum size of a
covering by zones. We also consider the computational complexity of those
problems, and establish some hardness results
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