254 research outputs found
Bayesian Active Edge Evaluation on Expensive Graphs
Robots operate in environments with varying implicit structure. For instance,
a helicopter flying over terrain encounters a very different arrangement of
obstacles than a robotic arm manipulating objects on a cluttered table top.
State-of-the-art motion planning systems do not exploit this structure, thereby
expending valuable planning effort searching for implausible solutions. We are
interested in planning algorithms that actively infer the underlying structure
of the valid configuration space during planning in order to find solutions
with minimal effort. Consider the problem of evaluating edges on a graph to
quickly discover collision-free paths. Evaluating edges is expensive, both for
robots with complex geometries like robot arms, and for robots with limited
onboard computation like UAVs. Until now, this challenge has been addressed via
laziness i.e. deferring edge evaluation until absolutely necessary, with the
hope that edges turn out to be valid. However, all edges are not alike in value
- some have a lot of potentially good paths flowing through them, and some
others encode the likelihood of neighbouring edges being valid. This leads to
our key insight - instead of passive laziness, we can actively choose edges
that reduce the uncertainty about the validity of paths. We show that this is
equivalent to the Bayesian active learning paradigm of decision region
determination (DRD). However, the DRD problem is not only combinatorially hard,
but also requires explicit enumeration of all possible worlds. We propose a
novel framework that combines two DRD algorithms, DIRECT and BISECT, to
overcome both issues. We show that our approach outperforms several
state-of-the-art algorithms on a spectrum of planning problems for mobile
robots, manipulators and autonomous helicopters
Efficient motion planning for problems lacking optimal substructure
We consider the motion-planning problem of planning a collision-free path of
a robot in the presence of risk zones. The robot is allowed to travel in these
zones but is penalized in a super-linear fashion for consecutive accumulative
time spent there. We suggest a natural cost function that balances path length
and risk-exposure time. Specifically, we consider the discrete setting where we
are given a graph, or a roadmap, and we wish to compute the minimal-cost path
under this cost function. Interestingly, paths defined using our cost function
do not have an optimal substructure. Namely, subpaths of an optimal path are
not necessarily optimal. Thus, the Bellman condition is not satisfied and
standard graph-search algorithms such as Dijkstra cannot be used. We present a
path-finding algorithm, which can be seen as a natural generalization of
Dijkstra's algorithm. Our algorithm runs in time, where~ and are the number of vertices and
edges of the graph, respectively, and is the number of intersections
between edges and the boundary of the risk zone. We present simulations on
robotic platforms demonstrating both the natural paths produced by our cost
function and the computational efficiency of our algorithm
Shared Autonomy via Hindsight Optimization
In shared autonomy, user input and robot autonomy are combined to control a
robot to achieve a goal. Often, the robot does not know a priori which goal the
user wants to achieve, and must both predict the user's intended goal, and
assist in achieving that goal. We formulate the problem of shared autonomy as a
Partially Observable Markov Decision Process with uncertainty over the user's
goal. We utilize maximum entropy inverse optimal control to estimate a
distribution over the user's goal based on the history of inputs. Ideally, the
robot assists the user by solving for an action which minimizes the expected
cost-to-go for the (unknown) goal. As solving the POMDP to select the optimal
action is intractable, we use hindsight optimization to approximate the
solution. In a user study, we compare our method to a standard
predict-then-blend approach. We find that our method enables users to
accomplish tasks more quickly while utilizing less input. However, when asked
to rate each system, users were mixed in their assessment, citing a tradeoff
between maintaining control authority and accomplishing tasks quickly
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
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