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

Anytime Point-Based Approximations for Large POMDPs

The Partially Observable Markov Decision Process has long been recognized as a rich framework for real-world planning and control problems, especially in robotics. However exact solutions in this framework are typically computationally intractable for all but the smallest problems. A well-known technique for speeding up POMDP solving involves performing value backups at specific belief points, rather than over the entire belief simplex. The efficiency of this approach, however, depends greatly on the selection of points. This paper presents a set of novel techniques for selecting informative belief points which work well in practice. The point selection procedure is combined with point-based value backups to form an effective anytime POMDP algorithm called Point-Based Value Iteration (PBVI). The first aim of this paper is to introduce this algorithm and present a theoretical analysis justifying the choice of belief selection technique. The second aim of this paper is to provide a thorough empirical comparison between PBVI and other state-of-the-art POMDP methods, in particular the Perseus algorithm, in an effort to highlight their similarities and differences. Evaluation is performed using both standard POMDP domains and realistic robotic tasks