Autonomous
robots that seek to work together with human co-workers must adopt
representations that span the hierarchy from the quantitative sensorimotor
signals to more qualitative task specifications. Despite significant recent
activity around methods for learning hierarchical representations, e.g., in
computer vision, the problem of defining and learning action-oriented symbols remains
somewhat open.
Motivated
in this way, we address the problem of trajectory
classification. We present a sampling-based approach that achieves this in
general configuration spaces relying only on the availability of collision-free
samples. Unlike previous sampling-based approaches in robotics, which use
graphs to capture information about the path-connectedness of a configuration
space, we construct a multiscale approximation of neighborhoods of the
collision free configurations based on filtrations of simplicial complexes. Our
approach thereby extracts additional homological information, which is
essential for a topological trajectory classification of sets of trajectories
starting and ending in two fixed points. Using a cone construction, we then
further generalize this approach to classify sets of trajectories even when
start and end points are allowed to vary in a path-connected subset. We furthermore
show how an augmented filtration of simplicial complexes based on an arbitrary
function on the configuration space, such as a costmap, can be defined to
incorporate additional constraints. We evaluate this in up to 6-dim configuration
spaces, in simulation as well as real world experiments with the Baxter and PR2
robots.
We
view this work as a step towards a broader family of algorithms that maintain
beliefs and plan actions in a multiscale fashion. I will conclude my talk with
a discussion on this, in the process giving a high level outline of some
related algorithms from our recent work addressing interactive decision making,
including one based on a stochastic game-theoretic formulation of the problem
of learning to interact with other agents without prior coordination.