  This paper presents a supervised learning method to generate continuous
cost-to-go functions of non-holonomic systems directly from the workspace
description. Supervision from informative examples reduces training time and
improves network performance. The manifold representing the optimal
trajectories of a non-holonomic system has high-curvature regions which can not
be efficiently captured with uniform sampling. To address this challenge, we
present an adaptive sampling method which makes use of sampling-based planners
along with local, closed-form solutions to generate training samples. The
cost-to-go function over a specific workspace is represented as a neural
network whose weights are generated by a second, higher order network. The
networks are trained in an end-to-end fashion. In our previous work, this
architecture was shown to successfully learn to generate the cost-to-go
functions of holonomic systems using uniform sampling. In this work, we show
that uniform sampling fails for non-holonomic systems. However, with the
proposed adaptive sampling methodology, our network can generate near-optimal
trajectories for non-holonomic systems while avoiding obstacles. Experiments
show that our method is two orders of magnitude faster compared to traditional
approaches in cluttered environments.
