  In this paper, we present a mesh-based approach to analyze stability and
robustness of the policies obtained via deep reinforcement learning for various
biped gaits of a five-link planar model. Intuitively, one would expect that
including perturbations and/or other types of noise during training would
likely result in more robustness of the resulting control policy. However, one
would also like to have a quantitative and computationally-efficient means of
evaluating the degree to which this might be so. Rather than relying on Monte
Carlo simulations, which can become quite computationally burdensome in
quantifying performance metrics, our goal is to provide more sophisticated
tools to assess robustness properties of such policies. Our work is motivated
by the twin hypotheses that contraction of dynamics, when achievable, can
simplify the required complexity of a control policy and that control policies
obtained via deep learning may therefore exhibit tendency to contract to
lower-dimensional manifolds within the full state space, as a result. The
tractability of our mesh-based tools in this work provides some evidence that
this may be so.
