  This paper proposes a data-driven method for learning convergent control
policies from offline data using Contraction theory. Contraction theory enables
constructing a policy that makes the closed-loop system trajectories inherently
convergent towards a unique trajectory. At the technical level, identifying the
contraction metric, which is the distance metric with respect to which a
robot's trajectories exhibit contraction is often non-trivial. We propose to
jointly learn the control policy and its corresponding contraction metric while
enforcing contraction. To achieve this, we learn an implicit dynamics model of
the robotic system from an offline data set consisting of the robot's state and
input trajectories. Using this learned dynamics model, we propose a data
augmentation algorithm for learning contraction policies. We randomly generate
samples in the state-space and propagate them forward in time through the
learned dynamics model to generate auxiliary sample trajectories. We then learn
both the control policy and the contraction metric such that the distance
between the trajectories from the offline data set and our generated auxiliary
sample trajectories decreases over time. We evaluate the performance of our
proposed framework on simulated robotic goal-reaching tasks and demonstrate
that enforcing contraction results in faster convergence and greater robustness
of the learned policy.
