  This paper develops a method for robots to integrate stability into actively
seeking out informative measurements through coverage. We derive a controller
using hybrid systems theory that allows us to consider safe equilibrium
policies during active data collection. We show that our method is able to
maintain Lyapunov attractiveness while still actively seeking out data. Using
incremental sparse Gaussian processes, we define distributions which allow a
robot to actively seek out informative measurements. We illustrate our methods
for shape estimation using a cart double pendulum, dynamic model learning of a
hovering quadrotor, and generating galloping gaits starting from stationary
equilibrium by learning a dynamics model for the half-cheetah system from the
Roboschool environment.
