  This paper develops KL-Ergodic Exploration from Equilibrium
($\text{KL-E}^3$), a method for robotic systems to integrate stability into
actively generating informative measurements through ergodic exploration.
Ergodic exploration enables robotic systems to indirectly sample from
informative spatial distributions globally, avoiding local optima, and without
the need to evaluate the derivatives of the distribution against the robot
dynamics. Using hybrid systems theory, we derive a controller that allows a
robot to exploit equilibrium policies (i.e., policies that solve a task) while
allowing the robot to explore and generate informative data using an ergodic
measure that can extend to high-dimensional states. We show that our method is
able to maintain Lyapunov attractiveness with respect to the equilibrium task
while actively generating data for learning tasks such, as Bayesian
optimization, model learning, and off-policy reinforcement learning. In each
example, we show that our proposed method is capable of generating an
informative distribution of data while synthesizing smooth control signals. We
illustrate these examples using simulated systems and provide simplification of
our method for real-time online learning in robotic systems.
