  Humans have internal models of robots (like their physical capabilities), the
world (like what will happen next), and their tasks (like a preferred goal).
However, human internal models are not always perfect: for example, it is easy
to underestimate a robot's inertia. Nevertheless, these models change and
improve over time as humans gather more experience. Interestingly, robot
actions influence what this experience is, and therefore influence how people's
internal models change. In this work we take a step towards enabling robots to
understand the influence they have, leverage it to better assist people, and
help human models more quickly align with reality. Our key idea is to model the
human's learning as a nonlinear dynamical system which evolves the human's
internal model given new observations. We formulate a novel optimization
problem to infer the human's learning dynamics from demonstrations that
naturally exhibit human learning. We then formalize how robots can influence
human learning by embedding the human's learning dynamics model into the robot
planning problem. Although our formulations provide concrete problem
statements, they are intractable to solve in full generality. We contribute an
approximation that sacrifices the complexity of the human internal models we
can represent, but enables robots to learn the nonlinear dynamics of these
internal models. We evaluate our inference and planning methods in a suite of
simulated environments and an in-person user study, where a 7DOF robotic arm
teaches participants to be better teleoperators. While influencing human
learning remains an open problem, our results demonstrate that this influence
is possible and can be helpful in real human-robot interaction.
