  In robotics, ergodic control extends the tracking principle by specifying a
probability distribution over an area to cover instead of a trajectory to
track. The original problem is formulated as a spectral multiscale coverage
problem, typically requiring the spatial distribution to be decomposed as
Fourier series. This approach does not scale well to control problems requiring
exploration in search space of more than 2 dimensions. To address this issue,
we propose the use of tensor trains, a recent low-rank tensor decomposition
technique from the field of multilinear algebra. The proposed solution is
efficient, both computationally and storage-wise, hence making it suitable for
its online implementation in robotic systems. The approach is applied to a
peg-in-hole insertion task requiring full 6D end-effector poses, implemented
with a 7-axis Franka Emika Panda robot. In this experiment, ergodic exploration
allows the task to be achieved without requiring the use of force/torque
sensors.
