  We present a framework for model-free batch localization and SLAM. We use
lifting functions to map a control-affine system into a high-dimensional space,
where both the process model and the measurement model are rendered bilinear.
During training, we solve a least-squares problem using groundtruth data to
compute the high-dimensional model matrices associated with the lifted system
purely from data. At inference time, we solve for the unknown robot trajectory
and landmarks through an optimization problem, where constraints are introduced
to keep the solution on the manifold of the lifting functions. The problem is
efficiently solved using a sequential quadratic program (SQP), where the
complexity of an SQP iteration scales linearly with the number of timesteps.
Our algorithms, called Reduced Constrained Koopman Linearization Localization
(RCKL-Loc) and Reduced Constrained Koopman Linearization SLAM (RCKL-SLAM), are
validated experimentally in simulation and on two datasets: one with an indoor
mobile robot equipped with a laser rangefinder that measures range to
cylindrical landmarks, and one on a golf cart equipped with RFID range sensors.
We compare RCKL-Loc and RCKL-SLAM with classic model-based nonlinear batch
estimation. While RCKL-Loc and RCKL-SLAM have similar performance compared to
their model-based counterparts, they outperform the model-based approaches when
the prior model is imperfect, showing the potential benefit of the proposed
data-driven technique.
