  A lifting-linearization method based on the Koopman operator and Dual Faceted
Linearization is applied to the control of a robotic excavator. In excavation,
a bucket interacts with the surrounding soil in a highly nonlinear and complex
manner. Here, we propose to represent the nonlinear bucket-soil dynamics with a
set of linear state equations in a higher-dimensional space. The space of
independent state variables is augmented by adding variables associated with
nonlinear elements involved in the bucket-soil dynamics. These include
nonlinear resistive forces and moment acting on the bucket from the soil, and
the effective inertia of the bucket that varies as the soil is captured into
the bucket. Variables associated with these nonlinear resistive and inertia
elements are treated as additional state variables, and their time evolution is
represented as another set of linear differential equations. The lifted linear
dynamic model is then applied to Model Predictive Contouring Control, where a
cost functional is minimized as a convex optimization problem thanks to the
linear dynamics in the lifted space. The lifted linear model is tuned based on
a data-driven method by using a soil dynamics simulator. Simulation experiments
verify the effectiveness of the proposed lifting linearization compared to its
counterpart.
