Dynamic Modeling of Bucket-Soil Interactions Using Koopman-DFL Lifting Linearization for Model Predictive Contouring Control of Autonomous Excavators

TL;DR

This paper introduces a Koopman-DFL lifting linearization method to model complex bucket-soil interactions in excavators, enabling convex optimization-based control for improved automation.

Contribution

It presents a novel data-driven lifting linearization approach for nonlinear soil dynamics, facilitating model predictive control of excavator buckets.

Findings

Enhanced linear modeling of nonlinear soil interactions

Improved control performance in simulation

Validation against soil dynamics simulator

Abstract

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.