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Feedforward Controllers from Learned Dynamic Local Model Networks with Application to Excavator Assistance Functions

Leon Greiser, Ozan Demir, Benjamin Hartmann, Henrik Hose, Sebastian Trimpe

Abstract

Complicated first principles modelling and controller synthesis can be prohibitively slow and expensive for high-mix, low-volume products such as hydraulic excavators. Instead, in a data-driven approach, recorded trajectories from the real system can be used to train local model networks (LMNs), for which feedforward controllers are derived via feedback linearization. However, previous works required LMNs without zero dynamics for feedback linearization, which restricts the model structure and thus modelling capacity of LMNs. In this paper, we overcome this restriction by providing a criterion for when feedback linearization of LMNs with zero dynamics yields a valid controller. As a criterion we propose the bounded-input bounded-output stability of the resulting controller. In two additional contributions, we extend this approach to consider measured disturbance signals and multiple inputs and outputs. We illustrate the effectiveness of our contributions in a hydraulic excavator control application with hardware experiments. To this end, we train LMNs from recorded, noisy data and derive feedforward controllers used as part of a leveling assistance system on the excavator. In our experiments, incorporating disturbance signals and multiple inputs and outputs enhances tracking performance of the learned controller. A video of our experiments is available at https://youtu.be/lrrWBx2ASaE.

Feedforward Controllers from Learned Dynamic Local Model Networks with Application to Excavator Assistance Functions

Abstract

Complicated first principles modelling and controller synthesis can be prohibitively slow and expensive for high-mix, low-volume products such as hydraulic excavators. Instead, in a data-driven approach, recorded trajectories from the real system can be used to train local model networks (LMNs), for which feedforward controllers are derived via feedback linearization. However, previous works required LMNs without zero dynamics for feedback linearization, which restricts the model structure and thus modelling capacity of LMNs. In this paper, we overcome this restriction by providing a criterion for when feedback linearization of LMNs with zero dynamics yields a valid controller. As a criterion we propose the bounded-input bounded-output stability of the resulting controller. In two additional contributions, we extend this approach to consider measured disturbance signals and multiple inputs and outputs. We illustrate the effectiveness of our contributions in a hydraulic excavator control application with hardware experiments. To this end, we train LMNs from recorded, noisy data and derive feedforward controllers used as part of a leveling assistance system on the excavator. In our experiments, incorporating disturbance signals and multiple inputs and outputs enhances tracking performance of the learned controller. A video of our experiments is available at https://youtu.be/lrrWBx2ASaE.
Paper Structure (18 sections, 3 theorems, 37 equations, 3 figures, 2 tables)

This paper contains 18 sections, 3 theorems, 37 equations, 3 figures, 2 tables.

Table of Contents

  1. INTRODUCTION
  2. Related Work
  3. Feedback Linearization of Local Model Networks
  4. Data-driven Control for Hydraulic Excavators
  5. PRELIMINARIES
  6. Problem Setting
  7. Local Model Networks
  8. Feedback Linearization of Local Model Networks
  9. PERMISSIBILITY OF FEEDBACK LINEARIZATION
  10. Criterion for Existence of Zero Dynamics
  11. A Novel, Parameter Based Criterion
  12. DISTURBANCE COMPENSATION
  13. SYSTEMS WITH MULTIPLE INPUTS/OUTPUTS
  14. EXPERIMENTAL RESULTS
  15. CONCLUSIONS AND FUTURE WORKS
  16. ...and 3 more sections

Key Result

Lemma 1

Let Assumptions ass:relDeg1 and ass:sameSign hold. Consider the open-loop dynamics of the feedforward controller eq:invLmnStateSpace Its equilibrium $\bm{\hat{x}}_{0}=\bm{0}$ is if there exists a positive definite matrix $\bm{P}$ such that The proof of the lemma is given in Appendix apx:proofStability.

Figures (3)

  • Figure 1: Controller design for and block diagram of the trajectory tracking control on a hydraulic excavator jcb_sales_limited_jcb_2018, the overall system structure is similar to rabenstein_2022weigand_2021. This paper focuses on the controller design by learning local model networks (red) from data (green) and using feedback linearization to automatically derive feedforward velocity controllers (blue).
  • Figure 2: Desired (dark) and measured (light) velocity of the arm (blue), boom (green), and bucket (red) cylinders over the course of one evaluation cycle using the controller derived from the model \ref{['itm:siso']} including pressure information.
  • Figure 3: The hydraulic excavator (JCB Hydradig 110W) with controlled hydraulic cylinders and the reference tool center point trajectory tracked in our experiments (top). The configurations of the excavator at the corner points (1-4) of the trajectory are shown at the bottom.

Theorems & Definitions (8)

  • Definition 1
  • Lemma 1
  • Theorem 1
  • Remark 1
  • Lemma 2
  • proof
  • proof
  • proof