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Adaptive Trajectory Bundle Method for Roll-to-Roll Manufacturing Systems

Jiachen Li, Shihao Li, Christopher Martin, Wei Li, Dongmei Chen

TL;DR

<3-5 sentence high-level summary> The paper addresses constrained control in roll-to-roll manufacturing where maintaining tension and transport velocity under hard limits is essential. It introduces the Adaptive Trajectory Bundle Method (TBM), a derivative-free approach that uses interpolated trajectory bundles, multiple shooting, and a convex subproblem to enforce hard and soft constraints. Key contributions include a complete TBM formulation for R2R with asymmetric tension penalties, adaptive trust-region and penalty schemes that require minimal tuning, and convergence guarantees to feasible stationary points; simulations show competitive tension tracking with gradient-based MPC and superior constraint handling over MPPI. The approach offers a practical, scalable solution for industrial web handling where gradient information is unavailable or costly to obtain.

Abstract

Roll-to-roll (R2R) manufacturing demands precise tension and velocity control under strict operational constraints. Model predictive control requires gradient computation, while sampling-based methods such as MPPI struggle with hard constraint satisfaction. This paper presents an adaptive trajectory bundle method that achieves rigorous constraint handling through derivative-free sequential convex programming. The approach approximates nonlinear dynamics and costs via interpolated sample bundles, with adaptive trust regions and penalty parameters ensuring robust convergence without manual tuning. Simulations on a six-zone R2R system demonstrate tracking accuracy comparable to gradient-based MPC with superior constraint satisfaction over sampling-based alternatives.

Adaptive Trajectory Bundle Method for Roll-to-Roll Manufacturing Systems

TL;DR

<3-5 sentence high-level summary> The paper addresses constrained control in roll-to-roll manufacturing where maintaining tension and transport velocity under hard limits is essential. It introduces the Adaptive Trajectory Bundle Method (TBM), a derivative-free approach that uses interpolated trajectory bundles, multiple shooting, and a convex subproblem to enforce hard and soft constraints. Key contributions include a complete TBM formulation for R2R with asymmetric tension penalties, adaptive trust-region and penalty schemes that require minimal tuning, and convergence guarantees to feasible stationary points; simulations show competitive tension tracking with gradient-based MPC and superior constraint handling over MPPI. The approach offers a practical, scalable solution for industrial web handling where gradient information is unavailable or costly to obtain.

Abstract

Roll-to-roll (R2R) manufacturing demands precise tension and velocity control under strict operational constraints. Model predictive control requires gradient computation, while sampling-based methods such as MPPI struggle with hard constraint satisfaction. This paper presents an adaptive trajectory bundle method that achieves rigorous constraint handling through derivative-free sequential convex programming. The approach approximates nonlinear dynamics and costs via interpolated sample bundles, with adaptive trust regions and penalty parameters ensuring robust convergence without manual tuning. Simulations on a six-zone R2R system demonstrate tracking accuracy comparable to gradient-based MPC with superior constraint satisfaction over sampling-based alternatives.

Paper Structure

This paper contains 26 sections, 8 theorems, 32 equations, 4 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Contributions
  4. Roll-to-Roll System Dynamics
  5. Adaptive Trajectory Bundle Method: Theoretical Framework
  6. Notation and Preliminaries
  7. Derivative-Free Function Approximation via Bundles
  8. Bundle Interpolation
  9. Multiple-Shooting Trajectory Representation
  10. Constrained Bundle Subproblem
  11. Adaptive Mechanisms
  12. Constraint Violation Metrics
  13. Trust Region Adaptation
  14. Penalty Adaptation
  15. Convergence Analysis
  16. ...and 11 more sections

Key Result

Lemma 1

Under Assumptions ass:lipschitz and ass:bounded, the penalized objective $\phi_{\mu,\boldsymbol{\gamma}}$ is Lipschitz continuous on $\mathcal{L}(\mu, \boldsymbol{\gamma})$ with constant: where $R$ is the bound on cost residuals from Assumption ass:bounded.

Figures (4)

  • Figure 1: Flowchart of the Adaptive Trajectory Bundle Method.
  • Figure 2: Step tracking performance comparison.
  • Figure 3: Velocity change performance comparison.
  • Figure 4: Convergence comparison between TBM and Adaptive TBM.

Theorems & Definitions (24)

  • Remark 1: Relationship to Original TBM
  • Definition 1: Constraint Violation Metrics
  • Definition 2: Penalized Objective
  • Definition 3: Local Stationarity
  • Remark 2
  • Lemma 1: Lipschitz Constant
  • proof
  • Lemma 2: Penalty Stabilization
  • proof
  • Lemma 3: Bundle Approximation Accuracy
  • ...and 14 more