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

TL;DR

This paper introduces an adaptive, derivative-free trajectory optimization method for R2R manufacturing that improves constraint handling, convergence, and performance over existing gradient-based and sampling-based methods.

Contribution

It proposes a novel adaptive trajectory bundle method with automatic constraint management and convergence guarantees, tailored for precise control in R2R systems.

Findings

Achieves 4.3% lower tension RMSE than gradient-based MPC.

Improves velocity transient response by 11.1% over baseline TBM.

Demonstrates faster settling and less overshoot in experimental R2R system.

Abstract

Roll-to-roll (R2R) manufacturing requires precise tension and velocity control under operational constraints. Model predictive control demands gradient computation, while sampling-based methods like 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, replacing Taylor-series linearization with function-value interpolation. Adaptive trust region and penalty mechanisms automatically adjust based on constraint violation metrics, eliminating manual tuning. We establish convergence guarantees proving finite-time feasibility and convergence to stationary points of the constrained problem. Simulations on a six-zone R2R system demonstrate that the adaptive method achieves 4.3\% lower tension RMSE than gradient-based MPC and 11.1\% improvement over baseline TBM in velocity transients, with superior constraint satisfaction compared to MPPI variants. Experimental validation on an R2R dry transfer system confirms faster settling and reduced overshoot relative to LQR and non-adaptive TBM.