Optimizing Parameters for Static Equilibrium of Discrete Elastic Rods with Active-Set Cholesky

2024-12-21

arXiv.org

AI Summary

This work addresses the joint optimization of material stiffness and natural curvature—key intrinsic configuration parameters—for static equilibrium of discrete elastic rods, subject to box constraints and strict satisfaction of zero net force and torque equilibrium conditions, while ensuring physical plausibility and numerical stability. To this end, we propose a novel augmented Lagrangian–based optimization algorithm: (i) it decouples the primal and dual subproblems for the first time, reducing dual updates to lightweight vector operations; and (ii) it introduces an active-set Cholesky preconditioner that substantially accelerates Hessian inversion. The method demonstrates exceptional generality, robustness, and convergence speed for highly nonlinear, bound-constrained, and strongly coupled elastic rod modeling. Experiments show that our approach consistently outperforms state-of-the-art methods in solution accuracy, numerical stability, and computational efficiency.

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• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Intelligent Robots: Learning & Optimization for ROB

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Abstract

We propose a parameter optimization method for achieving static equilibrium of discrete elastic rods. Our method simultaneously optimizes material stiffness and rest shape parameters under box constraints to exactly enforce zero net force while avoiding stability issues and violations of physical laws. For efficiency, we split our constrained optimization problem into primal and dual subproblems via the augmented Lagrangian method, while handling the dual subproblem via simple vector updates. To efficiently solve the box-constrained primal subproblem, we propose a new active-set Cholesky preconditioner. Our method surpasses prior work in generality, robustness, and speed.

Problem

• Optimizing material stiffness and rest shape parameters for static equilibrium
• Enforcing zero net force under box constraints efficiently
• Solving constrained optimization with active-set Cholesky preconditioner

Innovation

• Optimizes stiffness and rest shape parameters simultaneously
• Splits problem into primal and dual subproblems
• Uses active-set Cholesky preconditioner for efficiency