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arXiv · 2302.11891

Sequential Hierarchical Least-Squares Programming for Prioritized Non-Linear Optimal Control

Kai Pfeiffer·Abderrahmane Kheddar
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Abstract

We present a sequential hierarchical least-squares programming solver with trust-region and hierarchical step-filter with application to prioritized discrete non-linear optimal control. It is based on a hierarchical step-filter which resolves each priority level of a non-linear hierarchical least-squares programming via a globally convergent sequential quadratic programming step-filter. Leveraging a condition on the trust-region or the filter initialization, our hierarchical step-filter maintains this global convergence property. The hierarchical least-squares programming sub-problems are solved via a sparse reduced Hessian based interior point method. It leverages an efficient implementation of the turnback algorithm for the computation of nullspace bases for banded matrices. We propose a nullspace trust region adaptation method embedded within the sub-problem solver towards a comprehensive hierarchical step-filter. We demonstrate the computational efficiency of the hierarchical solver on typical test functions like the Rosenbrock and Himmelblau's functions, inverse kinematics problems and prioritized discrete non-linear optimal control.

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Kai Pfeiffer, Abderrahmane Kheddar. 2024-02-01. Sequential Hierarchical Least-Squares Programming for Prioritized Non-Linear Optimal Control. https://doi.org/10.1080/10556788.2024.2307467

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