Sequential Hierarchical Least-Squares Programming for Prioritized Non-Linear Optimal Control
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909134254768128 |
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| author | Pfeiffer, Kai Kheddar, Abderrahmane |
| author_facet | Pfeiffer, Kai Kheddar, Abderrahmane |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_11891 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Sequential Hierarchical Least-Squares Programming for Prioritized Non-Linear Optimal Control Pfeiffer, Kai Kheddar, Abderrahmane Optimization and Control Numerical Analysis Robotics 90C29, 65F50, 49M15, 49M37, 90C55 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. |
| title | Sequential Hierarchical Least-Squares Programming for Prioritized Non-Linear Optimal Control |
| topic | Optimization and Control Numerical Analysis Robotics 90C29, 65F50, 49M15, 49M37, 90C55 |
| url | https://arxiv.org/abs/2302.11891 |