Efficient Computation of Feedback Control for Equality-Constrained LQR

A method is presented for solving the discrete-time finite-horizon Linear Quadratic Regulator (LQR) problem subject to auxiliary linear equality constraints, such as fixed end-point constraints. The method explicitly determines an affine relationship between the control and state variables, as in st...

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Bibliographic Details
Published inProceedings - IEEE International Conference on Robotics and Automation pp. 6748 - 6754
Main Authors Laine, Forrest, Tomlin, Claire
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.05.2019
Subjects
Computational complexity
Dynamic programming
Feedback control
Optimal control
Robots
Trajectory optimization
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ISSN2577-087X
DOI10.1109/ICRA.2019.8793566

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Summary:A method is presented for solving the discrete-time finite-horizon Linear Quadratic Regulator (LQR) problem subject to auxiliary linear equality constraints, such as fixed end-point constraints. The method explicitly determines an affine relationship between the control and state variables, as in standard Riccati recursion, giving rise to feedback control policies that account for constraints. Since the linearly-constrained LQR problem arises commonly in robotic trajectory optimization, having a method that can efficiently compute these solutions is important. We demonstrate some of the useful properties and interpretations of said control policies, and we compare the computation time and complexity of our method against existing methods.
ISSN:2577-087X
DOI:10.1109/ICRA.2019.8793566