Ensemble Kalman Inversion for Constrained Nonlinear MPC: An ADMM-Splitting Approach
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arXiv
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| Format: | Preprint |
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2025
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| author | Khalil, Ahmed Safwat, Mohamed Bakolas, Efstathios |
| author_facet | Khalil, Ahmed Safwat, Mohamed Bakolas, Efstathios |
| contents | This work proposes a novel Alternating Direction Method of Multipliers (ADMM)-based Ensemble Kalman Inversion (EKI) algorithm for solving constrained nonlinear model predictive control (NMPC) problems. First, stage-wise nonlinear inequality constraints in the NMPC problem are embedded via an augmented Lagrangian with nonnegative slack variables. We then show that the resulting unconstrained augmented-Lagrangian primal subproblem admits a Bayesian interpretation: under independent Gaussian virtual observations, its minimizers coincide with MAP estimators, enabling solution via EKI. However, since the nonnegativity constraint on the slacks is a hard constraint not naturally encoded by a Gaussian model, our proposed algorithm yields a two-block ADMM scheme that alternates between (i) an inexact primal step that minimizes the augmented-Lagrangian objective (implemented via EKI rollouts), (ii) a nonnegativity projection for the slacks, and (iii) a dual ascent step. To balance exploration and convergence, an annealing schedule tempers sampling covariances while a penalty schedule increases constraint enforcement over outer iterations, encouraging global search early and precise constraint satisfaction later. We evaluate the proposed controller on a 6-DOF UR5e manipulation benchmark in MuJoCo, comparing it against DIAL-MPC (an iterative MPPI variant) as the arm traverses a cluttered tabletop environment. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_00559 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ensemble Kalman Inversion for Constrained Nonlinear MPC: An ADMM-Splitting Approach Khalil, Ahmed Safwat, Mohamed Bakolas, Efstathios Optimization and Control Systems and Control This work proposes a novel Alternating Direction Method of Multipliers (ADMM)-based Ensemble Kalman Inversion (EKI) algorithm for solving constrained nonlinear model predictive control (NMPC) problems. First, stage-wise nonlinear inequality constraints in the NMPC problem are embedded via an augmented Lagrangian with nonnegative slack variables. We then show that the resulting unconstrained augmented-Lagrangian primal subproblem admits a Bayesian interpretation: under independent Gaussian virtual observations, its minimizers coincide with MAP estimators, enabling solution via EKI. However, since the nonnegativity constraint on the slacks is a hard constraint not naturally encoded by a Gaussian model, our proposed algorithm yields a two-block ADMM scheme that alternates between (i) an inexact primal step that minimizes the augmented-Lagrangian objective (implemented via EKI rollouts), (ii) a nonnegativity projection for the slacks, and (iii) a dual ascent step. To balance exploration and convergence, an annealing schedule tempers sampling covariances while a penalty schedule increases constraint enforcement over outer iterations, encouraging global search early and precise constraint satisfaction later. We evaluate the proposed controller on a 6-DOF UR5e manipulation benchmark in MuJoCo, comparing it against DIAL-MPC (an iterative MPPI variant) as the arm traverses a cluttered tabletop environment. |
| title | Ensemble Kalman Inversion for Constrained Nonlinear MPC: An ADMM-Splitting Approach |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2510.00559 |