PolyMPC: An efficient and extensible tool for real‐time nonlinear model predictive tracking and path following for fast mechatronic systems

Listov, Petr; Jones, Colin N.

doi:10.1002/oca.2566

Cited by 14 publications

(8 citation statements)

References 20 publications

(24 reference statements)

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“…The numerical code for the simulation studies in this section was developed in C++ using a software package for nonlinear optimization and control PolyMPC . Throughout all experiments, the deterministic OCPs were discretized using the multi‐segment Chebyshev–Gauss–Lobatto (CGL) collocation scheme as described in Reference 18 with three segments and order of polynomial five for each segment. For the stochastic trajectory planning experiments, gPC expansion is performed using the Legendre basis with four terms.…”

Section: Trajectory Optimization Under Parametric Uncertaintiesmentioning

confidence: 99%

“…First, time invariant uncertainties are considered using a stochastic nonlinear OCP with gPC. Thereafter, the computational toolbox PolyMPC 18 is extended to transform stochastic OCPs with chance constraints into deterministic OCPs using gPC expansions. Using open loop predictions, especially for unstable systems, in the optimization algorithm leads to conservatism, which is demonstrated for an example problem of generating a vehicle trajectory respecting road boundaries.…”

Section: Introductionmentioning

confidence: 99%

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Stochastic optimal control for autonomous driving applications via polynomial chaos expansions

Listov,

Schwarz,

Jones

2023

Optim Control Appl Methods

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Model‐based methods in autonomous driving and advanced driving assistance gain importance in research and development due to their potential to contribute to higher road safety. Parameters of vehicle models, however, are hard to identify precisely or they can change quickly depending on the driving conditions. In this paper, we address the problem of safe trajectory planning under parametric model uncertainties motivated by automotive applications. We use the generalized polynomial chaos expansions for efficient nonlinear uncertainty propagation and distributionally robust inequalities for chance constraints approximation. Inspired by the tube‐based model predictive control, an ancillary feedback controller is used to control the deviations of stochastic modes from the nominal solution, and therefore, decrease the variance. Our approach allows reducing conservatism related to nonlinear uncertainty propagation while guaranteeing constraints satisfaction with a high probability. The performance is demonstrated on the example of a trajectory optimization problem for a simplified vehicle model with uncertain parameters.

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Section: Trajectory Optimization Under Parametric Uncertaintiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stochastic optimal control for autonomous driving applications via polynomial chaos expansions

Listov,

Schwarz,

Jones

2023

Optim Control Appl Methods

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“…The MPC problem can then be recursively solved using IPOPT with the warm-starting strategy from [57]. The main goal of this class is not to provide highly efficient numerical solvers aimed at embedded optimization, such as those implemented in the software packages acados [59] or PolyMPC [60]. Rather, this class provides a reliable controller that conveniently allows for offline closed-loop simulations.…”

Section: The Awebox Software Packagementioning

confidence: 99%

AWEbox: An Optimal Control Framework for Single- and Multi-Aircraft Airborne Wind Energy Systems

et al. 2023

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In this paper, we present AWEbox, a Python toolbox for modeling and optimal control of multi-aircraft systems for airborne wind energy (AWE). AWEbox provides an implementation of optimization-friendly multi-aircraft AWE dynamics for a wide range of system architectures and modeling options. It automatically formulates typical AWE optimal control problems based on these models, and finds a numerical solution in a reliable and efficient fashion. To obtain a high level of reliability and efficiency, the toolbox implements different homotopy methods for initial guess refinement. The first type of method produces a feasible initial guess from an analytic initial guess based on user-provided parameters. The second type implements a warm-start procedure for parametric sweeps. We investigate the software performance in two different case studies. In the first case study, we solve a single-aircraft reference problem for a large number of different initial guesses. The homotopy methods reduce the expected computation time by a factor of 1.7 and the peak computation time by a factor of eight, compared to when no homotopy is applied. Overall, the CPU timings are competitive with the timings reported in the literature. When the user initialization draws on expert a priori knowledge, homotopies do not increase expected performance, but the peak CPU time is still reduced by a factor of 5.5. In the second case study, a power curve for a dual-aircraft lift-mode AWE system is computed using the two different homotopy types for initial guess refinement. On average, the second homotopy type, which is tailored for parametric sweeps, outperforms the first type in terms of CPU time by a factor of three. In conclusion, AWEbox provides an open-source implementation of efficient and reliable optimal control methods that both control experts and non-expert AWE developers can benefit from.

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“…Local stability properties of such a scheme was further investigated in [8] while the corresponding opensource toolkit ACADO [15] provides a framework for direct optimal control in real-time iteration. Recently, a C++ library PolyMPC is proposed in [22] for pseudospectral based real-time NMPC. A more general framework of real-time predictive control has been investigated in [33], [34].…”

Section: Introductionmentioning

confidence: 99%

Block BFGS Based Distributed Optimization for NMPC Using PolyMPC

Jiang

Listov

Jones

2021

2021 European Control Conference (ECC)

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This paper presents a block BFGS based distributed optimization approach for nonlinear model predictive control (NMPC). The proposed method is a variant of the augmented Lagrangian based alternating direction inexact Newton method (ALADIN), which achieves a locally superlinear convergence rate. To deal with the NMPC problem in continuous time by employing the proposed method, we elaborate on a systematic implementation based on the C++ library PolyMPC. The performance and advantages of the proposed method are illustrated by applying the algorithm to a benchmark continuously stirred tank reactor case study.

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PolyMPC: An efficient and extensible tool for real‐time nonlinear model predictive tracking and path following for fast mechatronic systems

Cited by 14 publications

References 20 publications

Stochastic optimal control for autonomous driving applications via polynomial chaos expansions

Stochastic optimal control for autonomous driving applications via polynomial chaos expansions

AWEbox: An Optimal Control Framework for Single- and Multi-Aircraft Airborne Wind Energy Systems

Block BFGS Based Distributed Optimization for NMPC Using PolyMPC

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