Real-Time Nonlinear Model Predictive Control for Fast Mechatronic Systems

This thesis presents an efficient and extensible numerical software framework for real-time model-based control. We are motivated by complex and challenging mechatronic applications spanning from flight control of fixed-wing aircraft and thrust vector control drones to autonomous driving. In the first part, we present PolyMPC, a novel C++ software framework for real-time embedded nonlinear optimal control and optimisation. A key feature of the package is a highly optimised implementation of the pseudospectral collocation method that exploits instruction set parallelism available on many modern computer architectures. Polynomial representation of the state and control trajectories allows the tool to be used as a standalone controller and as an efficient solver for low-level tracking controllers in hierarchical schemes. Algorithmically, the choice is made towards computational speed. For nonlinear problems, we combine a sequential quadratic programming (SQP) strategy with the alternating direction method of multipliers (ADMM) for quadratic programs (QP), which is especially favourable for embedded applications thanks to the low computational cost per iteration. In the second part, the developed numerical methods and software are used to experimentally study optimisation-based control of airborne wind energy (AWE) systems. For this purpose, we designed and built a small-scale prototype of a single-line rigid-wing AWE kite which comprises an aircraft fitted with necessary sensors and computers and a fully autonomous ground station for tether control. The prototype serves as a research platform for studying flight navigation and control systems thanks to very flexible custom mission management and control software. We further develop a dynamic optimisation based methodology for parameter identification and provide a validated flight simulator that matches well the real behaviour of the system. Finally, a model-predictive path following flight controller is designed and tested in real-world experiments. The third part of the thesis is concerned with the application of real-time nonlinear model predictive control (NMPC) to autonomous driving at the limits of handling, which requires high sampling rates and robustness of the motion control system. We propose a dynamic optimization-based hierarchical framework for the local refinement of the racing lines that takes into account the nonlinear vehicle and actuator dynamics, adaptive tyre constraints, and the safety corridor around the initial path. The top layer receives a discrete obstacle-free local path computed by a coarse planner and transforms it into auto-differentiable look-up tables (LUT) for efficient continuous sampling. Separately, we investigated the problem of safe trajectory planning under parametric model uncertainties motivated by automotive applications. We use generalised polynomial chaos expansions for efficient nonlinear uncertainty propagation and distributionally robust inequalities for chance constraint approximation. Inspired by 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 reduces conservatism related to nonlinear uncertainty propagation while guaranteeing constraint satisfaction with a high probability

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

This paper presents PolyMPC, an open‐source C++ library for pseudospectral‐based real‐time predictive control of nonlinear systems. It provides a necessary background on the computational aspects of the pseudospectral approximation of optimal control problems and explains how various model predictive control and parameter estimation algorithms can be implemented using the software. We discuss the key algorithmic modules and architectural features of the PolyMPC library. The workflow of a path following controller design for a highly nonlinear mechatronic system is demonstrated in a tutorial example. Another example illustrates how the core functionality might be used to approximate and solve a custom optimal control problem

Block BFGS Based Distributed Optimization for NMPC Using PolyMPC

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

Feedback Control Design Maximizing the Region of Attraction of Stochastic Systems Using Polynomial Chaos Expansion

A feedback control design is proposed for stochastic systems with finite second moment which aims at maximising the region of attraction of the equilibrium point. Polynomial Chaos (PC) expansions are employed to represent the stochastic closed loop system by a higher dimensional set of deterministic equations. By using the PC expanded system representation, the available information on the uncertainty affecting the system explicitly enters the control design problem. Further, this allows Lyapunov methods for deterministic systems to be used to formulate the stability criteria certifying the region of attraction. These criteria are parametrized by the feedback gain and formulated in a polynomial optimization program which is solved using sum-of-squares methods. This approach offers flexibility in the choice of the stochastic feedback law and accounts for input constraints. The application is demonstrated by two numerical examples

Feedback Control Design Maximizing the Region of Attraction of Stochastic Systems Using Polynomial Chaos Expansion

A feedback control design is proposed for stochastic systems with finite second moment which aims at maximising the region of attraction of the equilibrium point. Polynomial Chaos (PC) expansions are employed to represent the stochastic closed loop system by a higher dimensional set of deterministic equations. By using the PC expanded system representation, the available information on the uncertainty affecting the system explicitly enters the control design problem. Further, this allows Lyapunov methods for deterministic systems to be used to formulate the stability criteria certifying the region of attraction. These criteria are parametrized by the feedback gain and formulated in a polynomial optimization program which is solved using sum-of-squares methods. This approach offers flexibility in the choice of the stochastic feedback law and accounts for input constraints. The application is demonstrated by two numerical examples.ISSN:2405-896

Real-time Nonlinear MPC Strategy with Full Vehicle Validation for Autonomous Driving

In this paper, we present the development and deployment of an embedded optimal control strategy for autonomous driving applications on a Ford Focus road vehicle. Non-linear model predictive control (NMPC) is designed and deployed on a system with hard real-time constraints. We show the properties of sequential quadratic programming (SQP) optimization solvers that are suitable for driving tasks. Importantly, the designed algorithms are validated based on a standard automotive XiL development cycle: model-in-the-loop (MiL) with high fidelity vehicle dynamics, hardware-in-the-loop (HiL) with vehicle actuation and embedded platform, and full vehicle-hardware-in-the-loop (VeHiL). The autonomous driving environment contains both virtual simulation and physical proving ground tracks. NMPC algorithms and optimal control problem formulation are fine-tuned using a deployable C code via code generation compatible with the target embedded toolchains. Finally, the developed systems are applied to autonomous collision avoidance, trajectory tracking, and lane change at high speed on city/highway and low speed at a parking environment.LA