In motorsport, simulating road vehicles driving at the limit of handling is a valuable tool to study and optimize their overall performance during the design and set-up phases. Along with Quasi-Steady-State optimization, optimal control (OC) is the most utilized technique to simulate the control and states of a vehicle during minimum-time maneuvers and has been used for offline lap-time optimization for more than twenty years now. Since the first applications of optimal control in this field, it has been clear that the solution of the minimum-time optimization does not represent a model of the human driver but instead substitutes him/her. However, the common points or divergences between the minimum-time strategy of human race drivers and the OC one are still unclear. Moreover, it seems that in the literature there is no agreement about what vehicle models must be used, and in general the choice of one model or the other is not clearly justified. Finally, thanks to the rise in popularity of autonomous driving and racing, optimal control has been used as path planner for automated vehicles: %nonetheless, the application of free-trajectory real-time nonlinear optimal control in Model Predictive Control (MPC) schemes, where the optimal controls are directly fed to the vehicle, is still an unexplored topic. nonetheless, the application of free-trajectory real-time nonlinear optimal control in Model Predictive Control (MPC) schemes, where the optimal controls are computed from a single optimization and directly fed to the vehicle, is a topic still open for exploration. The first aim of this thesis is to provide an objective comparison of several vehicle, tire, powertrain and road models to be used in minimum-time OC. In the first part of this work we thus detail several models of the vehicle and its subsystems. We then solve minimum-time OC problems on a series of test tracks adopting most of the model combinations and discuss the differences in the solutions. We then draw conclusions on the best model combinations to obtain realistic and reliable minimum-time maneuvers. The second part of the thesis aims to prove that the solutions of minimum-time OC problems are indeed different from the driving behavior of professional drivers, but they can be employed to coach the human driver and improve his/her racing performance. After modeling a high-performance vehicle manufactured by Ferrari, we again use optimal control to compute minimum-time maneuvers on two different tracks. A professional racer driving is then coached in following the OC strategy on the Ferrari driving simulator, and we objectively prove that the driver can outperform his previous lap times. In the third and last part of the thesis, we aim to prove that free-trajectory real-time optimal control is a valid alternative to hierarchical MPC frameworks based on high-level path planning and low-level path tracing. We first develop a novel kineto-dynamic vehicle model able to satisfy the trade-off between computational lightness and accuracy in representing the vehicle's pure and combined dynamics. Then, by solving a minimum-time OC in real-time, we are able to autonomously drive a real scaled vehicle around a track at the limits of tire adherence.

In autonomous racing there is a need to accurately localize the vehicle while simultaneously creating a map of the track. This information can be delivered to planning and control layers in order to achieve fully autonomous racing. The kinematic model is a commonly used motion model in feature-based SLAM. However, it is a poor representation of the vehicle when considering high lateral accelerations since the model is only based on trigonometric relationships. This Master’s Thesis investigates the consequence of using the kinematic model when undertaking demanding maneuvers; and if by switching to a dynamic model, which takes the tire forces into account, can improve the localization performance. An EKF-SLAM algorithm comprising the kinematic and dynamic model was implemented on a development platform. The pose estimation accuracy was compared using either model when subject to typical maneuvers in racing-scenarios. The results showed that the pose estimation accuracy was in general similar when using either of the vehicle models. When exposed to large slip angles, the implications of switching from a kinematic model to a dynamic model resulted in a significantly better pose estimation accuracy when driving in an unknown environment. However, switching to a dynamic model had little effect when driving in a known environment. The implications of the study suggest that, during the first lap of a racing track, the kinematic model should be switched to a dynamic model when subject to high lateral accelerations. For the consecutive laps, the choice of vehicle model has less impact. Keywords: SLAM, EKF-SLAM, Localization, Estimation, Vehicle Dynamics, Kinematic Model, Dynamic Model, Autonomous Racing / I autonom racing är det viktigt att kunna lokalisera fordonet med hög noggrannhet samtidigt som en karta över banan skapas. Den här informationen kan vidare bli hanterad av planerings- och reglersystem för att uppfylla autonom racing fullt ut. Den kinematiska modellen är en vanligt förekommande rörelsemodell i SLAM. Den är däremot en bristande representation av fordonet vid höga laterala accelerationer eftersom modellen enbart är baserad på trigonometriska samband. Det här masterarbetet undersöker den kinematiska modellens påverkan vid olika manövrar och huruvida den dynamiska modellen, som modellerar däckkrafterna, kan förbättra prestandan. En EKF-SLAM algorithm innehållande den kinematiska- och dynamiska modellen implementerades på en utvecklingsplattform. Estimeringsnoggrannheten av positionen och orienteringen jämfördes vid typiska manövrar för racingscenarier. Resultatet visade att estimeringsnoggrannheten av positionen och orienteringen var generellt sett lika vid användandet av antingen den kinematiska eller den dynamiska modellen. Implikationerna av att byta från den kinematiska modellen till den dynamiska modellen vid höga glidvinklar, resulterade i en signifikant bättre estimeringsnoggrannhet av positionen och orienteringen vid körning i en okänd miljö. Emellertid så var effekterna av att byta till en dynamisk modell insignifikanta vid körning i en känd miljö. Implikationerna av denna studie föreslår att under det första varvet av racingbanan byta från den kinematiska modellen till den dynamiska vid höga laterala accelerationer. Under kommande varv har valet av fordonsmodell mindre effekt. Nyckelord: SLAM, EKF-SLAM, lokalisering, estimering, fordonsmodellering, kinematisk modell, dynamisk modell, autonom racing.

In this work, an improved Learning Model Predictive Control (LMPC)architecture for autonomous racing is presented. The controller is referencefree and is able to improve lap time by learning from history data of previouslaps. A terminal cost and a sampled safe set are learned from history data toguarantee recursive feasibility and non-decreasing performance at each lap.Improvements have been proposed to implement LMPC on autonomousracing in a more efficient and reliable way. Improvements have been doneon three aspects. Firstly, system identification has been improved to be runin a more efficient way by collecting feature data in subspace, so that thesize of feature data set is reduced and time needed to run sorting algorithmcan be reduced. Secondly, different strategies have been proposed toimprove model accuracy, such as least mean square with/without lifting andGaussian process regression. Thirdly, for reducing algorithm complexity,methods combining different model construction strategies were proposed.Also, running controller in a multi-rate way has also been proposed toreduced algorithm complexity when increment of controller frequency isnecessary. Besides, the performance of different system identificationstrategies have been compared, which include strategy from newton’s law,strategy from classical system identification and strategy from machinelearning. Factors that can possibly influence converged result of LMPCwere also investigated, such as prediction horizon, controller frequency.Experiment results on a 1:10 scaled RC car illustrates the effectiveness ofproposed improvements and the difference of different system identificationstrategies. / I detta arbete, presenteras en förbättrad inlärning baserad modell prediktivkontroll (LMPC) för autonom racing, styralgoritm är referens fritt och har visatsig att kunna förbättra varvtid genom att lära sig ifrån historiska data från tidigarevarv. En terminal kostnad och en samplad säker mängd är lärde ifrån historiskdata för att garantera rekursiv genomförbarhet och icke-avtagande prestanda vidvarje varv.förbättringar har presenterats för implementering av LMPC på autonom racingpå ett mer effektivt och pålitligt sätt. Förbättringar har gjorts på tre aspekter.Först, för system identifiering, föreslår vi att samlar feature data i delrummet,så att storlek på samlade datamängd reduceras och tiden som krävs för attköra sorteringsalgoritm minskas. För det andra, föreslår vi olika strategierför förbättrade modellnoggrannheten, såsom LMS med/utan lyft och Gaussianprocess regression. För det tredje, För att reducerar komplexitet för algoritm,metoder som kombinerar olika modellbygg strategier föreslogs. Att körastyrenhet på ett multi-rate sätt har också föreslagits till för att reduceraalgoritmkomplexitet då inkrementet av styrfrekvensen är nödvändigt.Prestanda av olika systemidentifiering har jämförts, bland annat, Newtonslag, klassisk systemidentifierings metoder och strategier från maskininlärning.Faktorer som eventuellt kan påverka konvergens av LMPC resultat har ocksåundersökts. Såsom, prediktions horisont, styrfrekvensen.Experimentresultat på en 1:10 skalad RC-bilen visar effektiviteten hos föreslagnaförbättringarna och skillnaderna i olika systemidentifierings strategier.

Recent advancements in time-optimal trajectory planning, control, and state estimation for autonomous vehicles have paved the way for the emerging field of autonomous racing. In the last 5-10 years, this form of racing has become a popular and challenging testbed for autonomous driving algorithms, aiming to enhance the safety and performance of future intelligent vehicles. In autonomous racing, the main goal is to develop real-time algorithms capable of autonomously maneuvering a vehicle around a racetrack, even in the presence of moving opponents. However, as a vehicle approaches its handling limits, several challenges arise for online trajectory planning and control. The vehicle dynamics become nonlinear and hard to capture with low-complexity models, while fast re-planning and good generalization capabilities are crucial to execute optimal maneuvers in unforeseen scenarios. These challenges leave several open research questions, three of which will be addressed in this thesis. The first explores developing accurate yet computationally efficient vehicle models for online time-optimal trajectory planning. The second focuses on enhancing learning-based methods for trajectory planning, control, and state estimation, overcoming issues like poor generalization and the need for large amounts of training data. The third investigates the optimality of online-executed trajectories with simplified vehicle models, compared to offline solutions of minimum-lap-time optimal control problems using high-fidelity vehicle models. This thesis consists of four parts, each of which addresses one or more of the aforementioned research questions, in the fields of time-optimal vehicle trajectory planning, control and state estimation. The first part of the thesis presents a novel artificial race driver (ARD), which autonomously learns to drive a vehicle around an obstacle-free circuit, performing online time-optimal vehicle trajectory planning and control. The following research questions are addressed in this part: How optimal is the trajectory executed online by an artificial agent that drives a high-fidelity vehicle model, in comparison with a minimum-lap-time optimal control problem (MLT-OCP), based on the same vehicle model and solved offline? Can the artificial agent generalize to circuits and conditions not seen during training? ARD employs an original neural network with a physics-driven internal structure (PhS-NN) for steering control, and a novel kineto-dynamical vehicle model for time-optimal trajectory planning. A new learning scheme enables ARD to progressively learn the nonlinear dynamics of an unknown vehicle. When tested on a high-fidelity model of a high-performance car, ARD achieves very similar results as an MLT-OCP, based on the same vehicle model and solved offline. When tested on a 1:8 vehicle prototype, ARD achieves similar lap times as an offline optimization problem. Thanks to its physics-driven architecture, ARD generalizes well to unseen circuits and scenarios, and is robust to unmodeled changes in the vehicle’s mass. The second part of the thesis deals with online time-optimal trajectory planning for dynamic obstacle avoidance. The research questions addressed in this part are: Can time-optimal trajectory planning for dynamic obstacle avoidance be performed online and with low computational times? How optimal is the resulting trajectory? Can the planner generalize to unseen circuits and scenarios? At each planning step, the proposed approach builds a tree of time-optimal motion primitives, by performing a sampling-based exploration in a local mesh of waypoints. The novel planner is validated in challenging scenarios with multiple dynamic opponents, and is shown to be computationally efficient, to return near-time-optimal trajectories, and to generalize well to new circuits and scenarios. The third part of the thesis shows an application of time-optimal trajectory planning with optimal control and PhS-NNs in the context of autonomous parking. The research questions addressed in this part are: Can an autonomous parking framework perform fast online trajectory planning and tracking in real-life parking scenarios, such as parallel, reverse and angle parking spots, and unstructured environments? Can the framework generalize to unknown variations in the vehicle’s parameters and road adherence, and operate with measurement noise? The autonomous parking framework employs a novel penalty function for collision avoidance with optimal control, a new warm-start strategy and an original PhS-NN for steering control. The framework executes complex maneuvers in a wide range of parking scenarios, and is validated with a high-fidelity vehicle model. The framework is shown to be robust to variations in the vehicle’s mass and road adherence, and to operate with realistic measurement noise. The fourth and last part of the thesis develops novel kinematics-structured neural networks (KS-NNs) to estimate the vehicle’s lateral velocity, which is a key quantity for time-optimal trajectory planning and control. The KS-NNs are a special type of PhS-NNs: their internal structure is designed to incorporate the kinematic principles, which enhances the generalization capabilities and physical explainability. The research questions addressed in this part are: Can a neural network-based lateral velocity estimator generalize well when tested on a vehicle not used for training? Can the network’s parameters be physically explainable? The approach is validated using an open dataset with two race cars. In comparison with traditional and neural network estimators of the literature, the KS-NNs improve noise rejection, exhibit better generalization capacity, are more sample-efficient, and their structure is physically explainable.