Time-optimal Control Strategies for Electric Race Cars with Different Transmission Technologies

This paper presents models and optimization methods to rapidly compute the achievable lap time of a race car equipped with a battery electric powertrain. Specifically, we first derive a quasi-convex model of the electric powertrain, including the battery, the electric machine, and two transmission technologies: a single-speed fixed gear and a continuously variable transmission (CVT). Second, assuming an expert driver, we formulate the time-optimal control problem for a given driving path and solve it using an iterative convex optimization algorithm. Finally, we showcase our framework by comparing the performance achievable with a single-speed transmission and a CVT on the Le Mans track. Our results show that a CVT can balance its lower efficiency and higher weight with a higher-efficiency and more aggressive motor operation, and significantly outperform a fixed single-gear transmission.Comment: 5 pages, 4 figures, submitted to the 2020 IEEE Vehicle Power and Propulsion Conferenc

Energy Management Strategy for an Autonomous Electric Racecar using Optimal Control

The automation of passenger vehicles is becoming more and more widespread, leading to full autonomy of cars within the next years. Furthermore, sustainable electric mobility is gaining in importance. As racecars have been a development platform for technology that has later also been transferred to passenger vehicles, a race format for autonomous electric racecars called Roborace has been created. As electric racecars only store a limited amount of energy, an Energy Management Strategy (EMS) is needed to work out the time as well as the minimum energy trajectories for the track. At the same time, the technical limitations and component behavior in the electric powertrain must be taken into account when calculating the race trajectories. In this paper, we present a concept for a special type of EMS. This is based on the Optimal Control Problem (OCP) of generating a time-minimal global trajectory which is solved by the transcription via direct orthogonal collocation to a Nonlinear Programming Problem (NLPP). We extend this minimum lap time problem by adding our ideas for a holistic EMS. This approach proves the fundamental feasibility of the stated ideas, e.g. varying racepaths and velocities due to energy limitations, covered by the EMS. Also, the presented concept forms the basis for future work on meta-models of the powertrain's components that can be fed into the OCP to increase the validity of the control output of the EMS.Comment: Accepted at the IEEE Intelligent Transportation Systems Conference - ITSC 2019, Auckland, New Zealand 27 - 30 Octobe

Minimum-lap-time optimisation and simulation

The paper begins with a survey of advances in state-of-the-art minimum-time simulation for road vehicles. The techniques covered include both quasi-steady-state and transient vehicle models, which are combined with trajectories that are either pre-assigned or free to be optimised. The fundamentals of nonlinear optimal control are summarised. These fundamentals are the basis of most of the vehicular optimal control methodologies and solution procedures reported in the literature. The key features of three-dimensional road modelling, vehicle positioning and vehicle modelling are also summarised with a focus on recent developments. Both cars and motorcycles are considered

Integrated optimisation for dynamic modelling, path planning and energy management in hybrid race vehicles

Simulation software has for many years been developed to enhance the research and development phase of new vehicle introductions. With the introduction of the testing embargo in most forms of world championship motorsport, model validation is a necessity. To optimise the unknown vehicle and tyre parameters and to reduce the error between measured and simulated data in such a multi-input multi-output non-convex optimisation problem, a novel multi-objective particle swarm optimisation (PSO) technique is applied to ensure a fully validated vehicle model is developed and analysed for speed and performance. These optimisation algorithms are further developed to explore the trajectory planning problem to improve the lap time for the shortest path, minimum curvature and a combined approach, producing optimal racing line pathways and vehicle dynamic inputs and output responses by exploring trajectories and vehicle traction circle limits. Finally, a hybrid electric vehicle transient dynamics model for the control of energy management is presented. The hybrid powertrain contains an internal combustion engine, kinetic energy recovery system and heat energy recovery system with deployment and harvesting control parameters. The performance of single-objective and multi-objective particle swarm optimisation algorithms are compared and analysed. The proposed simulation model and optimisation techniques are applied to address an array of problems, including model validation, racing line trajectory design, fastest lap time problem, and energy management strategies. All results are validated and optimised with respect to the experimental data collected on the real track in Silverstone to ensure the results can be applied to physical real-world scenarios

Optimal energy management for formula-E cars with regulatory limits and thermal constraints

In this paper, novel solutions are proposed for energy and thermal management in Formula-E cars using optimal control theory. Optimal control techniques are used to optimize net energy consumption (accounting for loss-reductions from energy recovery from regenerative braking) to achieve minimal lap time which is a crucial element in developing a competitive race strategy in Formula E races. A thermal battery model is used to impose thermal constraints on the optimal energy management strategy in order to realistically capture working constraints during a race. The effects of energy and thermal constraints on the proposed strategy are then demonstrated and two different pedal lifting techniques were introduced. Both the current second generation and a concept third generation type of formula-E cars are studied and compared. While third generation is significantly more efficient with 10% to 30% less energy consumption, it potentially faces more critical thermal issues with more than 60% more heat generation

Numerical simulation of a 2018 F1 car cooling system for Silverstone Circuit

The thermal management of a Formula 1 car is a challenging task as it involves multiple components, systems and multiple sources of thermal energy. The present work attempts to model a representative F1 car following 2018 F1 regulations directly linked to the cooling systems requirements and performance. The main purpose of this work is to simulate the steady and transient behaviour of the cooling system when the vehicle is in a qualifying lap, and during the entire race, including the wait in the starting grid and the pit stops. This model includes the sub-models representing internal combustion engine, hybrid powertrain, vehicle, driver and an appropriate cooling system composed of radiators, pumps and expansion tanks. This work validates the cooling system of a representative 2018 F1 car for the Silverstone Circuit. This model is capable of simulating the overall thermal performance of the F1 car for sizing the cooling system for most of the F1 circuits. This paper presents a systematic approach followed for modelling a representative F1 car based on 2018 regulations, methods used for deriving appropriate data from various sources, approach used for validating the model and finally the strengths of the validated model for sizing the cooling system

Estudi de la termodinàmica de la bateria d’una moto elèctrica de competició

The frame of this project is the design and assembling of a competition electric motorcycle by the MotoSpirit Team. MotoSpirit is competing in MotoStudent, a university competition at worldwide level in which engineering student test their skills and knowledge gained during their studies. The electric automobile industry is in clear uprising nowadays, with more regulations in terms of emissions for the vehicle sector, the society gaining knowledge on the global and local environmental challenges that it faces and the emergence of new technologies that point to a more sustainable future, with the electric vehicle being the clearest and closest example to the citizen. MotoSpirit’s vision is aligned with this change. The team takes part in MotoStudent in its electric category betting for the new and sustainable technologies. As Steve Jobs once said "The only way for people to do great at work, is to get them to do work they love" and, if on top of that this work helps in making the world a little more sustainable than the day before, this is the purpose of any human being achieved. The batteries are the heart of electric vehicles, as a motor assembled in a car is useless without them. Batteries are able to store energy to then power vehicles with no emissions. Nevertheless, the battery is a complicated system containing chemicals and hazardous substances. This is why the management of the batteries is of main importance. The industry not only has to produce batteries to store the energy produced with renewable sources, but the batteries have to be studied and perfected so they can have a longer life cycle, and once they are dead, reuse them and recycle all of their parts to create second generation batteries minimizg waste. The thermal management of a battery plays a very important role in this aspect, as its role is to keep the battery working under the safety constraints and the best thermal conditions possible for obtaining better performance and longevity. The principal goal of this thesis is to study the thermodynamics of the electric motorcycle designed by MotoSpirit under different conditions and find out which and where are the points that can originate problems in the behaviour and life of the battery, being similar to an report of the thermal ability or capacity of the battery and where should it be improved. For this, the thesis starts with the collection of the theoretical principles behind the battery system and the examples of how the problem of thermal management of a battery is handled nowadays by the battery and electric vehicle manufacturers. Following is the presentation and more importantly the thermodynamics study of MotoSpirit’s battery pack, where the simulations made are explained. The discussion of the result points out the information collected during the sim- ulations and the results obtained. Finally, the conclusions list the most important aspects found, problems and ideas of the solutions to be adopted by MotoSpirit’s team in its final battery design

Optimal control of road vehicles: theory and applications

In this thesis Optimal Control (OC) of road vehicles is studied especially focusing on minimum lap time simulations. The theory underlying the most used optimal control solving techniques is described, including both the Pontryagin Maximum Principle and the reduction to Nonlinear Programming. Direct and indirect methods for optimal control problems are presented and compared against minimum lap time simulations (LTS). Modelling of vehicles for OC-LTSs is studied in order to understand how different design choices can affect simulation outcomes. Novel multibody models of four wheeled vehicles - a GP2 car and a go-kart - for OC-LTSs are developed and validated thorough comparison with experimental data. Particular attention is dedicated to the simulation of tyre load dynamics, that is achieved by a proper modelling of the chassis and suspension motions and of the aerodynamic forces. OC-LTSs are applied to electric vehicles too, specifically to optimise the design of an electric motorbike taking part at the Tourist Trophy Zero competition. A concise yet effective model is proposed in order to perform reliable simulations on a 60km long road in a reasonable amount of time. Experimental data is used to validate the model. A direct full collocation transcription method for OCPs dealing with implicit differential equations and control derivatives is presented, moreover the structure of the resulting NLP problem is accurately described. The relationship between the first order necessary conditions and the Lagrange multipliers of the NLP and OC problems are derived under the adopted discretisation scheme. The presented transcription method is implemented into a software which is currently in use at the University of Padova to solve OC-LTSs

A Controls-Oriented Approach For Modeling Professional Drivers During Ultra-High Performance Maneuvers

In the study of vehicle dynamics and controls, modeling ultra-high performance maneuvers (i.e., minimum-time vehicle maneuvering) is a fascinating problem that explores the boundaries of capabilities for a human controlling a machine. Professional human drivers are still considered the benchmark for controlling a vehicle during these limit handling maneuvers. Different drivers possess unique driving styles, i.e. preferences and tendencies in their local decisions and corresponding inputs to the vehicle. These differences in the driving style among professional drivers or sets of drivers are duly considered in the vehicle development process for component selection and system tuning to push the limits of achievable lap times. This work aims to provide a mathematical framework for modeling driving styles of professional drivers that can then be embedded in the vehicle design and development process. This research is conducted in three separate phases. The first part of this work introduces a cascaded optimization structure that is capable of modeling driving style. Model Predictive Control (MPC) provides a natural framework for modeling the human decision process. In this work, the inner loop of the cascaded structure uses an MPC receding horizon control strategy which is tasked with finding the optimal control inputs (steering, brake, throttle, etc.) over each horizon while minimizing a local cost function. Therein, we extend the typical fixed-cost function to be a blended cost capable of optimizing different objectives. Then, an outer loop finds the objective weights used in each MPC control horizon. It is shown that by varying the driver\u27s objective between key horizons, some of the sub-optimality inherent to the MPC process can be alleviated. In the second phase of this work, we explore existing onboard measurements of professional drivers to compare different driving styles. We outline a novel racing line reconstruction technique rooted in optimal control theory to reconstruct the driving lines for different drivers from a limited set of measurements. It is demonstrated that different drivers can achieve nearly identical lap times while adopting different racing lines. In the final phase of this work, we use our racing line technique and our cascaded optimization framework to fit computable models for different drivers. For this, the outer loop of the cascaded optimization finds the set of objective weights used in each local MPC horizon that best matches simulation to onboard measurements. These driver models will then be used to optimize vehicle design parameters to suit each driving style. It will be shown that different driving styles will yield different parameters that optimize the driver/vehicle system

Design, Field Evaluation, and Traffic Analysis of a Competitive Autonomous Driving Model in a Congested Environment

Recently, numerous studies have investigated cooperative traffic systems using the communication among vehicle-to-everything (V2X). Unfortunately, when multiple autonomous vehicles are deployed while exposed to communication failure, there might be a conflict of ideal conditions between various autonomous vehicles leading to adversarial situation on the roads. In South Korea, virtual and real-world urban autonomous multi-vehicle races were held in March and November of 2021, respectively. During the competition, multiple vehicles were involved simultaneously, which required maneuvers such as overtaking low-speed vehicles, negotiating intersections, and obeying traffic laws. In this study, we introduce a fully autonomous driving software stack to deploy a competitive driving model, which enabled us to win the urban autonomous multi-vehicle races. We evaluate module-based systems such as navigation, perception, and planning in real and virtual environments. Additionally, an analysis of traffic is performed after collecting multiple vehicle position data over communication to gain additional insight into a multi-agent autonomous driving scenario. Finally, we propose a method for analyzing traffic in order to compare the spatial distribution of multiple autonomous vehicles. We study the similarity distribution between each team's driving log data to determine the impact of competitive autonomous driving on the traffic environment