The increased demand for electric transportation has brought new challenges, many of which relate to the limited range and long charging time. This may be addressed by providing reliable and accurate residual-range estimates and energy-optimized route selections. Crucially, the performance of such systems is largely determined by the accuracy of the underlying energy demand prediction algorithm. Existing solutions typically predict energy demand but fail to derive the prediction uncertainty, an ever more sought-after quantity. Methods that attempt to provide such a measure often rely on data-driven techniques or computationally intensive Monte Carlo simulations. This paper is therefore set out to provide a dynamic model capable of handling varying operating conditions whilst remaining computationally efficient. By regarding the driver reference speed as a measurement, an observer-like prediction model can be formulated. Building on this principle, a vehicle-independent description is attained, owing to the use of merely exogenous parameters. The observer is realized as a Cubature Rauch-Tung-Striebel Smoother, which estimates both the state and the uncertainty, providing qualitative information about expected variation. The algorithm’s mean prediction is verified by analyzing the velocity profile, the Kalman gain, and the energy demand, all of which exhibit the expected behavior. Its uncertainty estimate is evaluated against real-world vehicle operation data, which show that the considered uncertainty sources significantly contribute to the energy demand prediction uncertainty. Further improvements in accuracy are expected as more uncertainties are accounted for.

The energy performance of road vehicles has traditionally been evaluated using driving cycles, in which a prescribed speed profile is tracked either in simulation or by a physical vehicle. Recent research has proposed an alternative framework based on operating conditions, where the driving environment is described in terms of factors such as road topography, legal speed limits, traffic, and weather, rather than by an explicit speed profile. This paper addresses the complementary problem of driver modeling, necessary to translate the operating conditions to a speed profile. A simple driver model designed to be compatible with the operating-condition framework and evaluates its ability to reproduce realistic driving behavior is investigated. Validation of the model is done through a controlled driving-simulator study vehicle log files collected during real-world operation and are used to identify the model parameters and assess the model's predictive performance. The results suggest that this simple model can be efficient in reproducing major effects of driver behavior, while further research is required to fully assess its validity.

Balancing a bicycle through steering is similar to balancing an inverted pendulum, with a travel-speed-dependent pivot point. This paper derives a speed-dependent balancing controller for a self-balancing bicycle. This controller is based on an identified gray box model. The identification procedure is formulated as a weighted least squares problem with the time-varying parameter of the model. Identification data was generated on a controlled bicycle robot. Excitation experiments were designed to account for the unstable nature of the problem. Based on this identified model, a gain-scheduled controller is derived for a speed-independent closed-loop performance for a speed range. The controller is further implemented on the bicycle and tested for a set of speeds. Tests performed on the bicycle illustrate the gain-scheduled controller's performance gain.

This paper presents a robust position controller for electric power assisted steering and steer-by-wire force-feedback systems. A position controller is required in steering systems for haptic feedback control, advanced driver assistance systems and automated driving. However, the driver's physical arm impedance causes an inertial uncertainty during coupling. Consequently, a typical position controller, i.e., based on single variable, becomes less robust and suffers tracking performance loss. Therefore, a robust position controller is investigated. The proposed solution is based on the multi-variable concept such that the sensed driver torque signal is also included in the position controller. The subsequent solution is obtained by solving the LMI-H_∞ optimization problem. As a result, the desired loop gain shape is achieved, i.e., large gain at low frequencies for performance and small gain at high frequencies for robustness. Finally, frequency response comparison of different position controllers on real hardware is presented. Experiments and simulation results clearly illustrate the improvements in reference tracking and robustness with the proposed H_∞ controller.

An autonomous bicycle has been developed for repeatable active safety tests of Advanced Driver Assistance Systems (ADAS). For effective interaction with other test objects, precise bicycle trajectory tracking control is essential. The repetitive nature of these tests suggest an Iterative Learning Control (ILC) approach. In this paper, we present a design of an ILC controller tailored for the trajectory tracking problem of an autonomous bicycle. To illustrate the performance of the controller, simulations have been conducted.

The introduction of Steer-by-wire systems for cars is believed to bring a wide range of advantages ranging from production simplifications to passive safety and advances in active safety. The intense work with autonomous driving has paved the way for redundancy and systems safety needed to introduce steer-by-wire to the broad market. This paper explores some of the fundamental aspects of mechanically disconnecting the driver and hand wheel from the vehicle and the road wheel, such as variable steering ratio and generation of haptic torque feedback. Simple strategies are developed and tested on test track in a prototype vehicle. Initial tests suggest that the simple strategies show promise.

Range prediction is vital for battery electric vehicles, and the main source of errors in range prediction is often the uncertainty in motion resistance. Rig and wind tunnel measurements can be used to find the motion resistance of a specific vehicle combination under specified weather conditions. However, real-life variation of the operating conditions of heavy-duty vehicles makes testing impractical. This paper proposes and validates a model of motion resistance with parameters adapted to actual road weather conditions. The model is validated in winter conditions with varying wind, using a vehicle equipped with a wind sensor. The results show that the proposed model captures the motion resistance with high accuracy. Results also indicate that it is crucial to take weather effects into account when modelling motion resistance, particularly in winter conditions.

Residual range estimation plays a crucial role in route selection and the trust of electric vehicles (EVs). With inspiration from longitudinal vehicle dynamics, a simple and computationally efficient model for traction power is presented. Such a model has the advantage of being exclusively based on vehicle exogenous parameters. The model allows for insight into variations in power usage along a transport operation and separation of power losses originating from air drag, rolling resistance, hill climbing, and inertial forces. A model of this structure can handle regenerative braking and estimate service brake usage as an additional feature. Also, it treats the inherent truncation bias resulting from truncating a stochastic process. Evaluation of the performance is presented using Monte Carlo simulations, comparing the estimation error against a simple benchmark model and vehicle log data.

To guide the development of driver assistant systems and fully automated solutions for reversing long combination vehicles (LCVs), the principles for reversing LCVs are investigated using the articulation angle gradient. The widely used Steady-state Circling Limitation (SSCL) in reversing LCVs has two main drawbacks: it restricts vehicles from operating with large articulation angles crucial for tight spaces and lacks a well-defined feasible range. Two new reverse principles are introduced that can provide better insight. The first principle extends SSCL to include more extreme articulation angles for single-articulated vehicles. It also addresses the necessity of considering articulation gradients when developing the continuous reverse limitation for multi-articulated vehicles. The second principle introduces limited distance reversing for vehicles that no longer meet the first principle's requirements, providing additional vehicle ending poses useful for tasks like loading and coupling.

Data-driven development of friction estimators for passenger vehicles is becoming popular. They rely mainly on training data to obtain an accurate estimate of the current road conditions. However, reference or training data for natural conditions containing available friction is sparse. This limits the development of data-driven approaches for friction estimation. The current paper presents progress in a project devoted to developing a method to use standard equipment for road monitoring to acquire reference data for friction estimation, relevant to specific tyres and operating conditions. Results show how a mapping between existing test equipment readings and the real experienced coefficient of friction of a car tyre can be made.

Detailed longitudinal dynamics simulations may be used to predict the energy performance of road vehicles. However, including uncertainty in the operating conditions often implies high computational costs. Model-based formulations, in conjunction with statistical methods, may obviate this limitation by directly accounting for stochasticity, thus eliminating the need for simulating large populations of driving and operating cycles. To this end, leveraging directly the methods of stochastic calculus, this work presents a novel theory of longitudinal vehicle dynamics and energy consumption, where the vehicle's speed varies stochastically depending on the characteristics of the operating environment. In particular, the proposed formulation, consisting of stochastic differential equations (SDEs) governing the longitudinal motion of road vehicles, inherently accounts for the statistical variation connected with uncertainties in the driver's behavior and road properties, including, e.g., topography and legal speed. A Fokker-Planck partial differential equation (PDE) that describes the time evolution of the joint probability density function (PDF) of the vehicle's speed, position, and road parameters is also derived from the SDEs established in the paper. The SDE and Fokker-Planck-based approaches enable statistical estimation of important quantities like speed fluctuations, instantaneous power requests, and energy consumption. The developed models may be used to assess the energy performance of road vehicles for different combinations of road transport missions. This is applicable at the early stages of the development, virtual testing, and certification processes, without the need to perform computationally expensive simulations, as corroborated by the virtual experiments conducted in the paper.

The accuracy of transient tyre models may be largely improved by considering the flexibility of the tyre carcass. Several formulations, whereby the unsteady behaviour of the tyre is approximated using linear or nonlinear systems of ordinary differential equations (ODEs), are already available in the literature. However, when the tread behaviour is described using a distributed representation, that is, in terms of partial differential equations (PDEs), the inclusion of even the simplest model to represent the deformation of the tyre carcass leads to rather involved PDE or interconnected PDE-ODE systems, with nonlocal and boundary terms. Such descriptions require detailed analyses that have not been attempted so far. Therefore, this paper investigates the salient properties of the classic brush and LuGre-brush models considering the effect of a flexible carcass. For both formulations, the existence and uniqueness of the solution are discussed. For the standard version of the brush models, a closed-form solution is provided under the assumption of vanishing sliding, whereas the case of limited friction is explored only qualitatively. Concerning the LuGre-brush variant, the preliminary intuition gained from the analysis of the distributed representation is effectively used to develop approximated lumped formulations to be used in control-oriented applications.

It is known that the rolling resistance decreases with increasing tire temperature. If the tires could be heated to a high temperature, the rolling resistance's energy loss could be reduced. The question arises whether the reduced rolling resistance energy consumption overcomes the energy required to heat the tire. This paper investigates the effects of external heating and improved tire insulation theoretically. The results indicate that external tire heating can be beneficial only if the heat used is waste heat, generated from a heat pump or similar with a coefficient of performance greater than one or taken from the grid.

ABSTRACT Tire slip losses have been shown to have a significant impact on vehicle performance in terms of energy efficiency, thus requiring accurate studies. In this paper, the transient dissipation mechanisms connected to the presence of micro-sliding phenomena occurring at the tire–road interface are investigated analytically. The influence of a two-dimensional velocity field inside the contact patch is also considered in light of the new brush theory recently developed by the authors. Theoretical results align with findings already known from literature but suggest that the camber and turn spins contribute differently to the slip losses and should be regarded as separate entities when the camber angle is sufficiently large. The present work shows that an additional amount of power which relates to the initial sliding conditions is generated or lost during the unsteady-state maneuvers. A simple example is presented to illustrate the discrepancy between the microscopic and macroscopic approaches during a transient maneuver.

Conventionally, the optimal design and selection processes of heavy-duty trucks are supported by the internal classification systems adopted by original equipment manufacturers (OEMs), which classify the energy usage of road vehicles based on the characteristics of the transport mission. These may include, for example, road properties like topography, mean legal speed and curviness, but also weather and traffic conditions. In this context, the definition of classes and thresholds in use by OEMs is however based on heuristics rather than a rigorous scientific approach. As a consequence, there is often no guarantee that vehicles optimally designed with respect to certain combinations of classes will exhibit robustness in energy performance when operated differently from the nominal conditions. This limitation might be overcome by optimally specifying classes and thresholds depending on a suitable energy metric. Therefore, this paper proposes a scientific method to build an energy-metric-optimal (EMO) classification system for road transport missions using statistical models to describe the operating environment. The problem is formulated in a multi-objective optimization form, where the vector-valued function to be minimized collects the total variation of a mean energy function over the considered intervals. The procedure is applied to the stochastic road models of the operating cycle (OC) description, yielding the optimal thresholds for a predefined number of classes. These are finally compared to those in use at Volvo and Scania, respectively.

The vehicle's mass is one of the most influential parameters in determining energy consumption. Indeed, the inertial terms are approximately proportional to the instantaneous power required by the prime mover to sustain or accelerate the vehicle. In particular, heavy-duty trucks used in goods distribution are subject to frequent changes in payload, depending on the specific task or sequence of tasks to be executed. In this context, the variability of the cargo weight is clearly reflected in the energy performance, which may exhibit a relatively large spread compared to the nominal operational conditions. The present paper proposes a stochastic model for mission stops and variable cargo weight for heavy-duty trucks. The model is parametrized using log data acquired during real-world road operations and differentiates between multiple working conditions of the vehicle. The model is formally analyzed concerning the probability distri-bution and expectation of the cargo weight and the mean number of mission stops. The stochastic description is finally integrated with full driver and vehicle models in a virtual simulation environment, and a comparison is performed against log data to validate the proposed formulation. The comparison shows an encouragingly good agreement with the empirical evidence.

This paper refines the two-regime transient theory developed by Romano et al. [Romano L, Bruzelius F, Jacobson B. Unsteady-state brush theory. Vehicle Syst Dyn. 2020;59:11–29. DOI: 10.1080/00423114.2020.1774625.] to include the effect of combined slip. A nonlinear system is derived that describes the non-steady generation of tyre forces and considers the coupling between the longitudinal and lateral characteristics. The proposed formulation accounts for both the carcass and the bristle dynamics, and represents a generalisation of the single contact point models. A formal analysis is conducted to investigate the effect of the tyre carcass anisotropy on the properties of the system. It is concluded that a fundamental role is played by the ratio between the longitudinal and lateral relaxation lengths. In particular, it is demonstrated that the maximum slip that guarantees (partial) adhesion conditions does not coincide with the stationary value and decreases considerably for highly anisotropic tyres. The dissipative nature of the model is also analysed using elementary tools borrowed from the classic theory for nonlinear systems. A comparison is performed against the single contact point models, showing a good agreement especially towards the full-nonlinear one. Furthermore, compared to the single contact point models, the two-regime appears to be able to better replicate the exact dynamics of the tyre forces predicted by the complete brush theory. Finally, the transient model is partially validated against experimental results.

This paper presents a novel tyre model which combines the LuGre formulation with the exact brush theory recently developed by the authors, and which accounts for large camber angles and turning speeds. Closed-form solutions for the frictional state at the tyre-road interface are provided for the case of constant slip inputs, considering rectangular and elliptical contact patches. The steady-state tyre characteristics resulting from the proposed approach are compared to those obtained by employing the standard formulation of the LuGre-brush tyre models and the exact brush theory for large camber angles. Then, to cope with the general situation of time-varying slips and spins, two approximated lumped models are developed that describe the aggregate dynamics of the tyre forces and moment. In particular, it is found that the transient evolution of the tangential forces may be approximated by a system of two coupled ordinary differential equations (ODEs), whilst the dynamics of the self-aligning moment may be described by combining two systems of two coupled ODEs. Given its stability properties and ease of implementation, the lumped one may be effectively employed for vehicle state estimation and control purposes.