Minimum-lap-time optimisation and simulation

Massaro, Matteo; Limebeer, D.J.N.

doi:10.1080/00423114.2021.1910718

Cited by 40 publications

(32 citation statements)

References 104 publications

(192 reference statements)

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“…In other words, we seek (s-dependent) Euler angles and polynomial coefficients a i ðsÞ in ( 7) that minimise the distance between the survey data and the track model. The method proposed builds on the methods described in [7,13,15]. The optimal-control problem (OCP) takes the standard form…”

Section: Road Reconstructionmentioning

confidence: 99%

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Curved-ribbon-based track modelling for minimum lap-time optimisation

2021

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Three-dimensional road models for vehicular minimum-lap-time manoeuvring are typically based on curvilinear coordinates and generalizations of the Frenet–Serret formulae. These models describe the road as a parametrized ‘ribbon’, which can be described in terms of three curvature variables. In this abstraction the road is assumed laterally flat. While this class of road models is appropriate in many situations, this is not always the case. In this research we extend the laterally-flat ribbon-type road model to include lateral curvature. This accommodates the case in which the road camber can change laterally across the track. Lateral-position-dependent camber is introduced as a generalisation that is required for some race tracks. A race track model with lateral curvature is constructed using high-resolution LiDAR measurement data. These ideas are demonstrated on a NASCAR raceway, which is characterized by large changes in lateral camber angle ($$\approx 10^\circ$$ ≈ 10 ∘ ) on some parts of the track. A free-trajectory optimization is employed to solve a minimum-lap-time optimal control problem. The calculations highlight the practically observed importance of lateral camber variations.

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Section: Road Reconstructionmentioning

confidence: 99%

“…where ½X x ; X y ; X z T is given by (15). These equations are identical to those of the standard three-dimensional road model, once the road curvatures of the centre line are replaced by those at P; see equation (7.106) in [10].…”

Section: Vehicle Positioning and Kinematicsmentioning

confidence: 99%

Curved-ribbon-based track modelling for minimum lap-time optimisation

2021

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“…Equation ( 4) constraints n and χ, while the speed along the centreline ṡ is the link between the space-and the time-domain formulations, since dx/dt = ṡdx/ds. Indeed, it is common to solve minimum-time problems in the space domain instead of the time domain [1].…”

Section: Vehicle Positioningmentioning

confidence: 99%

“…(cos µ cos χ + sin µ sin φ sin χ) cos θ − cos φ sin χ sin θ cos φ sin χ cos θ + (cos µ cos χ + sin µ sin φ sin χ) sin θ cos µ sin φ sin χ − sin µ cos χ   , (20) where R(θ, µ, φ) is from (1). The projection on the ground plane x-y is obtained from the norm of the first two components of ( 20)…”

Section: Racing-line Reconstructionmentioning

confidence: 99%

“…Minimum lap-time simulations (MLTS) of road vehicles have been in use for many years [1,2]: they were historically formulated using quasi-steady-state (QSS) vehicle models on pre-defined two-dimensional trajectories [3][4][5][6][7][8][9][10], and evolved to employ transient vehicle models on three-dimensional roads [11][12][13][14][15], where the trajectory is a result of the optimization. Free-trajectory methods with QSS models have also been proposed both for two-dimensional [16] and three-dimensional roads [17,18].…”

Section: Introductionmentioning

confidence: 99%

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Three-dimensional fixed-trajectory approaches to the minimum-lap time of road vehicles

Lovato

Massaro

2021

Vehicle System Dynamics

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Minimum-lap-time simulations with quasi-steady-state models and predefined trajectory have been in use for many years. However, most of the published works deal with twodimensional roads and employ the so-called 'apex-finding' method. This paper focuses on the application to three-dimensional roads, both with an extension of the 'apex-finding' approach to three-dimensional scenarios and with an optimal control method. Both approaches are based on g-g-g diagrams, i.e. the three-dimensional extension of the well-known g-g maps. In addition, under the assumption that the predefined trajectory is determined from noisy data (e.g. logged from the real vehicle), the three-dimensional trajectory reconstruction problem is addressed, to find a smooth and drift-free racing line to be used in the minimum-time simulation -again an optimal control approach is employed for the trajectory reconstruction. Examples of application are given both for a car and a motorcycle.

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Comparison of Electric and Internal Combustion Engine SuperSport Bikes

Boretti¹

2023

Energy Tech

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Electric and internal combustion engine super sport bikes are compared for performance, energy efficiency, and range, based on market data and simulations of acceleration and top speed. Electric motorcycles deliver better performances, despite still suffering from a larger weight. They offer a much larger maximum torque, available from zero speed, and a slightly larger maximum power, producing sharper acceleration and higher top speed. Working with a nearly constant torque up to maximum power, they also offer excellent drivability on straight lines. They produce less noise, and no pollutant emissions, and permit better energy economy. They suffer from a reduced range and drivability over corners, for the larger weight and the less favorable mass distribution. Crashworthiness is a major issue of electric motorcycles, as they need to be “written‐off” even after minor crashes since the safety of the battery is difficult to be established. Electric motorcycles are competitive for city driving, where range or long‐time recharge is not an issue, sport driving is impractical, and regenerative braking may further save energy. The introduction of solid‐state batteries may further improve the appeal of electric supersport motorcycles, reducing the weight penalty for acceptable ranges, and providing a more balanced vehicle much easier to handle.

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Minimum-lap-time optimisation and simulation

Cited by 40 publications

References 104 publications

Curved-ribbon-based track modelling for minimum lap-time optimisation

Curved-ribbon-based track modelling for minimum lap-time optimisation

Three-dimensional fixed-trajectory approaches to the minimum-lap time of road vehicles

Comparison of Electric and Internal Combustion Engine SuperSport Bikes

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