Minimum-time optimal control for vehicles with active rear-axle steering, transfer case and variable parameters

Sedlacek, Tadeas; Odenthal, Dirk; Wollherr, Dirk

doi:10.1080/00423114.2020.1742925

Cited by 9 publications

(4 citation statements)

References 41 publications

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“…The weight 𝜔 𝑖 (0 ≤ 𝑖 ≤ 𝑛 − 1) at the interpolation point is used to control the interpolation function, and the model is constructed with Lebesgue's constant minimised, i.e., min 𝑎≤𝑥≤𝑏 sup Λ 𝑛 , as the objective function, so that the centre of gravity interpolating function maintains a slanting asymptote whilst satisfying other constraints to ensure that the centre of gravity rational interpolation has no unreachable points and no poles [10].…”

Section: Rational Interpolation Of the Centre Of Gravity Based On Ske...mentioning

confidence: 99%

Based on Lebesgue's constant minimum skew-preserving asymptote of rational interpolation of the centre of gravity

Yang,

Zhao

2024

Fourth International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2024)

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This study focuses on an in-depth investigation of centre of gravity rational interpolation as an important rational interpolation method. An important feature is that different interpolation weights can be used to derive different centre of gravity rational interpolation functions. By carefully choosing the interpolation weights, we can ensure that the centre of gravity rational interpolation does not produce poles or unreachable points, thus improving the numerical stability of the interpolation. However, when we try to approximate the interpolated function with oblique asymptotic properties, the traditional rational interpolation method may not be able to maintain the original oblique asymptotic properties. To cope with this problem, this paper proposes a novel centre of gravity rational interpolation method aimed at maintaining the oblique asymptote. First, we systematically investigate the conditions that the centre of gravity rational interpolation method needs to satisfy in order to ensure that the slant asymptote property is maintained. Then, we develop a complex optimisation model with the minimum value of Lebesgue's constant as the objective function, along with multiple constraints, including the rational interpolation of the centre of gravity not generating poles and unreachable points, the maintenance of the slanting asymptote property by the rational interpolation function of the centre of gravity, as well as the normalisation of the centre of gravity weights. By solving this model, we obtain the optimal values of the interpolation weights, which leads to the centre of gravity rational interpolation function possessing the slanting asymptote property. Through detailed numerical examples, we validate the effectiveness of this algorithm, demonstrating its excellent performance in approximating the interpolated function with oblique asymptotic properties. This research work not only provides new insights into theoretical mathematics, but also offers a more accurate and controllable interpolation method for engineering, science and data analysis, further promoting research and applications in related fields.

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Section: Rational Interpolation Of the Centre Of Gravity Based On Ske...mentioning

confidence: 99%

Based on Lebesgue's constant minimum skew-preserving asymptote of rational interpolation of the centre of gravity

Yang,

Zhao

2024

Fourth International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2024)

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“…The NLP is IPOPT [47]. The same solution technique is employed in [76] to study the effect of active rear-axle steering, and longitudinal torque allocation. The illustration track is again the Nuerburgring.…”

Section: The 2010smentioning

confidence: 99%

Minimum-lap-time optimisation and simulation

Massaro

Limebeer

2021

Vehicle System Dynamics

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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 optimized. The fundamentals of nonlinear optimal control are summarized. 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 summarized with a focus on recent developments. Both cars and motorcycles are considered.

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“…The core of autonomous racing lies in trajectory optimization, which involves planning the time-optimal racing line for a given parameterized racetrack. This process typically entails a comprehensive consideration of various vehicle performance factors and optimization objectives, including drivetrain configuration [ 6 ], tire–road friction coefficients [ 7 ], active rear-axle steering [ 8 ], gear ratios, aerodynamics, roll stiffness, suspension characteristics, and other variable parameters [ 9 , 10 , 11 , 12 ]. Trajectory optimization problems are typically discretized via the direct collocation method and solved using nonlinear programming (NLP) solvers.…”

Section: Introductionmentioning

confidence: 99%

Time-Optimal Trajectory Planning and Tracking for Autonomous Vehicles

Li,

Chen,

Ren

2024

Sensors

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This article presents a hierarchical control framework for autonomous vehicle trajectory planning and tracking, addressing the challenge of accurately following high-speed, at-limit maneuvers. The proposed time-optimal trajectory planning and tracking (TOTPT) framework utilizes a hierarchical control structure, with an offline trajectory optimization (TRO) module and an online nonlinear model predictive control (NMPC) module. The TRO layer generates minimum-lap-time trajectories using a direct collocation method, which optimizes the vehicle’s path, velocity, and control inputs to achieve the fastest possible lap time, while respecting the vehicle dynamics and track constraints. The NMPC layer is responsible for precisely tracking the reference trajectories generated by the TRO in real time. The NMPC also incorporates a preview algorithm that utilizes the predicted future travel distance to estimate the optimal reference speed and curvature for the next time step, thereby improving the overall tracking performance. Simulation results on the Catalunya circuit demonstrated the framework’s capability to accurately follow the time-optimal raceline at an average speed of 116 km/h, with a maximum lateral error of 0.32 m. The NMPC module uses an acados solver with a real-time iteration (RTI) scheme, to achieve a millisecond-level computation time, making it possible to implement it in real time in autonomous vehicles.

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Minimum-time optimal control for vehicles with active rear-axle steering, transfer case and variable parameters

Cited by 9 publications

References 41 publications

Based on Lebesgue's constant minimum skew-preserving asymptote of rational interpolation of the centre of gravity

Based on Lebesgue's constant minimum skew-preserving asymptote of rational interpolation of the centre of gravity

Minimum-lap-time optimisation and simulation

Time-Optimal Trajectory Planning and Tracking for Autonomous Vehicles

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