The Optimal Manoeuvre

Biral, Francesco; Lio, Mauro Da

doi:10.1002/9781118536391.ch5

Cited by 3 publications

(5 citation statements)

References 26 publications

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“…The smooth absolute value function absReg(•) is defined in Appendix B. We introduce the additional superelliptic constraints (7e,7g) for a better modeling of the combined braking performance, which is conceptually similar to [23] and [44].…”

Section: ) E-nmpc Problemmentioning

confidence: 99%

A Physics-Driven Artificial Agent for Online Time-Optimal Vehicle Motion Planning and Control

Piccinini,

Taddei,

Larcher

et al. 2023

IEEE Access

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This paper presents a hierarchical framework with novel analytical and neural physics-driven models, to enable the online planning and tracking of minimum-time maneuvers, for a vehicle with partiallyunknown parameters. We introduce a lateral speed prediction model for high-level motion planning with economic nonlinear model predictive control (E-NMPC). A low-level steering controller is developed with a novel feedforward-feedback physics-driven artificial neural network (NN). A longitudinal dynamic model is identified to tune a low-level speed-tracking controller. The high-and low-level control models are identified with an automatic three-step scheme, combining open-loop and closed-loop maneuvers to model the maximum acceleration G-G-v performance constraint for E-NMPC, and to capture the effect of the longitudinal acceleration on the lateral dynamics. The proposed framework is used in a simulation environment, for the online closed-loop control of a highly detailed sedan vehicle simulator, whose parameters are partiallyunknown. Two different circuits are adopted to validate the approach, and a robustness analysis is performed by varying the vehicle mass and the load distribution. A minimum-time optimal control problem is solved offline and used for a comparison with the closed-loop results. A video demonstrating both the automatic three-step identification scheme and the motion planning and control results is available at the following link: https://www.youtube.com/watch?v=xQ_T96IjGP8. INDEX TERMSAutonomous racing, model learning, model predictive control (MPC), motion planning, neural networks, trajectory optimization. Open Access funding provided by 'Università degli Studi di Trento' within the CRUI CARE Agreement

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Section: ) E-nmpc Problemmentioning

confidence: 99%

A Physics-Driven Artificial Agent for Online Time-Optimal Vehicle Motion Planning and Control

Piccinini,

Taddei,

Larcher

et al. 2023

IEEE Access

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“…The solution of the OCP can be obtained via general optimal control software, as described,() where various methods for OCP are presented. However, they cannot take advantage of the analytic solution and hence, although having a more general purpose, they are slower than the present method when applied to this specific problem.…”

Section: The Ocpmentioning

confidence: 99%

“…All the boundary conditions are fixed: without loss of generality the initial position is 0, the final position is L (the length of the curve), the initial and final velocities are v i and v f , respectively, both assumed nonnegative. The solution of the OCP can be obtained via general optimal control software, as described [6,9,10,11,13,21,31], where various methods for OCP are presented. However they cannot take advantage of the analytic solution and hence, although being more general purpose, they are slower than the present method when applied to this specific problem.…”

Section: The Optimal Control Problemmentioning

confidence: 99%

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Semianalytical minimum‐time solution for the optimal control of a vehicle subject to limited acceleration

Bertolazzi

Frego

2017

Optim Control Appl Methods

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Summary A semianalytic solution of the minimum‐time optimal control problem of a carlike vehicle is herein presented. The vehicle is subject to the effect of laminar (linear) and aerodynamic (quadratic) drag, taking into account the asymmetric bounded longitudinal accelerations. This yields a nonlinear differential equation of the Riccati kind. The associated analytic solution exists in closed form, but it is numerically ill conditioned in some situations; hence, it is reformulated using asymptotic expansions that keep the numerical computations accurate and robust in all cases. Therefore, the proposed algorithm is designed to be fast and robust in sight to be the fundamental module of a more extended optimal control problem that considers a given clothoid curve as the trajectory and the presence of a constraint on the lateral acceleration of the vehicle. The numerical stability of the computation for limit values of the parameters is essential, as shown in the numerical tests.

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“…Borrowing upon principles of vehicle dynamics, the optimal trajectory [31] can be defined as the one that the cyclist has to follow to complete the track in the minimum time. The choice of the trajectory (i.e., the cornering strategy [32]) depends on the space available on the road and it is subject to dynamics and physical constraints, such as the maximum grip of the tyres and the available energy sources.…”

Section: Introductionmentioning

confidence: 99%

Prediction of pacing and cornering strategies during cycling individual time trials with optimal control

Zignoli

Biral

2020

Sports Eng

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A new dynamic model for predicting road cycling individual time trials with optimal control was created. The model included both lateral and longitudinal bicycle dynamics, 3D road geometry, and anaerobic source depletion. The prediction of the individual time trial performance was formulated as an optimal control problem and solved with an indirect approach to find the pacing and cornering strategies in the respect of the physical/physiological limits of the system. The model was tested against the velocity and power output data collected by professional cyclists in two individual time trial Giro d'Italia data sets: the first data set (Rovereto, n = 15) was used to adjust the parameters of the model and the second data set (Verona, n = 13) was used to test the predictive ability of the model. The simulated velocity fell in the CI 95% of the experimental data for 32 and 18% of the duration of the course for Rovereto and Verona stages, respectively. The simulated power output fell in the CI 95% of the experimental data for 50 and 25% of the duration of the course for Rovereto and Verona stages respectively. This framework can be used to input rider's physical/physiological characteristics, 3D road geometry, and conditions to generate realistic velocity and power output predictions in individual time trials. It, therefore, constitutes a tool that could be used by coaches and athletes to plan the pacing and cornering strategies before the race.

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The Optimal Manoeuvre

Cited by 3 publications

References 26 publications

A Physics-Driven Artificial Agent for Online Time-Optimal Vehicle Motion Planning and Control

A Physics-Driven Artificial Agent for Online Time-Optimal Vehicle Motion Planning and Control

Semianalytical minimum‐time solution for the optimal control of a vehicle subject to limited acceleration

Prediction of pacing and cornering strategies during cycling individual time trials with optimal control

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