Littérature scientifique sur le sujet « Optimal Control, Vehicle Dynamics, Autonomous Racing, Minimum Lap Time »

The aim of this study was to develop trajectory planning that would allow an autonomous racing car to be driven as close as possible to what a driver would do, defining the most appropriate inputs for the current scenario. The search for the optimal trajectory in terms of lap time reduction involves the modeling of all the non-linearities of the vehicle dynamics with the disadvantage of being a time-consuming problem and not being able to be implemented in real-time. However, to improve the vehicle performances, the trajectory needs to be optimized online with the knowledge of the actual vehicle dynamics and path conditions. Therefore, this study involved the development of an architecture that allows an autonomous racing car to have an optimal online trajectory planning and path tracking ensuring professional driver performances. The real-time trajectory optimization can also ensure a possible future implementation in the urban area where obstacles and dynamic scenarios could be faced. It was chosen to implement a local trajectory planning based on the Model Predictive Control(MPC) logic and solved as Linear Programming (LP) by Sequential Convex Programming (SCP). The idea was to achieve a computational cost, 0.1 s, using a point mass vehicle model constrained by experimental definition and approximation of the car’s GG-V, and developing an optimum model-based path tracking to define the driver model that allows A car to follow the trajectory defined by the planner ensuring a signal input every 0.001 s. To validate the algorithm, two types of tests were carried out: a Matlab-Simulink, Vi-Grade co-simulation test, comparing the proposed algorithm with the performance of an offline motion planning, and a real-time simulator test, comparing the proposed algorithm with the performance of a professional driver. The results obtained showed that the computational cost of the optimization algorithm developed is below the limit of 0.1 s, and the architecture showed a reduction of the lap time of about 1 s compared to the offline optimizer and reproducibility of the performance obtained by the driver.

The problem of maneuvering a vehicle through a race course in minimum time requires computation of both longitudinal (brake and throttle) and lateral (steering wheel) control inputs. Unfortunately, solving the resulting nonlinear optimal control problem is typically computationally expensive and infeasible for real-time trajectory planning. This paper presents an iterative algorithm that divides the path generation task into two sequential subproblems that are significantly easier to solve. Given an initial path through the race track, the algorithm runs a forward–backward integration scheme to determine the minimum-time longitudinal speed profile, subject to tire friction constraints. With this fixed speed profile, the algorithm updates the vehicle's path by solving a convex optimization problem that minimizes the resulting path curvature while staying within track boundaries and obeying affine, time-varying vehicle dynamics constraints. This two-step process is repeated iteratively until the predicted lap time no longer improves. While providing no guarantees of convergence or a globally optimal solution, the approach performs very well when validated on the Thunderhill Raceway course in Willows, CA. The predicted lap time converges after four to five iterations, with each iteration over the full 4.5 km race course requiring only 30 s of computation time on a laptop computer. The resulting trajectory is experimentally driven at the race circuit with an autonomous Audi TTS test vehicle, and the resulting lap time and racing line are comparable to both a nonlinear gradient descent solution and a trajectory recorded from a professional racecar driver. The experimental results indicate that the proposed method is a viable option for online trajectory planning in the near future.

Chapter 9 deals with the solution of minimum-time and minimum-fuel vehicular optimal control problems. These problems are posed as fuel usage optimization problems under a time-of-arrival constraint, or minimum-time problems under a fuel usage constraint. The first example considers three variants of a simple fuel usage minimization problem under a time-of-arrival constraint. The first variant is worked out theoretically, and serves to highlight several of the structural features of these problems; the other two more complicated variants are solved numerically.The second example is also a multi-stage fuel usage minimization problem under a timeof- arrival constraint.More complicated track and vehicle models are then employed; the problem is solved numerically. The third problem is a lap time minimization problem taken from Formula One and features a thermoelectric hybrid powertrain. The fourth and final problem is a minimum-time closed-circuit racing problem featuring a racing motorcycle and rider.

A web based VRCC (Virtual Racing Car Championship) application is here presented. The application is intended for educational purposes to teach students a variety of topics of the teaching course “Vehicle Dynamics and Control” in Mechatronics Master Degree Course; the present application forces students to understand the relevant parameters that govern the dynamic performance of racing cars. The application relies on an optimal control library, which is capable of calculating minimum lap times of a racing car on the basis of a comprehensive symbolic description of an open-wheel racing car dynamic model. Students are enrolled in a number of teams competing in a Championship to attain the minimum lap time (i.e., the pole position) on three circuits by choosing the appropriate setup of the racing car. The ranking is based on the best lap time obtained in the qualification session. The application stimulates students to adopt a multidisciplinary approach in a challenging and instructive environment, where they are in a position to apply a broad range of knowledges and abilities they have acquired during the Mechanotronics engineering course.

The problem of maneuvering a vehicle through a race course in minimum time requires computation of both longitudinal (brake and throttle) and lateral (steering wheel) control inputs. Unfortunately, solving the resulting nonlinear optimal control problem is typically computationally expensive and infeasible for real-time trajectory planning. This paper presents an iterative algorithm that divides the path generation task into two sequential subproblems that are significantly easier to solve. Given an initial path through the race track, the algorithm runs a forward-backward integration scheme to determine the minimum-time longitudinal speed profile, subject to tire friction constraints. With this speed profile fixed, the algorithm updates the vehicle’s path by solving a convex optimization problem that minimizes the resulting path curvature while staying within track boundaries and obeying affine, time-varying vehicle dynamics constraints. This two-step process is repeated iteratively until the predicted lap time no longer improves. While providing no guarantees of convergence or a globally optimal solution, the approach performs well when tested on the Thunderhill Raceway course in Willows, CA. The lap time reaches a minimum value after only three iterations, with each iteration over the full 5 km race course requiring only thirty seconds of computation time on a laptop computer. The resulting vehicle path and speed profile match very well with a nonlinear gradient descent solution and a path driven by a professional racecar driver, indicating that the proposed method is a viable option for online trajectory planning in the near future.