A hierarchical autonomous driver for a racing car: Real-time planning and tracking of the trajectory

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

A Gauss-Newton-Like Hessian Approximation for Economic NMPC

Economic Model Predictive Control (EMPC) has recently become popular because of its ability to control constrained nonlinear systems while explicitly optimizing a prescribed performance criterion. Large performance gains have been reported for many applications and closed-loop stability has been recently investigated. However, computational performance still remains an open issue and only few contributions have proposed real-time algorithms tailored to EMPC. We perform a step towards computationally cheap algorithms for EMPC by proposing a new positive-definite Hessian approximation which does not hinder fast convergence and is suitable for being used within the real-time iteration (RTI) scheme. We provide two simulation examples to demonstrate the effectiveness of RTI-based EMPC relying on the proposed Hessian approximation

Time-optimal Race Car Driving using an Online Exact Hessian based Nonlinear MPC Algorithm

This work presents an embedded nonlinear model predictive control (NMPC) strategy for autonomous vehicles under a minimum time objective. The time-optimal control problem is stated in a path-parametric formulation such that existing reliable numerical methods for real-time nonlinear MPC can be used. Building on previous work on timeoptimal driving, we present an approach based on a sequential quadratic programming type algorithm with online propagation of second order derivatives. As an illustration of our method, we provide closed-loop simulation results based on a vehicle model identified for small-scale electric race cars

Path planning for autonomous buses based on optimal control

This thesis presents an algorithm to generate trajectories for an autonomous bus approaching a bus stop. The path planning algorithm is formulated as an Optimal Control Problem (OCP) which is solved by means of nonlinear programming (NLP) using the direct multiple shooting method. This method has shown to be a good choice for solving nonlinear Boundary Value Problems (BVP) like this one -where there are constraints such as the limits of the road, the model dynamics or passengers comfort- due to its highly accurate solution and faster convergence and stability than other methods like direct single shooting methods. It uses a kinematic bicycle model with a coordinate transformation which uses the vehicle position along the path as independent variable instead of using time which permits the definition of the constraints independently of the vehicle’s speed. The OCP is solved in MATLAB using CasADi, a symbolic tool for solving nonlinear optimization problems that provides high level interfaces to make the problem writing easier, in addition of having better performance than similar tools. The proposed algorithm is evaluated in multiple scenarios like different kinds of bus stops and paths inside confined areas, giving as a result a trajectory that meets with the imposed constraints successfully. Experimental tests on a real autonomous bus are carried out, resulting in a smooth bus stop manoeuvre that the passengers evaluated as fully acceptable.Outgoin

A Controls-Oriented Approach For Modeling Professional Drivers During Ultra-High Performance Maneuvers

In the study of vehicle dynamics and controls, modeling ultra-high performance maneuvers (i.e., minimum-time vehicle maneuvering) is a fascinating problem that explores the boundaries of capabilities for a human controlling a machine. Professional human drivers are still considered the benchmark for controlling a vehicle during these limit handling maneuvers. Different drivers possess unique driving styles, i.e. preferences and tendencies in their local decisions and corresponding inputs to the vehicle. These differences in the driving style among professional drivers or sets of drivers are duly considered in the vehicle development process for component selection and system tuning to push the limits of achievable lap times. This work aims to provide a mathematical framework for modeling driving styles of professional drivers that can then be embedded in the vehicle design and development process. This research is conducted in three separate phases. The first part of this work introduces a cascaded optimization structure that is capable of modeling driving style. Model Predictive Control (MPC) provides a natural framework for modeling the human decision process. In this work, the inner loop of the cascaded structure uses an MPC receding horizon control strategy which is tasked with finding the optimal control inputs (steering, brake, throttle, etc.) over each horizon while minimizing a local cost function. Therein, we extend the typical fixed-cost function to be a blended cost capable of optimizing different objectives. Then, an outer loop finds the objective weights used in each MPC control horizon. It is shown that by varying the driver\u27s objective between key horizons, some of the sub-optimality inherent to the MPC process can be alleviated. In the second phase of this work, we explore existing onboard measurements of professional drivers to compare different driving styles. We outline a novel racing line reconstruction technique rooted in optimal control theory to reconstruct the driving lines for different drivers from a limited set of measurements. It is demonstrated that different drivers can achieve nearly identical lap times while adopting different racing lines. In the final phase of this work, we use our racing line technique and our cascaded optimization framework to fit computable models for different drivers. For this, the outer loop of the cascaded optimization finds the set of objective weights used in each local MPC horizon that best matches simulation to onboard measurements. These driver models will then be used to optimize vehicle design parameters to suit each driving style. It will be shown that different driving styles will yield different parameters that optimize the driver/vehicle system