Curvature-Based Geometric Approach for the Lateral Control of Autonomous Cars

Abstract

Several approaches exist for the lateral control of autonomous vehicles. Among them are the geometric approaches. They are shown to be robust to disturbances and able to manage complex tracks. Their main advantage lies on the fact that they are explainable, in the sense that their behavior can be analyzed to provide guarantees about their limitations. However, they do not give the quality of results that can be obtained using other control principles, mostly because of design issues. This paper aims to tackle these issues by proposing a novel geometric approach based on Frenet Serret formulas to reach the level of quality proposed by the other approaches, while still benefiting from the advantages of geometric approaches. A numerical analysis of the proposed control approach show its advantage: Simulation results and tests on a real autonomous car are provided.

Introduction

Researches about autonomous cars have now been a trendy topic for the last three decades, notably because of the numerous expected outcomes (increased safety, improved road capacity, shared vehicles, increased fuel efficiency, etc. [1], [2]), but also because designing a fully autonomous car (reaching SAE level 4 and 5 [3]) is still a challenging task [4]. Recently, a particular attention is given to the interactions of the robot-driver either with the other road users in the case of fully autonomous vehicles, or with the human-driver for safety and acceptability reasons. However, the perquisite of testing the emergent technologies is an automation driving system able to make the vehicle respecting its planned path. Hence, driving automation solutions that can be easily deployed on a wide variety of vehicles and situations help for saving a valuable amount of time needed for rapidly extending the scope of the autonomous driving systems.

A key point of car driving automation is the ability to follow a predefined path, which is known as “path tracking control” or “lateral control”. For Ackermann-like vehicles (like cars), the problem of path tracking control is to compute either the angle to apply on the steering wheel (i.e. the angle of the front wheels) or the effort to apply on it, to keep the vehicle on a predefined track. It is a famous and widely studied control problem [5]. The challenges for the definition of path tracking control are to be able to manage all possible tracks and to ensure passengers comfort and safety while being robust to the latency (the delay between the perception and the action by the control software), and the perturbations (the error in the data provided by the sensors and the error in the application of the action).

To perform the path following task, several approaches have been proposed that can be divided into the following categories: geometric controllers, dynamic controllers, optimal controllers (LQR), adaptive and intelligent controllers (neural networks and fuzzy logic [6], [7]), model-based controllers (MPC [8], [9]), and classical controllers (PID [10], [11]).

Each different category has its specific advantages and drawbacks. For instance, nowadays, neural networks are giving really interesting results [12], and can directly use as input the signal of a camera for lane-keeping [13] (reducing the required amount of sensors), but the drawback is the limited explainability of the command, making it hard to define the limits of the command and to predict its behavior in every situation, and in the end making it hard to get the legal approval required to use it on open roads. Dynamic and optimal controllers are also efficient [14], but needs tuning, are computationally demanding and requires a lot of data about the model and the dynamic of the vehicles, which can be difficult to obtain accurately (the vehicle’s split mass, the center of gravity location, the moment of inertia, the cornering stiffness of tires). PID and MPC controllers are difficult to design and to tune and are dependent on the track and the vehicles’ characteristics. On the other hand, most of the geometric approaches are easy to understand, study, and explain, and they are also known to be computationally efficient and robust to perturbations, however, the given results are not as good as the results provided by the other classes of solutions, and are also requiring tuning, which may lead to over-fitting a specific track.

The current limits of the geometric approaches are leaving room for improvement. A new geometric approach could provide better results while requiring a limited amount of parameters and tuning, and not being track-dependent. The contribution of this paper is to propose a new geometric approach for lateral control, with the benefits of geometric approaches, while overcoming some of their drawbacks.

Thus, after a quick overview of the common solutions for lateral control (Section 2), this paper proposes a contribution to the path tracking problem with a new geometric approach to define the angle of the wheel as a function of the state of the car (Section 3.1). A numerical analysis of the command is provided to highlight its characteristics (steady-state error, reaction-time, overshoot, etc.) compared to the most common geometric approaches (Section 3.3). Then, to ensure the efficiency and the robustness of the command, simulations are performed including simulated perturbations (with simulated latency and inaccuracy of the sensors), and the results are compared to existing commands (Section 4.1). Finally, to confirm the feasibility of the approach, implementation is made on a real autonomous car executing the presented command, and the results are then discussed (Section 4.2).