Self-driving vehicles are a maturing technology with the potential to reshape mobility by enhancing the safety, accessibility, efficiency, and convenience of automotive transportation. Safety-critical tasks that must be executed by a self-driving vehicle include planning of motions through a dynamic environment shared with other vehicles and pedestrians, and their robust executions via feedback control. The objective of this paper is to survey the current state of the art on planning and control algorithms with particular regard to the urban setting. A selection of proposed techniques is reviewed along with a discussion of their effectiveness. The surveyed approaches differ in the vehicle mobility model used, in assumptions on the structure of the environment, and in computational requirements. The side by side comparison presented in this survey helps to gain insight into the strengths and limitations of the reviewed approaches and assists with system level design choices.

A Survey of Motion Planning and Control Techniques for Self-Driving Urban Vehicles

In this paper, a model predictive control (MPC) approach for controlling an active front steering system in an autonomous vehicle is presented. At each time step, a trajectory is assumed to be known over a finite horizon, and an MPC controller computes the front steering angle in order to follow the trajectory on slippery roads at the highest possible entry speed. We present two approaches with different computational complexities. In the first approach, we formulate the MPC problem by using a nonlinear vehicle model. The second approach is based on successive online linearization of the vehicle model. Discussions on computational complexity and performance of the two schemes are presented. The effectiveness of the proposed MPC formulation is demonstrated by simulation and experimental tests up to 21 m/s on icy roads

Predictive Active Steering Control for Autonomous Vehicle Systems

Self-driving vehicles are a maturing technology with the potential to reshape mobility by enhancing the safety, accessibility, efficiency, and convenience of automotive transportation. Safety-critical tasks that must be executed by a self-driving vehicle include planning of motions through a dynamic environment shared with other vehicles and pedestrians, and their robust executions via feedback control. The objective of this paper is to survey the current state of the art on planning and control algorithms with particular regard to the urban setting. A selection of proposed techniques is reviewed along with a discussion of their effectiveness. The surveyed approaches differ in the vehicle mobility model used, in assumptions on the structure of the environment, and in computational requirements. The side-by-side comparison presented in this survey helps to gain insight into the strengths and limitations of the reviewed approaches and assists with system level design choices.

A Survey of Motion Planning and Control Techniques for Self-driving Urban Vehicles

The Magic Formula Tyre Model

An account is given of the latest version 3 of the Magic Formula tyre model. The model provides a set of mathematical formulae from which the forces and moment acting from road to tyre can be calculated at longitudinal, lateral and camber slip conditions, which may occur simultaneously. The model aims at an accurate description of measured steady-state tyre behaviour. The coefficients of the basic formula represent typifying quantities of the tyre characteristic. By selecting proper values, the characteristics for either side force, aligning torque or fore and aft force can be obtained. The new version of the model contains physically based formulations to avoid the introduction of correction factors. Double-sided, possibly non-symmetric pure slip curves are employed as the basis for combined slip calculations. Suggestions are given to estimate the driving part of the longitudinal slip curve and to represent the characteristic at rolling backwards.

The magic formula tyre model

Tyre characteristics and vehicle handling and stability Basic tyre modelling considerations Theory of steady-state slip force and moment generation Semi-empirical steady-state tyre models Non-steady-state out-of-plane string-based tyre model Theory of the wheel-shimmy phenomenon Single contact point transient tyre models Applications of transient tyre models Short wavelength intermediate frequency tyre model Dynamic Tyre Model Performance Motorcycle dynamics Steady state and dynamic tyre testing References Appendix List of symbols Index

Tyre and vehicle dynamics

This book, which is intended for practising and student engineers, provides a complete reference on the mechanical behaviour of pneumatic tyres and their impact on vehicle performance. The comprehensive scope of the book includes developing an understanding of mathematical models of tyre behaviour, the incorporation of these models into vehicle models, and presents an applied understanding of how the tyre influences vehicle handling. The book is supported by practical experimental observations and exercises. Pacejka's tyre model is the subject of continued development, particularly in extending its validity range to modelling higher frequencies and short wavelength obstacles and testing, which are covered in new chapters in the 2nd edition.

Tire and Vehicle Dynamics

A new way of representing tyre data obtained from measurements in pure cornering and pure braking conditions has been developed in order to further improve the Dynamic Safety of vehicles. The method makes use of a formula with coefficients which describe some of the typifying quantities of a tyre, such as slip stiffnesses at zero slip and force and torque peak values. The formula is capable of describing the characteristics of side force, brake force and self aligning torque with great accuracy. This mathematical representation is limited to steady-state conditions during either pure cornering or pure braking and forms the basis for a model describing tyre behaviour during combined braking and cornering.

Hans B. Pacejka

Papers

Tyre and vehicle dynamics

Tire and Vehicle Dynamics

The Magic Formula Tyre Model

Tyre Modelling for Use in Vehicle Dynamics Studies

The magic formula tyre model