About Strong String Stability of a Vehicle Chain with Time-Headway Control

Abstract

This paper deals with the problem of string stability in a chain of accelerationcontrolled vehicles, i.e. how input disturbances affect the distributed system for very long chains. There exist variants of string stability, like avoiding that a local disturbance gets amplified along the chain, or more strongly ensuring that the output vector's p−norm remains bounded for any bounded vector of input disturbances independently of the string length. They are all impossible to achieve with any linear controller if the vehicles only use relative information of few vehicles in front. Previous work has shown that adding absolute velocity into the controller, allows to at least avoid amplification of a local disturbance. In this paper, we consider the stronger definitions of string stability, under this same relaxation of using absolute velocity in the controller. We prove that the influence from input vector to output vector cannot be bounded independently of chain length in the most popular 2−norm sense, with any bounded stabilizing linear controller; while a proportional derivative (PD) controller can guarantee it in the practically relevant ∞−norm sense. Moreover, we identify the disturbance acting on the leader as the main issue for string stability. * Arash Farnam is with the ID Lab, Department of Electronics and Information Systems (ELIS), Faculty of Engineering and Architecture, Ghent University; Technologiepark Zwijnaarde 914, 9052 Zwijnaarde(Ghent), Belgium arash.farnam@ugent.be., Alain Sarlette. is with ELIS, Ghent University, Belgium; and with the QUANTIC lab, INRIA Paris; 2 rue Simone Iff, 75012 Paris, France. alain.sarlette@inria.fr †

String stability of energy-saving aircraft formations

“…But even supposing the location of the wakes can be measured precisely, there remains the problem that cascaded formations such as these are subject to disturbance amplification from agent to agent, which can grow unbounded as the number of agents increases. This phenomenon, known as string instability arises frequently in the literature on vehicle platoons traveling on roads [5][6][7]. For example, a small deceleration by one vehicle in a long sequence of self-driving vehicles on a highway might grow from one car to the next and eventually result in a collision.…”