Nonlinear dynamics of autonomous vehicles with limits on acceleration

Abstract

The stability of autonomous vehicle platoons with limits on acceleration and deceleration is determined.If the leading-vehicle acceleration remains within the limits, all vehicles in the platoon remain within the limits when the relative-velocity feedback coefficient is equal to the headway time constant [ ⁄ .Furthermore, if the sensitivity ⁄ , no collisions occur. String stability for small perturbations is assumed and the initial condition is taken as the equilibrium state. Other values of and that give stability with no collisions are found from simulations. For vehicles with non-negligible mechanical response, simulations indicate that the acceleration-feedback-control gain might have to be dynamically adjusted to obtain optimal performance as the response time changes with engine speed. Stability is demonstrated for some perturbations that cause initial acceleration or deceleration greater than the limits, yet do not cause collisions.

Failure of classical traffic flow theories: Stochastic highway capacity and automatic driving

“…Over time several scientific groups have used hypotheses of the three-phase theory and developed new models and new results in the framework of the three-phase theory (e.g., [550,551,552,553,554,555,556,557,558,559,560,561,562], Through the use of traffic models in the framework of the three-phase theory, Davis has derived a number of novel results related to ITS applications, in particular, for cooperative vehicle control to avoid synchronized flow at bottlenecks [558], for wirelessly connected ACC-vehicles [603], for predicting travel time to limit congestion [561], for realizing Wardrop equilibria with real-time traffic information [560], for traffic control at highway bottlenecks [559], and for on-ramp metering near the transition to the synchronous flow phase [552]. Davis was also one of the first who studied the effect of ACC-vehicles on traffic flow with a three-phase traffic flow model [551].…”

String stable cooperative adaptive cruise control under actuator saturation

“…İspat: (22)'de verilen denklemde ilk olarak ( ) ≤ eşitliğinin doğruluğunu ispatlayalım. ( 19)-( 21)'de bulunan denklemlerden aşağıdaki eşitlikleri yazabiliriz.…”

“…Literatür taramalarına baktığımızda, bu çalışma bu konuda yapılan ilk çalışmadır. Sadece [22]'de doğrusal araç modelini kullanarak ivme doyumunun dizi kararlılığı üzerindeki etkileri ile ilgili çalışma yapılmıştır. Çalışmada lider aracın ivmesi belirlenen sınırlar içerisinde kaldığında, dizide bulunan tüm araçların istenilen sınırlar içerisinde kaldığı görülmüştür.…”

Autonomous Driving in the Framework of Three-Phase Traffic Theory

“…(iii) Autonomous driving vehicles based on the three-phase theory decrease the probability of traffic breakdown at the bottleneck in mixed traffic flow consisting of human driving and autonomous driving vehicles; on the contrary, even a single autonomous driving vehicle based on the classical approach can provoke traffic breakdown at the bottleneck in mixed traffic flow. 64.60.Cn,05.65.+b It is generally assumed that future vehicular traffic is a mixed traffic flow consisting of human driving and autonomous driving vehicles [1][2][3][4][5][6][7][8][9]. Autonomous driving vehicles should considerably enhance capacity of a traffic network that is limited by traffic breakdown at network bottlenecks.…”

“…where v is the speed of the ACC-vehicle, v ℓ is the speed of the preceding vehicle; here and below v, v ℓ , and g are time-functions; K 1 and K 2 are coefficients of ACC adaptation. It is well-known that there can be string instability of a long enough platoon of ACCvehicles (1) [2][3][4][5][6][7][8][9] that occurs under condition K 2 <…”