Study on stability and scalability of vehicular platoon with a bidirectional ring interconnection

Abstract

This paper studies the stability and scalability of the platoon where multiple vehicles move in a closed roadway and are coupled in a bidirectional ring. Each vehicle regulates its longitudinal motion based on bidirectional asymmetric control with triple asymmetry factors. By exploiting Hermite stability criterion, we derive necessary and sufficient conditions of stability for the n-vehicle platoon. Based on parametric robustness analysis, necessary and sufficient conditions of scalably asymptotic stability are further obtained, meaning that the stability is independent of the number of vehicles in the platoon. It is proved that symmetric spacing feedback is necessary for scalably asymptotic stability and the first spatial mode is the least stable among all the non-zero modes. Numerical computations show that the stability region in the space of feedback gains is favourable when the asymmetry level on speed gain is small and the asymmetry level on acceleration gain is large, whereas it may deteriorate rapidly when these two asymmetry factors have different signs.

Study on the local and global performance of homogeneous platoon with a bidirectional ring interconnection

“…highway traffic [5,6,11]. By contrast, there does not exist a leading vehicle in ring interconnections, in which vehicles at the head and the tail of the platoon become neighbours at the interaction level [10,[12][13][14], and sometimes also geometry level [15][16][17][18]. Hence, the information flow topology exhibits a closed ring.…”

“…However, considering that the utilisation of information under the PF interaction is not sufficient, some works on platoon systems with ring interconnections used the bidirectional coupling [13,14]. Also, some literature has shown that when additionally incorporating the information of the vehicles behind into the CAVs' control, the capability of CAVs in dissipating traffic perturbations is further strengthened, which, though, was based on the control of a single CAV among human-driven vehicles [25].…”

“…Similar to unidirectional coupling, a commonly used assumption is that in order to make sure that vehicles can track a constant velocity with the zero steady-state error, the open-loop model of each vehicle, P (s)K (s), should contain at least two integrators, where P (s) and K (s) are the transfer functions of vehicle and controller, respectively. That is, P (s)K (s) can be expressed as P (s)K (s) = 1 s 2 L(s) with L(0) ≠ 0 [13,14]. Stüdli et al [13] studied ring vehicular platoons with the communication range r where the ego-vehicles used weighted information from r vehicles ahead with the normalised weighting vector [a 1 ⋯ a r ] and r vehicles behind with the normalised weighting vector [b 1 ⋯ b r ], where the normalisation means ∑ r i=1 a i + ∑ r i=1 b i = 1.…”

“…They found that symmetric weights defined by ∑ r i=1 (a i − b i )i = 0 was necessary for the stability of long platoons and furthermore showed that it is possible to achieve the general  2 string stability [26] by selecting a communication range r that increases linearly with the platoon size. Zhang et al [14] designed a decentralised controller fed with position, velocity, and acceleration from the immediate front neighbour and the immediate back neighbour, i.e. with the communication range r = 1 in the framework of ref.…”

“…In contrast to ref. [13] which used uniform biasing level of control gain for all state components, Zhang et al [14] brought each component with separate and independent asymmetry (biasing) level, thus introducing more flexibility for control. Based on the Hermite stability criterion, they obtained the necessary and sufficient conditions of scalably asymptotical stability (SAS), which was defined as the stability of the platoon being independent of the platoon size.…”