Parasitic actuation delay limits the minimum employable time headway in connected and autonomous vehicles

TL;DR

The paper addresses how parasitic actuation delays constrain the minimum time headway in ACC, CACC, and CACC+ platoons and derives explicit lower bounds on $h_w$ that guarantee robust string stability for all delays $\tau \in (0,\tau_0]$. It develops a unified delay-system framework, obtains closed-loop spacing-error propagation through transfer functions $H(s;\tau)$ (and $H_j(s;\tau)$ for CACC+), and uses Pontryagin's interlacing theorem to ensure internal stability. The main contributions are the headway bounds $h_w>2\tau_0$ for ACC, $h_w>\frac{2\tau_0}{1+k_a}$ for CACC, and $h_w>\frac{4\tau_0}{(1+r)(1+rk_a)}$ for CACC+ (with $k_a<1$ or $k_a<1/r$ respectively), together with feasibility regions for controller gains. These results provide actionable guidelines for designing CAV platoons that maintain safety and throughput despite actuator delays, and are corroborated by numerical simulations showing stability gains and instability when headways are too small.

Abstract

Adaptive andcooperative adaptive cruise control (ACC and CACC) and next generation CACC (CACC+) systems usually employ a constant time headway policy (CTHP) for platooning of connected and autonomous vehicles (CAVs). In ACC, the ego vehicle uses onboard sensors to measure the position and velocity of the predecessor vehicle to maintain a desired spacing. The CACC and CACC+systems use additional information, such as acceleration(s) communicated through vehicle-to-vehicle (V2V) communication of the predecessor vehicle(s); these systems have been shown to result in improved spacing performance, throughput, and safety over ACC. Parasitic dynamics are generally difficult to model and the parasitic parameters (delay, lag, etc.) are difficult to obtain. Parasitic actuation delays can have deleterious effects and impose limits on the mobility and safety of CAVs. It is reasonable to assume that the bounds on parasitic actuation delays are known a priori. For CAVs, we need to address both internal stability and string stability in the presence of parasitic actuation delays. This requires robustness of string and internal stability for all values of parasitic actuation delays that are within the specified upper bound. In this paper, we provide the minimum employable time headway for ACC, CACC, and CACC+ (`r' predecessors look-ahead), respectively. The inclusion of the internal stability in the string stability condition is analyzed based on Pontryagin's interlacing theorem for time delay systems. We provide comparative numerical results to corroborate the achieved theoretical results.

Figures (16)

• Figure 1: An illustration of a connected and autonomous vehicle platoon with V2V communication.
• Figure 2: The admissible region of $k_v$ and $k_p$ (CACC case).
• Figure 3: The profile of $\vert H(j \omega; \tau) \vert$ (CACC case).
• Figure 4: The responses and roots of the real and imaginary parts of $\tau_0^2 \mathcal{D}(j \theta)$ where $\theta = \tau_0 \omega$.
• Figure 5: The curve of $\mathcal{D}_i^{\prime}(\omega) \mathcal{D}_r(\omega) - \mathcal{D}_i(\omega) \mathcal{D}_r^{\prime}(\omega)$.

Theorems & Definitions (18)

• Definition 1
• Definition 2.1: konduri2017robust
• Lemma 2.2: bhattacharyya2018linear
• Lemma 2.3: bhattacharyya2018linear
• Theorem 3.1
• proof
• Theorem 3.2
• proof
• Theorem 3.3
• proof