Enhancing Vehicle Platooning Safety via Control Node Placement and Sizing under State and Input Bounds

TL;DR

The paper addresses safety in vehicle platooning under cyber-attacks that disrupt CACC communications. It introduces a two-stage ASAP algorithm that decouples actuator locations from input bounds, using a controllability Gramian $W_c$ to quantify placement impact and an ellipsoidal over-approximation of the reachable set $\\mathcal{R}_{\\mathcal S}$ to enforce safety against a dangerous set $\\mathcal D$. The AP stage uses a greedy, supermodular objective $\\log\\det(W_c^{-1})$ to select defense locations, while the AS stage minimizes the trace of the redesigned bounds $\\hat{\\boldsymbol\\Gamma}$ subject to $\\mathcal E(\\boldsymbol Y^{-1}, m) \\cap \\mathcal D = \\emptyset$, ensuring safety with limited actuators. Case studies on 3- and 20-vehicle platoons show that a small number of defensively placed actuators with tightened bounds can prevent intersection with danger regions, preserving safety and defense efficiency. The results suggest a scalable, practical defense framework for cyber-physical vehicle platoons.

Abstract

Vehicle platooning with Cooperative Adaptive Cruise Control improves traffic efficiency, reduces energy consumption, and enhances safety but remains vulnerable to cyber-attacks that disrupt communication and cause unsafe actions. To address these risks, this paper investigates control node placement and input bound optimization to balance safety and defense efficiency under various conditions. We propose a two-stage actuator placement and actuator saturation approach, which focuses on identifying key actuators that maximize the system's controllability while operating under state and input constraints. By strategically placing and limiting the input bounds of critical actuators, we ensure that vehicles maintain safe distances even under attack. Simulation results show that our method effectively mitigates the impact of attacks while preserving defense efficiency, offering a robust solution to vehicle platooning safety challenges.

Figures (4)

• Figure 1: A vehicle platooning scenario with $n$ vehicles, each using CACC and radar to detect adjacent vehicles. The $i$-th vehicle's speed is $v_i$, and the distance to the preceding vehicle is $d_{i}$. An attack can hijack communication to manipulate the input $u_i$ of the secondary control.
• Figure 2: Different ellipsoids encapsulating reachable set (i.e., estimated reachable sets) when selecting different actuator locations and input bounds (only the first two dimensions are shown after projecting a 5-D ellipsoids into a 2-D plane). The detailed simulation results are in Section \ref{['sec:three-vehiclesimulation']}.
• Figure 3: The 2-D and 3-D projections of two 5-D ellipsoids (red original $\mathcal{E}^{\mathcal{V}}$ before applying ASAP algorithm; blue final $\mathcal{E}^{\mathcal{S*}}$ after applying ASAP algorithm), two hyperplanes (gray; dangerous set $\mathcal{D}$), and the empirical reachable set (black; Monte Carlo simulation) for the three-vehicle platooning system when the number of actuators $m = 2$.
• Figure 4: The 3-D projections on $d_1-d_2-d_3$ and $d_6-d_7-d_8$ subspaces of 39-D ellipsoids (red original $\mathcal{E}^{\mathcal{V}}$ is cut to show blue final $\mathcal{E}^{\mathcal{S*}}$ clearly), two hyperplanes (gray; dangerous set $\mathcal{D}$), and the empirical reachable set (black; Monte Carlo simulation) for the 20-vehicle platooning system when the number of actuators $m = 12$.

Theorems & Definitions (1)

• Conjecture 1: Supermodularity of $\log\det(\boldsymbol W_c^{-1})$ MinimalActuatorPlacement