Leveraging Cooperative Connected Automated Vehicles for Mixed Traffic Safety

TL;DR

The paper tackles safety and stability in mixed traffic with two cooperating CAVs among HVs under varying connectivity. It develops a nonlinear nominal controller that combines ACC, HV feedback, and inter-CAV coordination, and then overlays a control barrier function (CBF) safety framework to guarantee CAV, HV, and platoon safety. The authors derive stability conditions via linearization and transfer functions, reveal how HV connectivity shifts stability regions, and show that safety can be maintained through safety-filtered control even when nominal gains would violate safety. Numerical simulations demonstrate that the safety-critical approach achieves both forward-safe operation and string stability across different HV connection scenarios and penetration rates, with robustness to uncertainties in human driver behavior.

Abstract

The introduction of connected and automated vehicles (CAV) is believed to reduce congestion, enhance safety, and improve traffic efficiency. Numerous research studies have focused on controlling pure CAV platoons in fully connected automated traffic, as well as single or multiple CAVs in mixed traffic with human-driven vehicles (HVs). CAV cruising control designs have been proposed to stabilize the car-following traffic dynamics, but few studies has considered their safety impact, particularly the trade-offs between stability and safety. In this paper, we study how cooperative control strategies for CAVs can be designed to enhance the safety and smoothness of mixed traffic under varying penetrations of connectivity and automation. Considering mixed traffic where a pair of CAVs travels amongst HVs, we design cooperative feedback controllers for the pair CAVs to stabilize traffic via cooperation and, possibly, by also leveraging connectivity with HVs. The real-time safety impact of the CAV controllers is investigated using control barrier functions (CBF). We construct CBF safety constraints, based on which we propose safety-critical control designs to guarantee CAV safety, HV safety and platoon safety. Both theoretical and numerical analyses have been conducted to explore the effect of CAV cooperation and HV connectivity on stability and safety. Our results show that the cooperation of CAVs helps to stabilize the mixed traffic while safety can be guaranteed with the safety filters. Moreover, connectivity between CAVs and HVs offers additional benefits: if an HV connects to an upstream CAV (i.e., the CAV looks ahead), it helps the CAV to stabilize the upstream traffic, while if an HV connects to a downstream CAV (i.e., the CAV looks behind), the safety of this connected HV can be enhanced.

Figures (14)

• Figure 1: Safety-critical stabilization of a pair of CAVs traveling in mixed traffic. The head CAV follows a downstream head HV and leads $N$ following HVs, while the tail CAV follows the last HV in this vehicle platoon. We design controllers for the CAVs to alleviate congestion and also maintain formal safety guarantees considering the mixed vehicle platoon shaded in grey.
• Figure 2: Stability charts in the $(\beta_{{{\scaleto{\mathrm{H}}{3.5pt}}},{{\scaleto{\mathrm{T}}{3.5pt}}}},\beta_{{{\scaleto{\mathrm{T}}{3.5pt}}},{{\scaleto{\mathrm{H}}{3.5pt}}}})$ space of control gains. Grey areas and red areas represent plant stability and head-to-tail string stability, respectively. The white one represents unstable region. In panel (a), the middle HVs are not connected and the CAVs do not respond to them. In panel (b), HV 1, HV 2, and HV 3 are connected to the tail CAV who responds to them with gains $\beta_{{{\scaleto{\mathrm{T}}{3.5pt}}},1} = 0.4$, $\beta_{{{\scaleto{\mathrm{T}}{3.5pt}}},2} = 0.5$, $\beta_{{{\scaleto{\mathrm{T}}{3.5pt}}},3} = 0.5$ (while also responding to HV-4 based on range sensors). In panel (c), HVs are connected to the head CAV who responds to them with controller gains $\beta_{{{\scaleto{\mathrm{H}}{3.5pt}}},1} = 0.3$, $\beta_{{{\scaleto{\mathrm{H}}{3.5pt}}},2} = 0.2$. $\beta_{{{\scaleto{\mathrm{H}}{3.5pt}}},3} = 0.1$, $\beta_{{{\scaleto{\mathrm{H}}{3.5pt}}},4} = 0.1$. In all the three cases, the remaining controller gains are $\alpha_{{{\scaleto{\mathrm{H}}{3.5pt}}}} = 0.4$, $\beta_{{{\scaleto{\mathrm{H}}{3.5pt}}},\mathrm{d}}=0.6$, $\alpha_{{{\scaleto{\mathrm{T}}{3.5pt}}}}= 0.4$, and $\beta_{{{\scaleto{\mathrm{T}}{3.5pt}}},4}= 0.6$. In panel (d), the stability charts from panels (a)-(c) are compared.
• Figure 3: Safety charts in the space of control gains for the the nominal controller \ref{['eq:nominal controller head CAV']}-\ref{['eq:nominal controller tail CAV']}. (a) Safe $(\beta_{{{\scaleto{\mathrm{H}}{3.5pt}}},\mathrm{d}},\alpha_{{{\scaleto{\mathrm{H}}{3.5pt}}}})$ gains considering the head CAV's safety (We take the spacing policy $V(s)$ the same as in Fig. \ref{['fig:stability chart']}. The CAV coordination gains are set as $\beta_{{{\scaleto{\mathrm{H}}{3.5pt}}},{{\scaleto{\mathrm{T}}{3.5pt}}}} = 0$. We choose safe time headway as $\tau_{{{\scaleto{\mathrm{H}}{3.5pt}}}} = 0.8$ s.); (b) safe $(\beta_{{{\scaleto{\mathrm{T}}{3.5pt}}},N},\alpha_{{{\scaleto{\mathrm{T}}{3.5pt}}}})$ gains associated with the tail CAV's safety (We take the spacing policy $V(s)$ the same as in Fig. \ref{['fig:stability chart']}. The CAV coordination gains are set as $\beta_{{{\scaleto{\mathrm{T}}{3.5pt}}},{{\scaleto{\mathrm{H}}{3.5pt}}}} = 0$. We choose safe time headway as $\tau_{{{\scaleto{\mathrm{T}}{3.5pt}}}} = 0.8$ s.); (c) safe ACC gain for $(\beta_{{{\scaleto{\mathrm{H}}{3.5pt}}},\mathrm{d}},\alpha_{{{\scaleto{\mathrm{H}}{3.5pt}}}})$ for the head CAV with different HV feedback gains (We set $\beta_{{{\scaleto{\mathrm{H}}{3.5pt}}},{{\scaleto{\mathrm{T}}{3.5pt}}}}=0$); and (d) safe $(\beta_{{{\scaleto{\mathrm{H}}{3.5pt}}},{{\scaleto{\mathrm{T}}{3.5pt}}}},\beta_{{{\scaleto{\mathrm{T}}{3.5pt}}},{{\scaleto{\mathrm{H}}{3.5pt}}}})$ gains for the safety of both CAVs. The shaded region indicates the range of gains that ensure safety for the respective CAVs based on Theorems \ref{['theorem:safety nominal head']} and \ref{['theorem:safety nominal tail']}. Notice that the gains of the nominal controller are restricted if one intends to achieve provably safe behavior (i.e., $\alpha_{{{\scaleto{\mathrm{H}}{3.5pt}}}}$ and $\alpha_{{{\scaleto{\mathrm{T}}{3.5pt}}}}$ must be very high or $\beta_{{{\scaleto{\mathrm{H}}{3.5pt}}},{{\scaleto{\mathrm{T}}{3.5pt}}}}$ and $\beta_{{{\scaleto{\mathrm{T}}{3.5pt}}},{{\scaleto{\mathrm{H}}{3.5pt}}}}$ must be very small). This motivates the introduction of safety filters to enforce safe behaviors by deviating from the nominal controller to prevent safety violation.
• Figure 4: Region of $(u_{{{\scaleto{\mathrm{H}}{3.5pt}}}},u_{{{\scaleto{\mathrm{T}}{3.5pt}}}})$ control inputs that ensure the safety of both the H-CAV using \ref{['eq:CBF explicit head']}, the T-CAV using \ref{['eq:CBF explicit tail']}, and the platoon using \ref{['eq:CBF explicit platoon']}.
• Figure 5: The head HV suddenly decelerates: simulated trajectory of mixed vehicle platoon . The nominal controllers cause unsafe driving conditions for the two CAVs, i.e., $h_{{{\scaleto{\mathrm{H}}{3.5pt}}}}<0$ and $h_{{{\scaleto{\mathrm{T}}{3.5pt}}}}<0$ occur. By enforcing CBF, the two CAVs become safe with positive $h$. Besides, the CBF also maintains string stability, i.e., $I<1$.

Theorems & Definitions (13)

• Definition 1: Internal stability
• Definition 2: Input-output stability
• Lemma 1
• Theorem 1
• Lemma 2: Nagumo's theorem nagumo1942lage
• Theorem 2: Safety of the nominal head CAV controller
• Theorem 3: Safety of the nominal tail CAV controller
• Definition 3: Control Barrier Function ames2019control
• Theorem 4: Safety guarantee by CBF ames2019control
• Lemma 3