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A rigorous control framework that enables platoon formation with the HDVs by only controlling the CAVs within the network.
Authors: A M Ishtiaque Mahbub, Andreas A. Malikopoulos
Abstract
Abstract
Connected and automated vehicles (CAVs) provide the most intriguing opportunity to reduce pollution, energy consumption, and travel delays. In this paper, we address the problem of vehicle platoon formation in a traffic network with partial CAV penetration rates. We investigate the interaction between CAV and human-driven vehicle (HDV) dynamics, and provide a rigorous control framework that enables platoon formation with the HDVs by only controlling the CAVs within the network. We present a complete analytical solution of the CAV control policy and the conditions under which a platoon formation is feasible. We evaluate the solution and demonstrate the efficacy of the proposed framework using numerical simulation.
Proposed Framework
Proposed Framework
A CAV (red) traveling with two trailing HDVs (yellow), where the HDV state is estimated (top scenario) by the coordinator within the buffer zone, and the platoon is formed (bottom scenario) by controlling the CAV at the control zone.
Numerical Example
Numerical Example
Number of vehicles: 3 (1 leading CAV, 2 trailing HDVs)
Simulation Parameters, N=3
Simulation Parameters, N=3
Simulation environment for vehicles {1,2,3}: MATLAB R2020b
Given parameters: t_p = 47.2 s, tau_r =4 s, eta_bar = 1 s
Control zone length, L_c = 2000 m
Initial time, t^c=0
Initial condition: v_1(t^c)=v_2(t^c)=v_3(t^c)=30 m/s, p_1(t^c)=200 m, p_2(t^c)=100$ m and $p_3(t^c)=0
The state and control constraints: v_max=30 m/s, v_min=25 m/s, u_min=-3.0$ m/s^2, u_max=2.0 m/s^2.
Other Parameters l_c=4 m, s_0 = 2 m, eta_i = 0, rho_i=1.5 and alpha=1.
For a desired platoon formation time t^p=47.2$ s and a given platoon stabilization duration \tau^s=5 s, we have \tau^t=42.5 s. Since \tau^t=42.5 is feasible according to Theorem 4, we use Theorem 3 to compute the corresponding control input parameter u_p=-0.1185 m/s^2 for CAV 1 such that u_1(t)=u_p, t in [0,30.6].
Simulation Video, N=3
Simulation Video, N=3
Simulation environment: PreScan+Simulink
Number of vehicles: 3 (1 leading CAV, 2 trailing HDVs)
Robustness Analysis: (N=2,3,4)
Robustness Analysis: (N=2,3,4)
Platoon formation duration
Platoon formation duration
This figure shows that the platoon is formed within $2.5\%$ deviation for all admissible $\tau^t$, where the higher $\tau^t$ values minimizes delayed platoon formation instances.
Driver's perception delay
Driver's perception delay
The robustness of the framework under different perception delay $\eta_i\in[0,1]$ is showed here. Since the platoon formation deviations are mostly non-positive, the conservative consideration of $\bar{\eta}$ guarantees platoon formation within the desired platoon formation time $t^p$.
Desired time gap
Desired time gap
Finally, we consider the variation of two car-following parameters, namely the desired time gap $\rho_i\in[0.5,1.5]$ and driver's sensitivity coefficient $\alpha\in[1,2]$, to investigate the performance of the proposed framework under random human driving behavior based on the OVM CF model. The proposed framework is mostly robust against variation of $\rho_i$, and shows delayed platoon formation only near the maximum value of $\rho_i$.
Driver's sensitivity coefficient
Driver's sensitivity coefficient
In contrast, the proposed framework shows delayed platoon formation with $<3\%$ deviation for variation of $\alpha$. Note that, since $\tau^s$ is dependent on $\alpha$, the appropriate computation of $\tau^s$ can minimize the platoon formation deviation with varying $\alpha$.
Minimum allowable speed
Minimum allowable speed
The framework shows conservative behavior under different allowable speed fluctuation. We observe that, with decreasing allowable speed fluctuation, the platoon formation deviation achieves higher accuracy.
Concluding Remarks
Concluding Remarks
In this paper, we presented a framework for platoon formation under a mixed traffic environment, where a leading CAV derives and implements its control input to force the following HDVs to form a platoon. Using a predefined car-following model, we provided a complete, analytical solution of the CAV control input intended for the platoon formation. We also provided a detailed analysis of the platoon formation framework, and provided conditions under which a feasible platoon formation time exists. Finally, we presented numerical example to validate the robustness of our proposed framework.
A direction for future research should extend the proposed framework to make it agnostic to additional car-following models. Ongoing research considers the notion of optimality to derive energy- or time-optimal platoon formation framework under relaxed assumption on the steady-state traffic flow.
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