Efficient Cooperative Adaptive Cruise Control Including Platoon Kinematics

Abstract

Cooperative adaptive cruise control (CACC) is acknowledged as an efficient solution to relieve traffic congestion while ensuring traffic safety. This paper aims to improve traffic efficiency via both the effective following spacing policy and the CACC with platoon kinematics. Firstly, the correlation mechanism of safety spacing policy and time headway policy is analyzed, a versatile generic spacing model is established, and an efficient spacing policy is proposed by leveraging the concept of safety redundancy. Secondly, based on the “virtual centroid” of the platoon, the CACC upper control strategy with platoon kinematics is proposed to improve traffic efficiency. The strategy is complemented by the design of a sliding mode controller, which precisely allocates longitudinal acceleration. Additionally, a lower controller is developed to track the desired acceleration accurately and rapidly under various driving and braking conditions. Thirdly, eight typical scenarios for urban traffic are reconstructed via three-layer decompositions, and the index named synchronization is proposed to evaluate the performance of CACC with platoon kinematics. Finally, a simulation test is conducted, demonstrating that the proposed CACC strategy synchronously responds to the kinematics of the preceding platoon, reducing the accumulation of response delay, ensuring both vehicle following safety and efficiency.

Appendices

Appendix A

The detailed derivation of Eq. (1):

In the extreme manual braking case, the host vehicle travels at constant acceleration ${a}_{{\text{max}}}$, and its preceding vehicle travels at constant deceleration ${a}_{{\text{bmax}}}$, the braking process can be described by Figs. A1 and A2.

Fig. 7

The braking process of the $i$th vehicle

Fig. 8

The position of the $i$th vehicle during braking process

${\tau }_{11}$ is the time required to detect that the preceding vehicle starts to brake, ${\tau }_{12}$ is the time for the driver to release the accelerator pedal completely; ${\tau }_{21}$ is the time to move the foot to the braking pedal and eliminate the mechanical clearance of the braking system, ${\tau }_{22}$ is the time to increase braking force, ${\tau }_{3}$ is the continuous braking time, and ${\tau }_{4}$ is the braking release time.

During the period of ${\tau }_{11}$, the host vehicle travels at a uniform acceleration, so the distance and velocity is derived as:

$$\begin{array}{l}{s}_{10}={v}_{i}{\tau }_{11}+\frac{1}{2}{a}_{{\text{max}}}{\tau }_{11}^{2} \end{array}$$

(A1)

$$\begin{array}{l}{v}_{1}={v}_{i}+{a}_{{\text{max}}}{\tau }_{11} \end{array}$$

(A2)

During the period of ${\tau }_{12}$, it is assumed that the acceleration decreases linearly, so the velocity and distance are calculated through integration:

$$\begin{array}{l}{v}_{2}={v}_{1}+{\frac{1}{2}{\tau }_{12}a}_{{\text{max}}}\end{array}$$

(A3)

$$\begin{array}{l}{s}_{11}={v}_{1}{\tau }_{12}+\frac{1}{6}{a}_{{\text{max}}}{\tau }_{12}^{2} \end{array}$$

(A4)

During the period of ${\tau }_{21}$, the vehicle travels at constant speed ${v}_{2}$:

$$\begin{array}{l}{s}_{20}={v}_{2}{\tau }_{21} \end{array}$$

(A5)

During the period of ${\tau }_{22}$, it is assumed the deceleration increases linearly, the velocity and distance are calculated through integration:

$$\begin{array}{l}{v}_{3}={v}_{2}-\frac{1}{2}{a}_{{\text{bmax}}}{\tau }_{22} \end{array}$$

(A6)

$$\begin{array}{l}{s}_{21}={v}_{2}{\tau }_{22}-\frac{1}{6}{a}_{{\text{bmax}}}{\tau }_{22}^{2} \end{array}$$

(A7)

During the period of ${\tau }_{3}$, the host vehicle travels at a uniform deceleration, so the distance and velocity is derived as:

$$\begin{array}{l}{s}_{3}=\frac{{v}_{3}^{2}}{2{a}_{{\text{bmax}}}} \end{array}$$

(A8)

Above all, the braking distance of the host vehicle is:

$$\begin{array}{l}{S}_{i}={s}_{10}+{s}_{11}+{s}_{20}+{s}_{21}+{s}_{3} \end{array}$$

(A9)

Since the preceding vehicle travels at a uniform deceleration, the braking distance is derived as:

$$\begin{array}{l}{S}_{i-1}=\frac{{v}_{i-1}^{2}}{2{a}_{{\text{bmax}}}} \end{array}$$

(A10)

To guarantee the safety, the distance that the host vehicle should maintain from the preceding vehicle is:

$$\begin{aligned} D_{{{\text{min}}i}} & = S_{i} - S_{{i - 1}} + d_{{ai}} = \frac{{v_{i}^{2} - v_{{i - 1}}^{2} }}{{2a_{{{\text{bmax}}}} }} + \left[ {\tau _{{11}} + \tau _{{12}} + \tau _{{21}} + \frac{{\tau _{{22}} }}{2}} \right. \\ & \quad \left. { + \frac{{a_{{{\text{max}}}} }}{{a_{{{\text{bmax}}}} }}\left( {\tau _{{11}} + \frac{{\tau _{{12}} }}{2}} \right)} \right]v_{i} - \frac{1}{{24}}a_{{{\text{bmax}}}} \tau _{{22}}^{2} \\ & \quad + a_{{{\text{max}}}} \left[ {\frac{{\tau _{{11}}^{2} }}{2} + \tau _{{11}} \tau _{{12}} + \frac{1}{6}\tau _{{12}}^{2} + \left( {\tau _{{11}} + \frac{{\tau _{{12}} }}{2}} \right)\left( {\tau _{{21}} + \frac{{\tau _{{22}} }}{2}} \right) + \frac{{a_{{{\text{max}}}} }}{{2a_{{{\text{bmax}}}} }}\left( {\tau _{{11}} + \frac{{\tau _{{12}} }}{2}} \right)^{2} } \right] + d_{{ai}} \\ \end{aligned}$$

(A11)

where ${d}_{ai}$ is a safety margin.

Appendix B: Description of parameters

${a}_{{\text{bmax}}}$:

Maximum deceleration $({\text{m}}/{{\text{s}}^{2}})$

${a}_{{\text{max}}}$:

Maximum acceleration $({\text{m}}/{{\text{s}}^{2}})$

${\tau }_{11}$:

Time to detect that the preceding vehicle starts to brake (${\text{s}}$)

${\tau }_{12}$:

Time for driver to release the accelerator pedal completely (${\text{s}}$)

${\tau }_{21}$:

Time to move the foot to the braking pedal and eliminate the mechanical clearance (${\text{s}}$)

${\tau }_{22}$:

Time to increase braking force (${\text{s}}$)

${\tau }_{3}$:

Continuous braking time $({\text{s}})$

${\tau }_{4}$:

Braking force release time (${\text{s}}$)

${d}_{{\text{min}}}$:

Centroid distance between the host vehicle and preceding vehicle when their velocities are 0 $({\text{m}})$

$th$:

Constant time headway $({\text{s}})$

${v}_{i}$:

Velocity of the $i$th vehicle (${\text{m}}/{\text{s}}$)

${d}_{{\text{emei}}}$:

Safe distance of the emergency braking case $({\text{m}})$

${d}_{{\text{stei}}}$:

Safe distance of the steady following case $({\text{m}})$

${d}_{{\text{saf}}i}$:

Safe distance of the safety spacing policy $({\text{m}})$

${{th}}_{{\text{gen}}i}$:

Time headway of the generic spacing model (${\text{s}}$)

$th({v}_{i})$:

Time headway on ${v}_{i}$ (${\text{s}}$)

${t}_{{\text{safe}}}$:

Time headway of the safety spacing policy $({\text{s}})$

${v}_{\text{c}}$:

Critical velocity (${\text{m}}/{\text{s}}$)

${d}_{{\text{ef}}i}$:

Distance from the $i$th vehicle to its preceding vehicle of the efficient spacing policy $({\text{m}})$

${d}_{i}$:

Centroid distance between the $i$th vehicle and its preceding vehicle ($({\text{m}})$)

${e}_{i}$:

Centroid distance tracking error of the $i$th vehicle (${\text{m}}$)

${d}_{{\text{G}}}$:

Distance of the virtual centroid (${\text{m}}$)

${v}_{{\text{G}}}$:

Velocity of the virtual centroid (${\text{m}}/{\text{s}}$)

${a}_{{\text{G}}}$:

Acceleration of the virtual centroid (${\text{m}}/{{\text{s}}}^{2}$)

${d}_{{\text{des}}i}$:

Desired centroid distance between the $i$th vehicle and following target $({\text{m}})$

${a}_{{\text{des}}i}$:

Desired acceleration of the $i$th vehicle $({\text{m}}/{{\text{s}}^{2}})$

$\lambda$:

Sliding surface convergence speed

$c$:

Sliding surface parameter

${\widehat{\tau }}_{s}$:

Estimation of the vehicle response time

${W}_{i}$:

Weight of $i$th vehicle in the platoon

${u}_{{\text{throttle}}}$:

Throttle opening

${u}_{{\text{b}}}$:

Brake master cylinder pressure

${I}_{{\text{s}}}$:

CACC Synchronic index $({\text{s}})$

${\tau }_{s}$:

Vehicle response time (${\text{s}}$)

$\tau$:

Braking response time (${\text{s}}$)

${a}_{i,{\text{des}}}$:

Desired acceleration of the $i$th vehicle for ACC (${\text{m}}/{{\text{s}}}^{2}$)