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Benefits of V2V Communication for Autonomous and Connected Vehicles

Swaroop Darbha, Shyamprasad Konduri, Prabhakar R. Pagilla

arXiv:1803.02900v1eess.SY

TL;DR

The paper asks how V2V communication can reduce the time headway required for string-stable autonomous-vehicle platoons subject to parasitic actuation lags. It analyzes CTHP with communicated predecessor information and reports lower headway bounds for multiple information configurations, while identifying communication overhead as a practical consideration.

  • Problem

    CTHP with onboard predecessor position and velocity information requires an employable time headway lower bounded by 2τ_0 under parasitic actuation lag.

  • Method

    The paper models homogeneous platoons with parasitic lags and analyzes robust string stability under CTHP using communicated position, velocity, and acceleration information from selected predecessors.

  • Results

    The reported lower bounds are 4τ_0/(1+r) using position and velocity from r immediate predecessors, and 2τ_0/(1+r) when acceleration is also used or when only the immediate and r-th predecessors are used.

  • Takeaways & Limitations

    V2X predecessor information can reduce the minimum employable time headway and increase platoon capacity when paired with an appropriate spacing policy.

Abstract

from arXiv · show

In this paper, we investigate the benefits of Vehicle-to-Vehicle (V2V) communication for autonomous vehicles and provide results on how V2V information helps reduce employable time headway in the presence of parasitic lags. For a string of vehicles adopting a Constant Time Headway Policy (CTHP) and availing the on-board information of predecessor's vehicle position and velocity, the minimum employable time headway ($h_{\min}$) must be lower bounded by $2τ_0$ for string stability, where $τ_0$ is the maximum parasitic actuation lag. In this paper, we quantify the benefits of using V2V communication in terms of a reduction in the employable time headway: (1) If the position and velocity information of $r$ immediately preceding vehicles is used, then $h_{\min}$ can be reduced to ${4τ_0}/{(1+r)}$; (2) furthermore, if the acceleration of `$r$' immediately preceding vehicles is used, then $h_{\min}$ can be reduced to ${2τ_0}/{(1+r)}$; and (3) if the position, velocity and acceleration of the immediate and the $r$-th predecessors are used, then $h_{\min} \ge {2τ_0}/{(1+r)}$. Note that cases (2) and (3) provide the same lower bound on the minimum employable time headway; however, case (3) requires much less communicated information.

I. INTRODUCTION

The paper motivates V2V communication as a way to reduce the time headway required for robustly string-stable autonomous-vehicle platoons despite parasitic actuation lags. It quantifies reductions under different predecessor-information configurations and notes a trade-off between lower headway and communication burden.

  • Motivation and contribution: 2τ_0 is the lower bound on employable time headway for CTHP with onboard predecessor position and velocity information.τ_0 denotes the maximum parasitic actuation lag.
  • Motivation and contribution: Reducing employable time headway can increase traffic throughput, while typical truck-platooning spacings may otherwise limit capacity and fuel-efficiency gains.The paper gives typical headways of 0.5–1 s and explains that a 1 s minimum can correspond to 30 m spacing at approximately 30 m/s.
  • Scope: The study focuses on CTHP because finite predecessor information does not guarantee string stability for the constant spacing policy.The paper characterizes this as a communication burden and scope limitation for CSP.
  • Motivation and contribution: 4τ_0/(1+r) is the reported bound when position and velocity information from r immediate predecessors is used.The result expresses the reduction relative to the onboard-information bound.
  • Motivation and contribution: 2τ_0/(1+r) is the reported bound when position, velocity, and acceleration information from r immediate predecessors is used.This configuration uses communicated acceleration in addition to position and velocity.
  • Motivation and contribution: 2τ_0/(1+r) is also obtained when information from the immediate and r-th predecessors is used, requiring less communicated information than using all r predecessors.The paper identifies this as having the same lower bound as the all-predecessor acceleration case.

II. BACKGROUND AND PROBLEM DESCRIPTION

The paper models a homogeneous platoon with parasitic actuation lags and evaluates CTHP using spacing-error dynamics and frequency-domain string-stability conditions. It defines robust stability over all lags up to a known maximum and introduces predecessor-information exchange patterns for reducing the minimum employable headway.

  • Vehicle and lag model: The vehicle model represents each homogeneous vehicle as a point mass with parasitic actuation dynamics.The model uses position, acceleration, and control input variables for each vehicle.
  • Vehicle and lag model: Robust string stability requires stability for every parasitic lag τ in [0, τ_0], where τ_0 is the maximum possible lag.The paper defines the minimum employable headway as the smallest headway satisfying this condition.
  • CTHP formulation: CTHP makes desired following distance proportional to vehicle speed through the time-headway parameter h_w.The ACC controller considered uses onboard predecessor information for position and velocity feedback.
  • String-stability analysis: Spacing-error transfer functions describe how one vehicle’s error propagates from its predecessor through the platoon.The analysis treats spacing errors as states of a spatially discrete system and applies spectral-radius conditions for string stability.
  • String-stability analysis: The frequency-domain requirement reduces to ||H_1(jω)||_∞ ≤ 1 when each vehicle uses only its immediate predecessor’s information.This is presented as a frequently imposed condition for string stability in the r = 1 case.
  • Communication patterns: The communication patterns considered are immediate predecessor, r immediate predecessors, and immediate plus r-th predecessor information flowing upstream.These patterns support the paper’s analysis of how communicated predecessor states change the allowable headway.

III. CTHP WITH COMMUNICATED INFORMATION

The communicated-information analysis examines whether acceleration and predecessor look-ahead can reduce the minimum employable time headway while preserving robust string stability. It proceeds from immediate-predecessor acceleration feedback to information from multiple or strategically selected predecessors.

  • Communicated predecessor information: Acceleration feedback from a preceding vehicle is analyzed first as a way to reduce minimum employable time headway.The paper identifies this as the Cooperative ACC case.
  • Communicated predecessor information: Information from r immediate predecessors is then analyzed to determine whether robust string stability can coexist with a lower employable time headway.The generalized controller uses communicated acceleration, velocity, and position information.

A. CTHP with Immediate Predecessor Acceleration

The paper analyzes how immediate-predecessor acceleration information affects string stability and the minimum employable time headway under parasitic actuation lag. Theorem 1 gives conditions under which suitable controller gains guarantee robust string stability.

  • Acceleration feedback from the immediate predecessor is used to quantify its effect on minimum employable time headway.The theorem analyzes a control law incorporating predecessor acceleration and uses an error-attenuation condition to lower-bound the headway.
  • Theorem 1 states that appropriate kp and kv can achieve ∥He(jω; τ)∥∞ ≤ 1 under the stated acceleration-feedback condition.This is the frequency-domain criterion used for robust string stability in the theorem.
  • For ka ∈ (0, 1), hw ≥ 2τ0/(1+ka) permits gains kp and kv that ensure robust string stability for all τ ∈ [0, τ0].The result assumes a maximum parasitic lag τ0 and provides a sufficient gain-selection condition.
  • ka ≥ 0 is required because negative acceleration feedforward would command braking in response to predecessor acceleration and worsen the headway bound.The paper therefore restricts the acceleration-feedforward gain to nonnegative values.
  • The same methodology can analyze acceleration feedback of the controlled vehicle by recasting the dynamics as CTHP with modified actuation lag and gains.The recast formulation preserves the applicability of the proposed analysis to that controller modification.
  • In practice, ka is limited, so predecessor information alone cannot maintain arbitrarily small headway or string stability at the zero-headway constant-spacing limit.The paper notes that a higher-order parasitic-dynamics model can impose a maximum stable acceleration-feedback gain.

B. CTHP with Information from ‘r’ Predecessors

The generalized CTHP uses position, velocity, and acceleration information from r predecessor vehicles through communicated feedback. Under stated gain conditions, this architecture guarantees robust string stability while reducing the minimum employable time headway.

  • Control architecture: Information from r predecessor vehicles is incorporated through predecessor acceleration, velocity, and position feedback gains.The generalized control law requires information obtained through vehicular communication.
  • Analysis: The error-propagation analysis defines transfer functions describing how predecessor spacing errors affect the controlled vehicle.The governing spacing-error equation is obtained by substituting the communicated-feedback control law into the vehicle dynamics.
  • Stability condition: Robust string stability is established for the r-predecessor control action under the stated gain conditions.Theorem 2 specifies equal predecessor gains and requires rka ∈ (0, 1).
  • Stability condition: For every ¯ka ∈ [0, 1), suitable velocity and position gains can guarantee robust string stability for every parasitic lag τ ∈ [0, τ0].The condition is expressed through the infinity norm of the resulting transfer function.

C. CTHP with Immediate and rthPredecessor Information

The paper also studies feedback from the immediate and rth predecessors as a lower-communication alternative. The results show that carefully selected acceleration feedback can substantially reduce the employable time headway, while communication range and bandwidth constrain practical choices.

  • Control architecture: The immediate-and-rth-predecessor controller is a special case of the r-vehicle look-ahead law with equal feedback gains.The two communicated predecessors are the immediate predecessor and the rth predecessor.
  • Stability condition: Robust string stability is guaranteed under the sufficient condition 2∥H0(jω)∥∞≤1 for the two-predecessor feedback architecture.The corollary applies when acceleration, velocity, and position gains are equal across the two communicated predecessors.
  • Design implications: τ0 is the lower-limit scale: with immediate-predecessor acceleration feedback gain near one, the minimum employable headway can approach τ0.This nearly halves the lower limit relative to the no-acceleration-feedback case described in the section.
  • Design implications: 2τ0/3 is attainable with two predecessor vehicles when equal position, velocity, and acceleration gains have acceleration gains summing near one.The result is also corroborated by numerical simulations cited in the passage.
  • Design implications: τ0/2 can be approached with r = 3 and equal position and velocity gains when rka is close to one.Without acceleration feedback, matching the r = 2 acceleration-feedback reduction requires position and velocity information from five predecessors.
  • Practical considerations: Communication overhead and near-field communication restrictions favor using information from two or three nearby predecessors as a practical compromise.Using only the immediate predecessor still provides benefits over relying solely on on-board sensors.

D. Non-negativity of impulse response for string stability

The paper adds a non-negative impulse-response requirement to string-stability analysis and studies when controller gains can satisfy it under parasitic lag. A scaling transformation and numerical gain construction support the resulting conditions for single-vehicle look-ahead and their extension to multiple vehicles.

  • String-stability criterion: String stability is analyzed through spacing-error transfer functions, with non-amplification characterized by ∥h∥1 ≤1 and an additional non-negative impulse-response requirement.For multiple look-ahead vehicles, non-negative impulse responses support geometric non-amplification of errors.
  • Feasibility condition: The non-negativity problem requires gains kp and kv such that h(t) ≥ 0 for every parasitic lag τ ∈[0, τ0] when hw ≥ 2τ0/(1+ka).The text identifies this as analytically difficult and related to an open fixed-structure controller problem.
  • Analysis approach: A scaling transformation s = s′/τ0 reduces the analysis to normalized lag and headway variables, with ˜τ ∈[0,1] and ˜hw = 2/(1+ka).The transformed representation is used to search for gains producing a non-negative impulse response.
  • Numerical construction: For ka = 0.95 and τ0 = 1, the gains {kv, kp} = {0.082, 0.001} numerically indicate h_e(t) ≥ 0.The gains can be rescaled for other τ0 values using ˜kp = kpτ0^2 and ˜kv = kvτ0.
  • Extension: The construction extends the benefit analysis from single-vehicle look-ahead information to multiple-vehicle look-ahead while retaining the additional non-negativity requirement.The paper states that demonstrating the multiple-vehicle benefit reduces to the single-vehicle look-ahead case.

IV. NUMERICAL SIMULATIONS

Numerical simulations test CTHP platoons under time headways above and below the theoretical lower bound for r = 1, 2, and 3. The simulations show that V2V communication permits lower time-headway values, while an additional gain study checks non-negative impulse-response conditions.

  • Simulation setup: Simulations apply a sinusoidal lead-vehicle disturbance from 5 to 10 seconds and display only odd-numbered vehicles to reduce plot clutter.The CTHP controller and common numerical parameters are taken from the paper’s specified tables.
  • Compared conditions: Two cases are compared: hw > hmin and hw < hmin, across r = 1, r = 2, and r = 3.The corresponding figures and table values distinguish cases satisfying or violating the lower bound.
  • Simulation result: Lower time-headway values can be employed when V2V communication is used.This conclusion is drawn from the figures and numerical values for the tested predecessor-information cases.
  • Additional gain study: For ka = 0.95, τ0 = 0.5 seconds, and ˜hw = 1.02, gain values are evaluated against non-negative impulse-response, real-pole, and normalized-lag conditions.The gain search uses gridding over ˜kv and ˜kp.

V. CONCLUSIONS

The paper studies V2X communication for autonomous-vehicle platoons using CTHP and shows that predecessor information can preserve robust string stability while lowering the minimum employable time headway. The stated consequence is increased platoon capacity.

  • Main conclusion: Using information from r predecessor vehicles with a CTHP controller provides robust string stability and decreases the minimum employable time headway.The conclusion concerns information obtained through V2X communication, including V2V and V2I.
  • Implication: The reduced minimum employable time headway increases the capacity of the platoon.The paper presents predecessor-vehicle feedback through V2X as the communication-based mechanism for this result.

APPENDIX

The appendix establishes string-stability conditions by requiring frequency-domain inequalities across the full parasitic-lag range and by selecting controller gains that satisfy stability, nominal, and perturbed cases.

  • Frequency-domain condition: String stability is tested through the condition ∥He(jω; τ)∥≤1, equivalent to a nonnegative difference between the relevant numerator and denominator expressions for all ω.The proof begins from the error-propagation transfer function and reduces the condition to a bi-quadratic inequality.
  • Perturbed case: The perturbed-case analysis requires the inequality to hold for every τ ∈(0, τ0], using either a coefficient relation or a non-positive discriminant.The proof separately analyzes these alternatives before imposing the Hurwitz stability condition.
  • Sufficiency: Sufficiency is shown by finding kp and kv satisfying stability, the nominal case at τ = 0, and non-negativity of the perturbed polynomial family.The three requirements are stated as the conditions for the constructive gain argument.
  • Gain constraints: The stability condition itself imposes no further restriction on positive kv and kp once kv + hwkp > τ0kp.The appendix derives this relation from the stated gain inequalities.
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