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Joint Communication and Control for Wireless Autonomous Vehicular Platoon Systems

Tengchan Zeng, Omid Semiari, Walid Saad, Mehdi Bennis

arXiv:1804.05290v2cs.IT

TL;DR

Wireless delays can destabilize autonomous vehicular platoons, creating a need to jointly design communication and control systems. The paper derives stability-based delay requirements, analyzes V2V end-to-end delay and reliability, and optimizes control parameters. Simulations corroborate the analysis, show parameter effects on reliability, and demonstrate benefits from integrated design.

  • Problem

    Wireless V2V delays can impair platoon stability, while prior work does not jointly model wireless-network performance and vehicle-control stability.

  • Method

    The paper integrates stability analysis, V2V delay modeling, reliability derivation, and control-parameter optimization.

  • Results

    Simulations corroborate the analytical derivations and demonstrate that joint control and wireless-network design improves platoon reliability.

  • Takeaways & Limitations

    Designing control parameters together with wireless-network conditions provides guidelines for achieving required reliability and control-system stability.

Abstract

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Autonomous vehicular platoons will play an important role in improving on-road safety in tomorrow's smart cities. Vehicles in an autonomous platoon can exploit vehicle-to-vehicle (V2V) communications to collect information, such as velocity and acceleration, from surrounding vehicles so as to maintain the target velocity and inter-vehicle distance. However, due to the dynamic on-vehicle data processing rate and the uncertainty of the wireless channel, V2V communications within a platoon will experience a delay. Such delay can impair the vehicles' ability to stabilize the operation of the platoon. In this paper, a novel framework is proposed to optimize a platoon's operation while jointly consider the delay of the wireless network and the stability of the vehicle's control system. First, stability analysis for the control system is performed and the maximum wireless system delay requirements which can prevent the instability of the control system are derived. Then, delay analysis is conducted to determine the end-to-end delay, including queuing, processing, and transmission delay for the V2V link in the wireless network. Subsequently, using the derived delay, a lower bound and an approximated expression of the reliability for the wireless system, defined as the probability that the wireless system meets the control system's delay needs, are derived. Then, the control parameters are optimized to maximize the derived wireless system reliability. Simulation results corroborate the analytical derivations and study the impact of parameters, such as the platoon size, on the reliability performance of the vehicular platoon. More importantly, the simulation results disclose the benefits of integrating control system and wireless network design while providing guidelines for designing autonomous platoons so as to realize the required wireless network reliability and control system stability.

I. INTRODUCTION

The paper addresses the missing joint analysis of wireless communication delays and platoon-control stability. It develops an integrated framework that derives delay requirements, models V2V end-to-end delay and reliability, optimizes control parameters, and validates the design through simulation.

  • Motivation: Wireless V2V delays can reach hundreds of milliseconds and jeopardize stable platoon operation, motivating joint control and network design.The framework targets low latency and stability under uncertain wireless conditions.
  • Research gap: Existing work lacks a joint study of wireless and control-system performance for autonomous vehicular platoons.Communication-centric studies abstract control, while control-centric studies assume deterministic communication performance.
  • Framework: The proposed framework derives plant- and string-stability delay limits, then analyzes V2V end-to-end delay using stochastic geometry and queuing theory.The delay analysis includes queuing, processing, and transmission components.
  • Reliability analysis: Wireless reliability is defined by whether the network meets control-imposed delay requirements, with lower-bound and approximated expressions derived from the delay analysis.The approximation targets scenarios in which transmission delay dominates total wireless delay.
  • Optimization and results: Optimizing control-system parameters increases the wireless-network reliability lower bound and approximation by as much as 15%.The paper uses dual-update mechanisms to select sub-optimal control parameters.
  • Simulation findings: Simulations corroborate the analytical results and show that interference density, packet size, vehicle spacing, and platoon size affect reliability.The results provide guidelines for jointly designing vehicular-platoon control and wireless networks.

II. SYSTEM MODEL

The system model represents a highway with one platoon lane, surrounding non-platoon traffic, and leader–follower V2V coordination. Spatial vehicle distributions and information exchange are specified to model platoon formation and movement.

  • A. Highway Traffic Model: The highway contains a platoon lane and N−1 non-platoon lanes, with vehicles communicating through V2V links.Non-platoon transmitters are organized by lane, while platoon-lane traffic is divided into vehicles ahead of and behind the platoon.
  • A. Highway Traffic Model: Non-platoon vehicle locations are modeled with homogeneous or nonhomogeneous Poisson point processes according to lane and position relative to the platoon.The model uses stochastic geometry to capture transmitting-vehicle distributions over a large highway area.
  • A. Highway Traffic Model: A leader–follower platoon comprises one leader and M followers that exchange speed, location, and spacing information over successive V2V links.Followers use these measurements to coordinate movement and maintain target distances from preceding vehicles.

B. Channel Model and Interference Analysis

The communication and control models connect wireless channel conditions and end-to-end V2V delay to platoon stability. The framework derives delay requirements, models tandem queuing, and optimizes control parameters for wireless reliability.

  • B. Channel Model and Interference Analysis: OFDMA assigns orthogonal subcarriers to platoon vehicles, avoiding interference among concurrent intra-platoon V2V transmissions.V2V links outside the platoon reuse cellular bandwidth and can therefore contribute interference.
  • B. Channel Model and Interference Analysis: The model uses Nakagami fading for intra-platoon links and Rayleigh fading for channels from non-platoon vehicles.Received power follows a path-loss and Gamma-fading model, while external interference is formed from non-platoon transmissions.
  • B. Channel Model and Interference Analysis: The framework jointly designs communication and control by matching V2V delay requirements to control-system stability conditions.Control parameters can relax communication delay requirements, while network design can help prevent control instability.
  • B. Channel Model and Interference Analysis: End-to-end V2V delay includes tandem queuing, processing, and transmission components, and wireless reliability is the probability of meeting the control delay requirement.The paper derives lower-bound and approximate reliability expressions and optimizes control parameters to maximize them.

III. STABILITY ANALYSIS OF THE CONTROL SYSTEM

Wireless delay can destabilize the leader–follower platoon, so the paper analyzes plant and string stability to derive admissible V2V delay thresholds. Plant stability requires spacing and velocity errors to converge to zero.

  • III. STABILITY ANALYSIS OF THE CONTROL SYSTEM: The analysis derives wireless delay thresholds that ensure both plant stability and string stability of the control system.Plant stability concerns local spacing and velocity errors, whereas string stability concerns their propagation through the platoon.
  • A. Plant Stability: The plant-stability analysis models the delayed platoon dynamics using an augmented vector of spacing and velocity errors.This formulation supports deriving the delay threshold needed for asymptotic convergence.
  • A. Plant Stability: Plant stability requires each follower’s spacing and velocity errors to converge asymptotically to zero.The augmented error vector therefore must converge to the zero state.
  • A. Plant Stability: Theorem 1 specifies a maximum V2V-link delay condition under which followers eventually match the leader’s speed and maintain the corresponding distance.The condition is expressed through eigenvalue bounds involving the control-system matrices.

B. String Stability

String stability is analyzed through the adjacent-vehicle transfer function and a delay approximation. The resulting conditions prevent spacing and velocity disturbances from amplifying along the platoon while modeling the V2V data path and end-to-end delay.

  • B. String Stability: The transfer-function analysis uses Padé approximation for the communication delay and imposes |Ti(jf)| ≤ 1 across excitation frequencies.The proposition also requires the gain condition a + 2b −2 ≥ 0.
  • B. String Stability: String stability is guaranteed when the control gains and V2V delay satisfy the derived conditions, preventing spacing and velocity errors from amplifying along the vehicle string.Joint plant and string stability requires τi−1,i(t) ≤ min(τ1, τ2), together with both stated control-gain inequalities.
  • B. String Stability: Vehicle sensors collect location information, processors convert and handle it, and transceivers send it to neighboring vehicles for control updates.Receiving vehicles combine received information with sensor data to adjust acceleration or deceleration.
  • B. String Stability: Each transmitted packet traverses processor and transceiver queues, with total end-to-end delay including queuing, processing, and transmission time.The first queue captures processor-side delay and the second captures transceiver-side delay.

A. Queuing Delay and Processing Delay in Queue Q1

The V2V delay model represents local processing and communication queues to derive the end-to-end delay between consecutive platoon vehicles.

  • Processing model: Sensor packets arrive at the processor according to a Poisson process, while an infinite-buffer, first-come-first-served processor uses exponential service with rate μ1 > λa.These assumptions ensure stability of the first queue Q1.
  • Queue Q1 delay: The processor’s queuing and service components are combined to obtain the average delay for packets in Q1 before transmission.The passage set introduces average queuing and processing delays and their combination at the first queue.
  • Service-time analysis: Theorem 2 derives the mean and variance of the single-packet service time from the interference characterization and packet-size notation.The service-time moments support the analysis of the second queue’s delay.
  • Communication queue Q2: The transceiver queue Q2 uses Poisson arrivals and a general service-time distribution determined by the uncertain V2V channel.Its average delay, including waiting and transmission, is obtained using the M/G/1 Pollaczek–Khinchine framework.
  • End-to-end delay: The average end-to-end V2V delay is the sum of the average delays at Q1 and Q2.The receiving vehicle is assumed to obtain the preceding vehicle’s velocity after the wireless packet arrives.

C. Control-Aware Reliability of the Wireless Network

The paper defines wireless reliability as the probability that end-to-end V2V delay meets the control system’s stability requirement and derives bounds and approximations for it.

  • Reliability definition: Wireless reliability is defined as P(T1+T2 ≤ min(τ1, τ2)), linking instantaneous communication delay to the control system’s stability limits.The minimum delay requirement jointly captures the relevant control stability conditions.
  • Analytical challenge: Because exact instantaneous-delay PDFs are difficult to derive for combined queuing, processing, and transmission delays, the analysis uses a lower-bound formulation.The paper explicitly identifies exact PDF derivation as challenging.
  • Reliability lower bound: Theorem 3 provides a lower bound on reliability when the average wireless delay is below min(τ1, τ2).The bound is designed to characterize whether the wireless system meets the control system’s delay needs.
  • Design implications: The bounds yield design guidance for selecting bandwidth, transmission power, and control parameters to meet a target reliability.The paper illustrates this guidance with a 95% reliability threshold and notes that interference and noise affect stability support.
  • Transmission-dominated approximation: When processor and arrival conditions make transmission delay dominant, Corollary 2 gives an approximated reliability expression based primarily on Q2 transmission delay.This approximation applies when Q1 and Q2 queuing delays are relatively small.

V. OPTIMIZED CONTROLLER DESIGN

The controller-design procedure optimizes control parameters to enlarge the delay margin available to the wireless network while preserving plant and string stability.

  • Control–network trade-off: With fixed control parameters, wireless-network improvements can meet the delay requirements; with adjustable parameters, controller design can relax those constraints without jeopardizing stability.The optimization depends on processor capability and packet arrival rate.
  • Optimization objective: The design maximizes the smaller of the plant- and string-stability delay requirements, represented by max min(τ1, τ2).The equivalent formulation introduces τ as the common lower stability-delay limit.
  • Constraints: The optimization imposes feasibility constraints on control gains and requires the selected delay threshold to remain below both stability limits.Additional constraints keep a, b, and τ within reasonable ranges.
  • Solution method: Because the optimization is nonconvex, the method uses dual updates and Lagrange multipliers to obtain an efficient sub-optimal solution.The control gains are recovered by solving the resulting dual optimization problem.
  • Computational procedure: The dual-variable procedure converges in O(49log(1/ε)) iterations under the stated implementation.The ellipsoid method is used to find the dual variables.

B. Optimization of the Lower Bound for the Reliability

The reliability optimization and simulations connect stability-delay thresholds, wireless conditions, and platoon configuration to integrated communication–control performance.

  • Reliability optimization: The reliability lower-bound optimization selects control gains to maximize the bound, with the same sub-optimal solution applying when average delay meets the stability requirement.This establishes a direct controller-design route for improving the reliability guarantee.
  • Practical trade-off: Changing control parameters may improve reliability but can increase manufacturer and maintenance costs.The paper presents this as a practical trade-off of controller redesign.
  • Simulation setup: The simulations evaluate reliability under a time-varying wireless delay bounded by the minimum stability delay and examine platoons with different configurations.The setup uses a target velocity of 15 m/s and target inter-vehicle distance of 20 m.
  • Wireless validation: The SINR simulations match Theorem 2’s analytical calculations, and smaller platoon spacing produces higher-SINR outcomes.For SINR above 10 dB, the probability is around 0.76 at 5 m spacing versus around 0.24 at 15 m.
  • Reliability performance: The analysis studies how reliability varies with platoon size and other wireless or control parameters while using an integrated communication–control model.The supplied figure passages identify approximated reliability analyses for differing platoon conditions.

B. Reliability Analysis

The analysis quantifies how wireless conditions, control parameters, spacing, bandwidth, and platoon size affect reliability and provides design thresholds for stable operation.

  • Bandwidth and stability: For reliability 0.90, plant stability requires approximately 31 MHz bandwidth, whereas string stability requires around 2 MHz.The required bandwidth therefore depends strongly on the stability criterion.
  • Traffic and packet conditions: Reliability decreases as inter-vehicle spacing, interfering-vehicle density, or packet size increases because these conditions reduce data rate or increase transmission delay.The analysis attributes the degradation to lower SINR and longer packet transmission time.
  • Spacing guidelines: With low non-platoon-vehicle density and small packets, spacing no greater than 25 m keeps approximated reliability at least 0.9.Spacing is correlated with target velocity, providing a corresponding velocity-design guideline.
  • Reliability bounds: Reliability lower bounds require spacing below 12 m for reliability 0.9, versus 25 m under the approximated reliability.The tighter bound accounts for queuing and processing delays omitted by the approximation.

VII. CONCLUSIONS

The paper integrates control stability and V2V wireless reliability by linking tolerable delay, end-to-end network delay, and reliability optimization. Simulations corroborate the analysis and yield guidelines for configuring platoon size, spacing, bandwidth, and control parameters.

  • Framework and analysis: The proposed framework jointly analyzes plant and string stability, wireless end-to-end delay, and the probability that delay meets control requirements.End-to-end delay includes queuing, processing, and transmission components.
  • Reliability optimization: The paper derives reliability lower bounds and an approximated reliability expression, then proposes two mechanisms for selecting control parameters.The optimization targets wireless reliability while respecting control-system delay requirements.
  • Simulation findings: Simulations corroborate the analytical derivations and show reliability effects from interfering-vehicle density, packet size, and platoon size.These factors are evaluated as design-relevant parameters of vehicular platoons.
  • Design guidance: The results provide guidelines for choosing follower count, inter-vehicle spacing, and control parameters to maintain stable autonomous-platoon operation.The conclusions frame joint communication-control design as beneficial within the studied platoon setting.
  • Future work: Future work will extend the framework to a more dynamic model with multiple platoons.The stated extension identifies the current scope boundary.

APPENDIX

The appendix supplies the stability and reliability derivations underlying the framework, including delay thresholds, channel and queueing analysis, and reliability bounds.

  • Plant stability: A Lyapunov-Razumikhin argument derives a maximum V2V delay threshold sufficient for asymptotic plant stability.The delay of each V2V link must not exceed the resulting threshold τmax.
  • String stability: The appendix derives string-stability conditions from the vehicle-control model and common control gains across platoon vehicles.The resulting proposition characterizes gain conditions that assure string stability.
  • Wireless delay analysis: Wireless delay analysis uses stochastic geometry, queuing theory, and fading-channel distributions to obtain service-time moments and end-to-end delay components.The channel analysis uses Rayleigh or Nakagami fading assumptions and Poisson-point-process tools.
  • Reliability bounds: Reliability bounds are obtained with Markov and Chernoff inequalities, with the tighter bound selected to better approximate wireless reliability.The appendix explicitly identifies the first maximization term as a lower bound and combines two candidate bounds.
  • Optimization structure: The control-parameter optimization is shared by the approximated-reliability and lower-bound problems when the mean delay satisfies the relevant stability thresholds.The equivalence relies on satisfying ¯T1 + ¯T2 ≤ min(τ1, τ2).
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