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A Hierarchical Robust Control Strategy for Decentralized Signal-Free Intersection Management

Xiao Pan, Boli Chen, Li Dai, Stelios Timotheou, Simos A. Evangelou

TL;DR

This article focuses on cooperative vehicle management at a signal-free intersection with consideration of vehicle modeling uncertainties and sensor measurement disturbances and shows that a minor reduction in journey time can considerably reduce energy consumption, which emphasizes the necessity of optimizing their tradeoff.

Abstract

The development of connected and automated vehicles is the key to improving urban mobility safety and efficiency. This paper focuses on cooperative vehicle management at a signal-free intersection with consideration of vehicle modeling uncertainties and sensor measurement disturbances. The problem is approached by a hierarchical robust control strategy in a decentralized traffic coordination framework where optimal control and tube-based robust model predictive control methods are designed to hierarchically solve the optimal crossing order and the velocity trajectories of a group of CAVs in terms of energy consumption and throughput. To capture the energy consumption of each vehicle, their powertrain system is modeled in line with an electric drive system. With a suitable relaxation and spatial modeling approach, the optimization problems in the proposed strategy can be formulated as convex second-order cone programs, which provide a unique and computationally efficient solution. A rigorous proof of the equivalence between the convexified and the original problems is also provided. Simulation results illustrate the effectiveness and robustness of the proposed strategy and reveal the impact of traffic density on the control solution. The study of the Pareto optimal solutions for the energy-time objective shows that a minor reduction in journey time can considerably reduce energy consumption, which emphasizes the necessity of optimizing their trade-off. Finally, the numerical comparisons carried out for different prediction horizons and sampling intervals provide insight into the control design.

A Hierarchical Robust Control Strategy for Decentralized Signal-Free Intersection Management

TL;DR

This article focuses on cooperative vehicle management at a signal-free intersection with consideration of vehicle modeling uncertainties and sensor measurement disturbances and shows that a minor reduction in journey time can considerably reduce energy consumption, which emphasizes the necessity of optimizing their tradeoff.

Abstract

The development of connected and automated vehicles is the key to improving urban mobility safety and efficiency. This paper focuses on cooperative vehicle management at a signal-free intersection with consideration of vehicle modeling uncertainties and sensor measurement disturbances. The problem is approached by a hierarchical robust control strategy in a decentralized traffic coordination framework where optimal control and tube-based robust model predictive control methods are designed to hierarchically solve the optimal crossing order and the velocity trajectories of a group of CAVs in terms of energy consumption and throughput. To capture the energy consumption of each vehicle, their powertrain system is modeled in line with an electric drive system. With a suitable relaxation and spatial modeling approach, the optimization problems in the proposed strategy can be formulated as convex second-order cone programs, which provide a unique and computationally efficient solution. A rigorous proof of the equivalence between the convexified and the original problems is also provided. Simulation results illustrate the effectiveness and robustness of the proposed strategy and reveal the impact of traffic density on the control solution. The study of the Pareto optimal solutions for the energy-time objective shows that a minor reduction in journey time can considerably reduce energy consumption, which emphasizes the necessity of optimizing their trade-off. Finally, the numerical comparisons carried out for different prediction horizons and sampling intervals provide insight into the control design.
Paper Structure (9 sections, 3 theorems, 64 equations, 11 figures, 4 tables)

This paper contains 9 sections, 3 theorems, 64 equations, 11 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. System Modeling and General Problem Setup
  4. Convex Modeling Approach
  5. Hierarchical Robust Control Strategy
  6. Crossing Order Scheduler
  7. Trajectory Optimizer
  8. Numerical Results
  9. Conclusions

Key Result

Proposition 1

Under ass:fittingparameters and ass:brakeforce, the globally optimal solution of prob:ocp2 always finds the equality condition of eq:syst3, and therefore the solution of the relaxed, nonlinear convex problem prob:ocp2 is identical to the solution of the non-convex problem prob:ocp.

Figures (11)

  • Figure 1: The system architecture of autonomous intersection crossing problem.
  • Figure 2: Left: efficiency map of the electric motor (positive torque indicates battery discharging and negative torque represents battery charging) with operational bounds (dotted lines). The area surrounded by red lines denotes the operational region for the feasible vehicle speed specified by \ref{['eq:Bound_E_i']}. Right: nonlinear regression of the battery output power data (red dots, calculated based on the efficiency map shown in the left figure of Fig. \ref{['fig:motormap_Pbfitting']}) by solving \ref{['eq:fit']} with an R-square fit of 99.25% whereas the result of unconstrained fitting (without \ref{['eq:fit2']}) is 99.53%.
  • Figure 3: The schematic of the decentralized HRCS. The objective functions in \ref{['prob:ocp3']} and \ref{['prob:ocp4']} take $J_{d,i}$\ref{['eq:J_decentralized']} and $\bar{J}_{d,i}$\ref{['eq:decentralized_objective']}, respectively.
  • Figure 4: Traveled distance trajectories (distance to the end of MZ) by solving the HRCS subject to an average travel time $12.31$ s at an arrival rate of 800 veh/h per lane and with prediction horizon length $N_p\!=\!15$. The horizontal dashed lines correspond to the entry of the MZ, while the horizontal continuous black line denotes the end of the MZ. The four vehicle heading directions are denoted using different colors. Note that the numbers in the brackets highlight the arriving orders of the vehicles at the CZ, which are different from their order entering the MZ. The upper-level scheduler sorts the vehicles in order of $\mathcal{N}=\{1,2,3,4,5,7,6,8,10,9,11,12,13,14,15,16,17,18,20,19\}$.
  • Figure 5: Optimal speed profiles by solving the HRCS subject to an average travel time $12.31$ s for all CAVs at an arrival rate of 800 veh/h per lane. Note that the numbers in the brackets highlight the arriving orders of the vehicles at the CZ, which are different from their order entering the MZ.
  • ...and 6 more figures

Theorems & Definitions (7)

  • Definition 1
  • Proposition 1
  • Lemma 1
  • Remark 1: Active friction brakes
  • Corollary 1
  • Remark 2
  • Remark 3