Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
167 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
42 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Parsimonious shooting heuristic for trajectory control of connected automated traffic part I: Theoretical analysis with generalized time geography (1511.04810v1)

Published 16 Nov 2015 in math.OC and cs.SY

Abstract: This paper studies a problem of controlling trajectories of a platoon of vehicles on a highway segment with connected and automated vehicles. This problem is complex because each vehicle trajectory is an infinite-dimensional object and neighboring trajectories have complex interactions (e.g., car-following behavior). A parsimonious shooting heuristic algorithm is proposed to construct vehicle trajectories on a signalized highway segment that comply with boundary conditions for vehicle arrivals, vehicle mechanical limits, traffic lights and vehicle following safety. This algorithm breaks each vehicle trajectory into a few sections and each is analytically solvable. This decomposes the original hard trajectory control problem to a simple constructive heuristic. Then we slightly adapt this shooting heuristic algorithm to efficiently solve a leading vehicle problem on an uninterrupted freeway. To study theoretical properties of the proposed algorithms, the time geography theory is generalized by considering finite accelerations. With this generalized theory, it is found that under mild conditions, these algorithms can always obtain a feasible solution to the original complex trajectory control problem. Further, we discover that the shooting heuristic solution is a generalization of the solution to the classic kinematic wave theory by incorporating finite accelerations. We identify the theoretical bounds to the difference between the shooting heuristic solution and the kinematic wave solution. Numerical experiments are conducted to verify the theoretical results and to draw additional insights into the potential of trajectory control in improving traffic performance. Building upon this foundation, an optimization framework will be presented in a following paper as Part II of this study.

Citations (193)

Summary

  • The paper introduces a parsimonious shooting heuristic that decomposes infinite-dimensional trajectory optimization into analytically solvable segments using four acceleration parameters.
  • The methodology outperforms traditional models by significantly reducing travel times and curtailing backward wave propagation, thereby improving highway traffic flow and safety.
  • The study links the heuristic to kinematic wave theory via generalized quadratic time geography, offering a novel framework for effective CAV trajectory control under varied traffic conditions.

Analysis of Parsimonious Shooting Heuristic for CAV Trajectory Control

The paper authored by Fang Zhou, Xiaopeng Li, and Jiaqi Ma explores the complexities of trajectory control for connected and automated vehicles (CAVs) on highways, specifically examining both interrupted and uninterrupted traffic scenarios. This inquiry is motivated by the inadequacies of traditional infrastructure-based traffic control, which are largely unable to smooth traffic flow or adequately account for stop-and-go traffic characteristics prevalent in both signalized highway sections and freeways. The paper offers a significant augmentation over previous models by integrating CAV dynamics, which enable disaggregated control through vehicle-to-vehicle and vehicle-to-infrastructure communications, optimizing trajectories in ways that were previously unattainable.

Methodology and Numerical Results

Central to the paper is the parsimonious shooting heuristic (SH) algorithm, structured to address the infinite-dimensional nature of trajectory optimization under non-linear constraints. This algorithm uniquely decomposes vehicle trajectories into pieces that are analytically solvable, circumventing the computational challenges that typically plague trajectory optimization problems. This decomposition into piece-wise parabolic segments, combined with manipulation using just four acceleration control parameters, benchmarks the algorithm's efficiency against traditional methods, which are often hamstrung by severity in both process and time consumption.

The SH algorithm is validated numerically, as demonstrated by comparisons with benchmark manual driving models exemplified by the Intelligent Driver Model. Distinct enhancements are revealed in areas such as travel time reduction—where SH boasts superior performance, reducing travel times significantly over manual driving paradigms. The paper clearly indicates marked improvements in traffic throughput and overall streamlining, further correlating reduced travel time with potential diminutions in emissions and fuel consumption, as well as increased safety.

The authors extend the shooting heuristic to the well-known lead vehicle problem (LVP) on freeways. The proposed SH and its parallel variant, PSHL, assert considerable benefits over established methods by curtailing backward wave propagation efficiently. The SHL solution for LVP is apt for parallel computation being equivalent to PSHL, heralding computing efficiency advances.

Theoretical Implications and Future Directions

The theoretical exposition of the paper is centered around the use of generalized quadratic time geography, an extension that incorporates finite accelerations into traditional time geography. This extension underscores the algorithm’s ability to consistently navigate theoretical bounds, ensuring feasible solutions under mild conditions. Moreover, the linkage identified between the heuristic solutions and kinematic wave theory (KWT)—with SH described as its smoothed variant—offers a novel perspective and extends the utility of classical models where finite-speed transitions are considered.

The feasibility analysis reflects the dichotomous nature of the SH solutions under variable boundary conditions. With respect to variations in traffic density and segment length, it showcases how trajectory feasibility transitions, emphasizing the essentiality of optimizing for real-world applications.

The research sets the stage for refined CAV traffic management systems. Future research should focus on enhancing field calibration, extending framework for mixed automated-manual traffic conditions, and addressing heterogeneous vehicle dynamics. An optimized trajectory control framework, as hinted in the sequel Part II paper, holds promise for advancing traffic flow management objectives encompassing safety, environmental impact minimization, and maximizing traffic efficiency.

Overall, this paper contributes substantial advancements in traffic modeling, laying a framework that bridges theoretical rigor and computational efficiency in optimized CAV trajectory control systems.