[Paper Review] Joint Time and Energy-Optimal Control of Connected Automated Vehicles at Signal-Free Intersections with Speed-Dependent Safety Guarantees

Yue Zhang, Christos G. Cassandras|arXiv (Cornell University)|Mar 13, 2019

Traffic control and management25 references4 citations

TL;DR

This paper proposes a decentralized, joint time- and energy-optimal control framework for connected automated vehicles (CAVs) at signal-free intersections, incorporating speed-dependent rear-end safety, time-dependent lateral collision avoidance, and actuation constraints. The approach derives explicit optimal control laws that ensure safety while minimizing travel time and energy consumption, with simulations demonstrating improved road utilization and safety under dynamic constraints.

ABSTRACT

We extend earlier work establishing a framework for optimally controlling Connected Automated Vehicles (CAVs) crossing a signal free intersection by jointly optimizing energy and travel time. We derive explicit optimal control solutions in a decentralized manner that guarantee both a speed-dependent rear-end safety constraint and a time-dependent lateral collision constraint, in addition to lower/upper bounds on speed and acceleration. Extensive simulation examples are included to illustrate this framework.

Motivation & Objective

• To address the challenge of optimizing both travel time and energy consumption for CAVs at signal-free intersections.
• To improve safety and traffic efficiency by introducing a speed-dependent rear-end safety constraint that adapts to vehicle speed.
• To ensure lateral collision avoidance between vehicles from different roads using a time-dependent constraint based on exit times from the merging zone.
• To enable decentralized, on-board computation by deriving explicit control solutions that depend only on limited information from preceding vehicles.
• To extend prior work by integrating the merging zone into the optimal control horizon and relaxing the constant-speed assumption.

Proposed method

• Formulates a joint time- and energy-optimal control problem for each CAV over the Control Zone (CZ) and Merging Zone (MZ).
• Incorporates a speed-dependent rear-end safety constraint: $ p_i(t) + \varphi v_i(t) + \delta_0 - p_k(t) \leq 0 $, where $ \varphi $ and $ \delta_0 $ are safety parameters.
• Introduces a time-dependent lateral collision constraint: $ t_i^m \geq t_c^f $, ensuring a CAV enters the MZ only after the preceding one exits.
• Derives explicit optimal control solutions using Pontryagin's Minimum Principle, with structural properties that allow feasibility checking at entry.
• Handles multiple active constraints (speed, acceleration, safety, lateral) through piecewise control arcs, including acceleration-limited, unconstrained, and cruising phases.
• Ensures continuity of control and state trajectories at switching points between constrained and unconstrained arcs.

Experimental results

Research questions

• RQ1 How can joint time- and energy-optimal control be achieved for CAVs at signal-free intersections while ensuring safety?
• RQ2 What is the impact of using a speed-dependent rear-end safety constraint compared to a distance-dependent one on traffic flow and road utilization?
• RQ3 How can lateral collision avoidance be modeled as a time-dependent constraint in the presence of multiple conflicting vehicle streams?
• RQ4 Can optimal control solutions be computed in a decentralized manner using only local information from preceding vehicles?
• RQ5 What are the structural properties of optimal trajectories when multiple constraints (safety, speed, acceleration) are active?

Key findings

• The speed-dependent rear-end safety constraint increases inter-vehicle distance at higher speeds, improving safety margins dynamically.
• When the speed-dependent constraint is active, vehicles can maintain tighter spacing at low speeds, enhancing road utilization compared to distance-based constraints.
• The time-dependent lateral collision constraint ensures that a CAV only enters the MZ after the preceding vehicle has fully exited, preventing lateral collisions.
• Optimal control profiles exhibit continuity at switching points between constrained and unconstrained arcs, such as at $ \tau_1 = 4.0 $ s and $ \tau_2 = 31 $ s in the speed- and acceleration-constrained example.
• The inclusion of the MZ in the optimal control horizon allows for smoother, more flexible vehicle trajectories compared to assuming constant speed in the MZ.
• Simulation results confirm that the proposed framework enables decentralized, real-time optimal control with explicit solutions that satisfy all safety and performance constraints.