Optimal cooperative motion planning for vehicles at intersections

Abstract: We consider the problem of cooperative intersection management. It arises in automated transportation systems for people or goods but also in multi-robots environment. Therefore many solutions have been proposed to avoid collisions. The main problem is to determine collision-free but also deadlock-free and optimal algorithms. Even with a simple definition of optimality, finding a global optimum is a problem of high complexity, especially for open systems involving a large and varying number of vehicles. This paper advocates the use of a mathematical framework based on a decomposition of the problem into a continuous optimization part and a scheduling problem. The paper emphasizes connections between the usual notion of vehicle priority and an abstract formulation of the scheduling problem in the coordination space. A constructive locally optimal algorithm is proposed. More generally, this work opens up for new computationally efficient cooperative motion planning algorithms.

• The paper's main contribution is the development of a cooperative intersection management framework that decomposes motion planning into continuous optimization and discrete scheduling subproblems.
• It employs a coordination space formulation with fixed priority relations and iterative heuristics to achieve collision-free, deadlock-free, and near-optimal vehicle trajectories.
• The methodology lays a foundation for integrating these algorithms into real-world intelligent transportation systems, advancing autonomous intersection management.

Summary of "Optimal cooperative motion planning for vehicles at intersections"

Introduction

The paper "Optimal cooperative motion planning for vehicles at intersections" addresses the problem of cooperative intersection management for autonomous vehicles and robots, focusing on achieving collision-free, deadlock-free, and optimal motion planning. The complexity of achieving a global optimum in such systems, especially when there is a varying number of vehicles, necessitates a mathematical framework that decomposes the problem into continuous optimization and scheduling subproblems. The paper introduces a locally optimal algorithm and advocates for the use of coordination space to develop efficient cooperative motion planning algorithms.

Problem Formulation

In designing intelligent transportation systems, intersections are crucial points where safety and efficiency often collide. The paper divides the motion planning task into two main parts: determining fixed paths for vehicles and adjusting their velocities to cross intersections optimally without collisions. Vehicles follow predefined paths, and their motion is planned within a coordination space formed by their normalized curvilinear coordinates. Constraints such as maximum velocity and non-negativity ensure safety and feasibility of the paths. The notion of obstacle regions, comprising collision possibilities, is crucial, and the coordination space is used to dynamically plan movements and resolve conflicts.

Coordination and Priority Relations

A key contribution of the paper is the definition of a priority relation between vehicles that reflects the precedence in crossing intersections. Priority relations are represented as complete directed graphs that inherently introduce order among vehicle trajectories. However, feasible priority relations, which allow coherent and non-cyclic precedence in vehicle movement, are not always orders but can be characterized by the spatial configuration of collision cylinders. The paper proves that feasible priority graphs are free of cyclic dependencies that would lead to inaccessible goal states, thus ensuring feasible trajectories in practical scenarios.

Motion Planning and Algorithm Design

The algorithmic approach to motion planning is divided into solving the trajectory optimization problem for fixed priority graphs and proposing heuristics when priorities are not predetermined. For fixed priorities, optimal trajectories are achieved by maximizing vehicle movement within the prescribed speed limits and avoiding collisions and forbidden gates dynamically. This methodology links discrete scheduling problems with continuous optimization in coordination spaces, which is pivotal for designing efficient algorithms. The paper delineates a heuristic method that builds trajectories iteratively while maintaining consistency with established priorities, effectively providing near-optimal solutions without prohibitive computational costs.

Implications and Future Work

The proposed framework offers practical insights into the development of autonomous vehicle systems at intersections, presenting a mathematical foundation adaptable to dynamic real-world scenarios. Its implications span both theoretical understanding of motion planning problems and practical applications in intelligent transportation systems, particularly in coordinating autonomous vehicles in complex environments. The paper concludes by suggesting further exploration into dynamic scenarios with variable vehicle numbers and incorporating realistic dynamic constraints. Future work involves integrating these algorithms into real-world applications, such as automated transportation systems like cooperative cybercars.

Conclusion

The paper's contributions lie in formalizing a cooperative motion planning algorithm using coordination space and priority relations. By providing a foundation for optimal and deadlock-free vehicle coordination, it opens avenues for effective algorithm design suited for real-time applications in autonomous driving environments. As intelligent transportation systems become increasingly prevalent, understanding and further developing these techniques will be essential for enhancing intersection safety and efficiency.