Multi-agent Path Planning and Network Flow

This paper connects multi-agent path planning on graphs (roadmaps) to network flow problems, showing that the former can be reduced to the latter, therefore enabling the application of combinatorial network flow algorithms, as well as general linear program techniques, to multi-agent path planning problems on graphs. Exploiting this connection, we show that when the goals are permutation invariant, the problem always has a feasible solution path set with a longest finish time of no more than $n + V - 1$ steps, in which $n$ is the number of agents and $V$ is the number of vertices of the underlying graph. We then give a complete algorithm that finds such a solution in $O(nVE)$ time, with $E$ being the number of edges of the graph. Taking a further step, we study time and distance optimality of the feasible solutions, show that they have a pairwise Pareto optimal structure, and again provide efficient algorithms for optimizing two of these practical objectives.Comment: Corrected an inaccuracy on time optimal solution for average arrival tim

Design and Evaluation of a Traffic Safety System based on Vehicular Networks for the Next Generation of Intelligent Vehicles

La integración de las tecnologías de las telecomunicaciones en el sector del automóvil permitirá a los vehículos intercambiar información mediante Redes Vehiculares, ofreciendo numerosas posibilidades. Esta tesis se centra en la mejora de la seguridad vial y la reducción de la siniestralidad mediante Sistemas Inteligentes de Transporte (ITS). El primer paso consiste en obtener una difusión eficiente de los mensajes de advertencia sobre situaciones potencialmente peligrosas. Hemos desarrollado un marco para simular el intercambio de mensajes entre vehículos, utilizado para proponer esquemas eficientes de difusión. También demostramos que la disposición de las calles tiene gran influencia sobre la eficiencia del proceso. Nuestros algoritmos de difusión son parte de una arquitectura más amplia (e-NOTIFY) capaz de detectar accidentes de tráfico e informar a los servicios de emergencia. El desarrollo y evaluación de un prototipo demostró la viabilidad del sistema y cómo podría ayudar a reducir el número de víctimas en carretera

Motion Planning for Unlabeled Discs with Optimality Guarantees

We study the problem of path planning for unlabeled (indistinguishable) unit-disc robots in a planar environment cluttered with polygonal obstacles. We introduce an algorithm which minimizes the total path length, i.e., the sum of lengths of the individual paths. Our algorithm is guaranteed to find a solution if one exists, or report that none exists otherwise. It runs in time $\tilde{O}(m^4+m^2n^2)$, where $m$ is the number of robots and $n$ is the total complexity of the workspace. Moreover, the total length of the returned solution is at most $\text{OPT}+4m$, where OPT is the optimal solution cost. To the best of our knowledge this is the first algorithm for the problem that has such guarantees. The algorithm has been implemented in an exact manner and we present experimental results that attest to its efficiency

Optimization approaches for robot trajectory planning

[EN] The development of optimal trajectory planning algorithms for autonomous robots is a key issue in order to efficiently perform the robot tasks. This problem is hampered by the complex environment regarding the kinematics and dynamics of robots with several arms and/or degrees of freedom (dof), the design of collision-free trajectories and the physical limitations of the robots. This paper presents a review about the existing robot motion planning techniques and discusses their pros and cons regarding completeness, optimality, efficiency, accuracy, smoothness, stability, safety and scalability.Llopis-Albert, C.; Rubio, F.; Valero, F. (2018). Optimization approaches for robot trajectory planning. Multidisciplinary Journal for Education, Social and Technological Sciences. 5(1):1-16. doi:10.4995/muse.2018.9867SWORD1165