Related papers: A Hopf-Lax Type Formula for Multi-Agent Path Plann…
Optimal control of diffusion processes is intimately connected to the problem of solving certain Hamilton-Jacobi-Bellman equations. Building on recent machine learning inspired approaches towards high-dimensional PDEs, we investigate the…
Multi-agent pathfinding (MAPF) is the problem of finding a set of conflict-free paths for a set of agents. Typically, the agents' moves are limited to a pre-defined graph of possible locations and allowed transitions between them, e.g. a…
Multi-Agent Path Finding (MAPF) requires collision-free trajectories for multiple agents on a shared graph, often with the objective of minimizing the sum-of-costs (SOC). Many optimal and bounded-suboptimal solvers rely on time-expanded…
The objective of designing a control system is to steer a dynamical system with a control signal, guiding it to exhibit the desired behavior. The Hamilton-Jacobi-Bellman (HJB) partial differential equation offers a framework for optimal…
Many high-level multi-agent planning problems, including multi-robot navigation and path planning, can be effectively modeled using deterministic actions and observations. In this work, we focus on such domains and introduce the class of…
Large-scale multi-agent pathfinding (MAPF) presents significant challenges in several areas. As systems grow in complexity with a multitude of autonomous agents operating simultaneously, efficient and collision-free coordination becomes…
Complex scheduling problems require a large amount computation power and innovative solution methods. The objective of this paper is the conception and implementation of a multi-agent system that is applicable in various problem domains.…
Multi-agent path finding (MAPF) is the problem of finding collision-free paths for a team of agents to reach their goal locations. State-of-the-art classical MAPF solvers typically employ heuristic search to find solutions for hundreds of…
In a previous work (Akian, Fodjo, 2016), we introduced a lower complexity probabilistic max-plus numerical method for solving fully nonlinear Hamilton-Jacobi-Bellman equations associated to diffusion control problems involving a finite…
We formalize Multi-Agent Path Finding with Deadlines (MAPF-DL). The objective is to maximize the number of agents that can reach their given goal vertices from their given start vertices within the deadline, without colliding with each…
Conflict-Based Search is one of the most popular methods for multi-agent path finding. Though it is complete and optimal, it does not scale well. Recent works have been proposed to accelerate it by introducing various heuristics. However,…
This paper addresses a continuous-time continuous-space chance-constrained stochastic optimal control (SOC) problem via a Hamilton-Jacobi-Bellman (HJB) partial differential equation (PDE). Through Lagrangian relaxation, we convert the…
Multi-robot path finding in dynamic environments is a highly challenging classic problem. In the movement process, robots need to avoid collisions with other moving robots while minimizing their travel distance. Previous methods for this…
The goal of Multi-Agent Path Finding (MAPF) is to find a set of paths for a fleet of agents moving in a shared environment such that the agents reach their goals without colliding with each other. In practice, some of the robots executing…
We consider the problem of computing safety regions, modeled as nonconvex backward reachable sets, for a nonlinear car collision avoidance model with time-dependent obstacles. The Hamilton-Jacobi-Bellman framework is used. A new formulation…
This paper proposes FMAP (Forward Multi-Agent Planning), a fully-distributed multi-agent planning method that integrates planning and coordination. Although FMAP is specifically aimed at solving problems that require cooperation among…
This article proposes a numerical scheme for computing the evolution of vehicular traffic on a road network over a finite time horizon. The traffic dynamics on each link is modeled by the Hamilton-Jacobi (HJ) partial differential equation…
This paper proposes an actor-critic algorithm for controlling the temperature of a battery pack using a cooling fluid. This is modeled by a coupled 1D partial differential equation (PDE) with a controlled advection term that determines the…
This paper presents centralized and distributed Alternating Direction Method of Multipliers (ADMM) frameworks for solving large-scale nonconvex optimization problems with binary decision variables subject to spanning tree or rooted…
Large language model (LLM)-based agents have demonstrated remarkable capabilities in decision-making tasks, but struggle significantly with complex, long-horizon planning scenarios. This arises from their lack of macroscopic guidance,…