相关论文: A Hopf-Lax Type Formula for Multi-Agent Path Plann…

The Dynamic Programming approach allows to compute a feedback control for nonlinear problems, but suffers from the curse of dimensionality. The computation of the control relies on the resolution of a nonlinear PDE, the…

We use optimal control via a distributed exterior field to steer the dynamics of an ensemble of N interacting ferromagnetic particles which are immersed into a heat bath by minimizing a quadratic functional. By using dynamic programing…

We introduce a new and efficient numerical method for multicriterion optimal control and single criterion optimal control under integral constraints. The approach is based on extending the state space to include information on a "budget"…

This paper addresses the model-free nonlinear optimal problem with generalized cost functional, and a data-based reinforcement learning technique is developed. It is known that the nonlinear optimal control problem relies on the solution of…

This work proposes a novel numerical scheme for solving the high-dimensional Hamilton-Jacobi-Bellman equation with a functional hierarchical tensor ansatz. We consider the setting of stochastic control, whereby one applies control to a…

We propose a mixed-integer linear program (MILP) for multi-agent motion planning that embeds Polytopic Action-based Motion Planning (PAAMP) into a sequence-then-solve pipeline. Region sequences confine each agent to adjacent convex…

We introduce a framework for solving a class of parabolic partial differential equations on triangle mesh surfaces, including the Hamilton-Jacobi equation and the Fokker-Planck equation. PDE in this class often have nonlinear or stiff terms…

The ad hoc coordination problem is to design an autonomous agent which is able to achieve optimal flexibility and efficiency in a multiagent system with no mechanisms for prior coordination. We conceptualise this problem formally using a…

We present a novel framework for addressing the challenges of multi-Agent planning and formation control within intricate and dynamic environments. This framework transforms the Multi-Agent Path Finding (MAPF) problem into a Multi-Agent…

Missions for autonomous systems often require agents to visit multiple targets in complex operating conditions. This work considers the problem of visiting a set of targets in minimum time by a team of non-communicating agents in a Markov…

We mathematically analyze and numerically study an actor-critic machine learning algorithm for solving high-dimensional Hamilton-Jacobi-Bellman (HJB) partial differential equations from stochastic control theory. The architecture of the…

Stochastic optimal principle leads to the resolution of a partial differential equation (PDE), namely the Hamilton-Jacobi-Bellman (HJB) equation. In general, this equation cannot be solved analytically, thus numerical algorithms are the…

In this paper we propose and analyze a method based on the Riccati transformation for solving the evolutionary Hamilton-Jacobi-Bellman equation arising from the stochastic dynamic optimal allocation problem. We show how the fully nonlinear…

Multi-agent path planning (MAPP) is the problem of planning collision-free trajectories from start to goal locations for a team of agents. This work explores a relatively unexplored setting of MAPP where streams of agents have to go through…

The framework of deep operator network (DeepONet) has been widely exploited thanks to its capability of solving high dimensional partial differential equations. In this paper, we incorporate DeepONet with a recently developed policy…

Multi-Agent Path Finding (MAPF) seeks collision-free paths for multiple agents from their respective starting locations to their respective goal locations while minimizing path costs. Although many MAPF algorithms were developed and can…

Robot path planning plays a pivotal role in enabling autonomous systems to navigate safely and efficiently in complex and uncertain environments. Despite extensive research on classical graph-based methods and sampling-based planners,…

This is the first in a series of papers in which we study an efficient approximation scheme for solving the Hamilton-Jacobi-Bellman equation for multi-dimensional problems in stochastic control theory. The method is a combination of a WKB…

In a multi-agent system, an agent's optimal policy will typically depend on the policies chosen by others. Therefore, a key issue in multi-agent systems research is that of predicting the behaviours of others, and responding promptly to…

We present a scalable and effective multi-agent safe motion planner that enables a group of agents to move to their desired locations while avoiding collisions with obstacles and other agents, with the presence of rich obstacles,…