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Multi-agent path finding (MAPF) is an abstract model for the navigation of multiple robots in warehouse automation, where multiple robots plan collision-free paths from the start to goal positions. Reinforcement learning (RL) has been…

Robotics · Computer Science 2023-11-06 Jianqi Gao , Yanjie Li , Xiaoqing Yang , Mingshan Tan

Recent observations have been made that bridge splitting methods arising from optimization, to the Hopf and Lax formulas for Hamilton-Jacobi Equations with Hamiltonians $H(p)$. This has produced extremely fast algorithms in computing…

Optimization and Control · Mathematics 2018-03-06 Alex Tong Lin , Yat Tin Chow , Stanley Osher

This paper presents a new methodology to craft navigation functions for nonlinear systems with stochastic uncertainty. The method relies on the transformation of the Hamilton-Jacobi-Bellman (HJB) equation into a linear partial differential…

Robotics · Computer Science 2014-09-23 Matanya B. Horowitz , Joel W. Burdick

We propose an efficient framework using Dynnikov coordinates for homotopy-aware multi-agent path planning in planar domains that may contain obstacles. We developed a method for generating multiple homotopically distinct solutions for the…

Multiagent Systems · Computer Science 2026-02-19 Kazumi Kasaura

In this paper, we investigate the distributed optimal control problem for a kind of nonlinear multi-agent systems. In particular,both the state and the system dynamic structures of each agent are private and can only be shared among…

Optimization and Control · Mathematics 2026-04-08 Ruixue Li , Wenjing Yang , Zhaorong Zhang , Xun Li , Juanjuan Xu

We present an accelerated algorithm for the solution of static Hamilton-Jacobi-Bellman equations related to optimal control problems. Our scheme is based on a classic policy iteration procedure, which is known to have superlinear…

Optimization and Control · Mathematics 2016-02-22 Alessandro Alla , Maurizio Falcone , Dante Kalise

We address the multi-agent motion planning problem where interactions, collisions, and congestion co-exist. Conventional game-theoretic planners capture interactions among agents but often converge to conservative, congested equilibria.…

This paper investigates a Hamilton-Jacobi (HJ) analysis to solve finite-horizon optimal control problems for high-dimensional systems. Although grid-based methods, such as the level-set method [1], numerically solve a general class of HJ…

Systems and Control · Electrical Eng. & Systems 2021-06-28 Donggun Lee , Claire J. Tomlin

Cooperative path planning, a crucial aspect of multi-agent systems research, serves a variety of sectors, including military, agriculture, and industry. Many existing algorithms, however, come with certain limitations, such as simplified…

Robotics · Computer Science 2024-10-22 Yuchen Wu , Yifan Yang , Gang Xu , Junjie Cao , Yansong Chen , Licheng Wen , Yong Liu

Efficient robotic extraterrestrial exploration requires robots with diverse capabilities, ranging from scientific measurement tools to advanced locomotion. A robotic team enables the distribution of tasks over multiple specialized…

Robotics · Computer Science 2026-04-02 Matthias Rubio , Julia Richter , Hendrik Kolvenbach , Marco Hutter

CASL-HJX is a computational framework designed for solving deterministic and stochastic Hamilton-Jacobi equations in two spatial dimensions. It provides a flexible and efficient approach to modeling front propagation problems, optimal…

Optimization and Control · Mathematics 2025-05-21 Faranak Rajabi , Jacob Fingerman , Andrew Wang , Jeff Moehlis , Frederic Gibou

To sidestep the curse of dimensionality when computing solutions to Hamilton-Jacobi-Bellman partial differential equations (HJB PDE), we propose an algorithm that leverages a neural network to approximate the value function. We show that…

Machine Learning · Computer Science 2017-03-28 Frank Jiang , Glen Chou , Mo Chen , Claire J. Tomlin

We consider piecewise-deterministic optimal control problems in which the environment randomly switches among several deterministic modes, and the goal is to optimize the expected cost up to the termination while taking the likelihood of…

Optimization and Control · Mathematics 2015-12-31 Zhengdi Shen , Alexander Vladimirsky

This paper presents a novel hybrid motion planning method for holonomic multi-agent systems. The proposed decentralised model predictive control (MPC) framework tackles the intractability of classical centralised MPC for a growing number of…

Two key challenges in optimal control include efficiently solving high-dimensional problems and handling optimal control problems with state-dependent running costs. In this paper, we consider a class of optimal control problems whose…

Optimization and Control · Mathematics 2023-05-16 Paula Chen , Jérôme Darbon , Tingwei Meng

This paper presents a hybrid control framework for the motion planning of a multi-agent system including N robotic agents and M objects, under high level goals expressed as Linear Temporal Logic (LTL) formulas. In particular, we design…

Systems and Control · Computer Science 2018-03-06 Christos K. Verginis , Dimos V. Dimarogonas

This paper introduces a novel methodology that leverages the Hamilton-Jacobi solution to enhance non-linear model predictive control (MPC) in scenarios affected by navigational uncertainty. Using Hamilton-Jacobi-Theoretic approach, a…

Optimization and Control · Mathematics 2025-04-01 Amit Jain , Roshan T. Eapen , Puneet Singla

We address the problem of optimal path planning for a simple nonholonomic vehicle in the presence of obstacles. Most current approaches are either split hierarchically into global path planning and local collision avoidance, or neglect some…

Optimization and Control · Mathematics 2020-05-08 Christian Parkinson , Andrea L. Bertozzi , Stanley Osher

Multi-Agent Path Finding has been widely studied in the past few years due to its broad application in the field of robotics and AI. However, previous solvers rely on several simplifying assumptions. They limit their applicability in…

Robotics · Computer Science 2022-01-06 Licheng Wen , Zhen Zhang , Zhe Chen , Xiangrui Zhao , Yong Liu

It is well known that time dependent Hamilton-Jacobi-Isaacs partial differential equations (HJ PDE), play an important role in analyzing continuous dynamic games and control theory problems. An important tool for such problems when they…

Optimization and Control · Mathematics 2016-05-09 Jérôme Darbon , Stanley Osher