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

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…

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…

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…

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…

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…

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…

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…

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…

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…

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…

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…

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…

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…

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…

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…

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…

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…

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…