This paper is published at 2024 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2024. Full paper at

Abstract

Abstract — When coordinating the motion of connected autonomous vehicles at a signal-free intersection, the vehicles from each direction naturally forms a team and each team seeks to minimize their own traversal time through the intersection, without concerning the traversal times of other teams. Since the intersection is shared by all teams and agent-agent collision must be avoided, the coordination has to trade the traversal time of one team for the other. This paper thus investigates a problem called Multi-Agent Teamwise Cooperative Path Finding (TCPF), which seeks a set of collision-free paths for the agents from their respective start to goal locations, and agents are grouped into multiple teams with each team having its own objective function to optimize. In general, there are more than one teams and hence multiple objectives. TCPF thus seeks the Pareto-optimal front that represents possible tradeoffs among the teams. We develop a centralized planner for TCPF by leveraging the Multi-Agent Path Finding techniques to resolve agent-agent collision, and Multi-Objective Optimization to find Pareto-optimal solutions. We analyze the completeness and optimality of the planner, which is then tested in various settings with up to 40 agents to verify the runtime efficiency and showcase the usage in intersection coordination.

五线谱

五线谱主要是四个内容：什么调，什么节奏，不同位置音符代表不同音高（由下图，从下往上依次是MI FA SOL LA SI DO RE MI FA），以及音符不同时值带来的节奏。

两线时间叫做间。

节奏是用音强弱组织起来的音的长短关系，强调长短，合拍。

节奏型是曲中典型的、反复出现的节奏片段。

节拍是强拍和弱拍按照一定顺序的循环，强调强弱。节拍的节是循环的节点，即小节，图中表示为竖线，后面跟一个强拍。

常说的四四拍：

论文原址

This paper presents a network-based approach to solving the Min-Max Multiple Traveling Salesman Problem (MTSP) by integrating a deep learning model with a traditional TSP solver. The MTSP problem is formulated as a bilevel optimization problem:

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PLANNING ALGORITHMS

Steven M. LaValle

University of Illinois

Copyright Steven M. LaValle 2006

Available for downloading at here.

Published by Cambridge University Press

1.1 What is planning?

2.1 Introduction to Discrete Feasible Planning

2.1.1 Problem Formulation

Formulation 2.1

State: $x$

本节介绍NS模型基本内容、改进NS模型以及对应代码的实现。

1 基本概念

1.1 Nagel–Schreckenberg model NS模型

Nagel–Schreckenberg model，简称NS model，最初由德国物理学家Kai Nagel and Michael Schreckenberg,是一种基于CA模型的用于交通仿真的理论模型。

本节整理卷积方面基本概念

基本概念

1. 卷积：卷积就是用一个可移动的窗口（卷积核），按一定步长，与图像对应元素进行点乘相加的操作。卷积本质上也是一种对数据维度的变换，提取图像的特征，相较于全连接层直接把图像展开成一个行向量，其能更好地捕获图像的空间特征，当然通过改变参数的形状，任何全连接层都能被转换为一个等价卷积层。

Convolution: Convolution is to use a movable window (convolution kernel) to perform a dot multiplication and addition operation with the corresponding elements of the image at a certain step size. Convolution is essentially a transformation of the data dimension to extract the features of the image. Compared with the fully connected layer that directly expands the image into a row vector, it can better capture the spatial features of the image. Of course, by changing the shape of the parameters, any fully connected layer can be converted into an equivalent convolution layer.