C#，人工智能，机器人，路径规划，A*（AStar Algorithm）算法、源代码及计算数据可视化-编程知识

Peter Hart

Nils Nilsson

Bertram Raphael

参考：

C#，人工智能（AI）机器人路径规划（Path Planning）的ARA*（Anytime Replanning A* Algorithm）算法与源程序https://blog.csdn.net/beijinghorn/article/details/125464754

一、A*算法概述

A*算法最初由斯坦福研究院（Stanford Institute）的 Peter Hart，Nils Nilsson，Bertram Raphael 发表于1968年，属于Dijkstra算法的拓展之一。

论文原文https://www.cs.auckland.ac.nz/courses/compsci709s2c/resources/Mike.d/astarNilsson.pdf

A*算法是常用的路径规划、最短路径搜索、图遍历算法。

借助於启发函数，A*同时拥有较好的性能与准确度，因而备受人工智能、机器人研究者们的欢迎。

除了 A* ，现在发展了 D*，D*Lite。。。诸多改进的算法，后续都会给出 C# 源代码。

A* 的算法不复杂，属于入门级别的。

二、计算结果的动画演示

三、A* 源代码

1、节点信息 NodeInfo

#define ANIMATEusing System;
using System.IO;
using System.Text;
using System.Linq;
using System.Collections.Generic;
using System.Text.RegularExpressions;namespace Legalsoft.Truffer.Algorithm
{/// <summary>/// 节点信息/// </summary>public class NodeInfo{/// <summary>/// 前一节点/// </summary>public NodeInfo Last { get; set; } = null;/// <summary>/// 邻接距离(权值)/// </summary>public int ManhattanWeight { get; set; } = 0;/// <summary>/// 曼哈顿距离(权值)/// </summary>public int RemoteWeight { get; set; } = 0;/// <summary>/// 综合距离(权值)/// </summary>public int TotalWeight { get; set; } = 0;/// <summary>/// 行号/// </summary>public int Column { get; set; } = 0;/// <summary>/// 列号/// </summary>public int Row { get; set; } = 0;/// <summary>/// 是否为墙(节点)？/// </summary>public bool IsWall { get; set; } = false;/// <summary>/// 是否被加入到了close中/// </summary>public bool InClose { get; set; } = false;/// <summary>/// 开口节点？/// </summary>public bool InOpen { get; set; } = false;/// <summary>/// 路过？/// </summary>public bool Visited { get; set; } = false;/// <summary>/// 构造函数/// </summary>/// <param name="y">行号</param>/// <param name="x">列号</param>/// <param name="iswall"></param>public NodeInfo(int y, int x, bool iswall){Row = y;Column = x;IsWall = iswall;}}
}

2、地图信息MapInfo

#define ANIMATEusing System;
using System.IO;
using System.Text;
using System.Linq;
using System.Collections.Generic;
using System.Text.RegularExpressions;namespace Legalsoft.Truffer.Algorithm
{/// <summary>/// 地图信息（墙1与空0）/// </summary>public class MapInfo{/// <summary>/// 行数/// </summary>public int Row { get; set; } = 0;/// <summary>/// 列数/// </summary>public int Column { get; set; } = 0;/// <summary>/// 所有节点/// </summary>public NodeInfo[,] Nodes { get; set; } = null;/// <summary>/// 从文本创建地图/// </summary>/// <param name="buf"></param>public void FromBuffer(string buf){buf = buf.Replace("\r", "").Trim();string[] xlines = buf.Split(new char[] { '\n' }, StringSplitOptions.RemoveEmptyEntries);Nodes = new NodeInfo[xlines.Length, xlines[0].Trim().Length];Row = Nodes.GetLength(0);Column = Nodes.GetLength(1);int y = 0;foreach (string xu in xlines){for (int x = 0; x < xu.Trim().Length; x++){NodeInfo node = new NodeInfo(y, x, Int32.Parse(xu.Trim().Substring(x, 1)) > 0);Nodes[y, x] = node;}y++;}}/// <summary>/// 从文件创建地图/// </summary>/// <param name="filename"></param>/// <exception cref="Exception"></exception>public void FromFile(string filename){try{string buf = File.ReadAllText(filename);FromBuffer(buf);}catch (Exception ex){throw new Exception("");}}/// <summary>/// this重载/// </summary>/// <param name="y"></param>/// <param name="x"></param>/// <returns></returns>public NodeInfo this[int y, int x]{set { Nodes[y, x] = value; }get { return Nodes[y, x]; }}/// <summary>/// 第一个节点/// </summary>public NodeInfo First{get { return Nodes[0, 0]; }}/// <summary>/// 最后一个节点/// </summary>public NodeInfo Last{get { return Nodes[Row - 1, Column - 1]; }}/// <summary>/// 清除路径/// </summary>public void ClearPath(){for (int i = 0; i < Row; i++){for (int j = 0; j < Column; j++){this[i, j].Visited = false;}}}}
}

3、核心代码 AStar Kernal

#define ANIMATEusing System;
using System.IO;
using System.Text;
using System.Linq;
using System.Collections.Generic;
using System.Text.RegularExpressions;namespace Legalsoft.Truffer.Algorithm
{public class AStar{/// <summary>/// 开放列表/// </summary>private List<NodeInfo> openList { get; set; } = new List<NodeInfo>();/// <summary>/// 当前访问的节点/// </summary>private NodeInfo curNode { get; set; } = null;/// <summary>/// 起始节点/// </summary>private NodeInfo startNode { get; set; } = null;/// <summary>/// 终止节点/// </summary>private NodeInfo endNode { get; set; } = null;/// <summary>/// 地图/// </summary>public MapInfo map { get; set; } = new MapInfo();/// <summary>/// 构造函数/// </summary>public AStar(){}/// <summary>/// 节点加入列表，并计算相关权值/// </summary>/// <param name="node"></param>private void AddToList(NodeInfo node){if (node.IsWall) return;if (node.InClose) return;if (node.InOpen) return;openList.Add(node);node.InOpen = true;node.ManhattanWeight = curNode.ManhattanWeight + WeightOf(node, curNode);node.RemoteWeight = WeightOf(node, endNode);node.TotalWeight = node.ManhattanWeight + node.RemoteWeight;node.Last = curNode;}/// <summary>/// 路径规划A*算法(最短路径A*算法)/// 默认左上角(0,0)为起点；右下角为终点；/// </summary>/// <param name="start">起点</param>/// <param name="end">终点</param>public void Tracing(NodeInfo start = null, NodeInfo end = null){List<int[]> steps = new List<int[]>() {new int[2] {  1, 1 },new int[2] {  0, 1 },new int[2] {  1, 0 },new int[2] {  0,-1 },new int[2] { -1, 0 },new int[2] {  1,-1 },new int[2] { -1, 1 },new int[2] { -1,-1 },};startNode = (start == null) ? map.First : start;endNode = (end == null) ? map.Last : end;// 将起点加入到开放列表中openList.Add(startNode);while (true){openList.Sort(SortByCost);curNode = openList[0];openList.Remove(curNode);curNode.InOpen = false;curNode.InClose = true;// 终点?if (curNode == endNode){return;}MarkPath();map.ClearPath();}}/// <summary>/// 节点1到节点2的Weight/// </summary>/// <param name="a">节点1</param>/// <param name="b">节点2</param>/// <returns></returns>private int WeightOf(NodeInfo a, NodeInfo b){// 直行步长double straightDistance = 1.0;// 斜行步长double diagonalDistance = 1.414;int deltaX = Math.Abs(a.Column - b.Column);int deltaY = Math.Abs(a.Row - b.Row);if (deltaX == deltaY){return (int)(deltaX * diagonalDistance);}else if (deltaX < deltaY){return (int)(deltaX * diagonalDistance + (deltaY - deltaX) * straightDistance);}else{return (int)(deltaY * diagonalDistance + (deltaX - deltaY) * straightDistance);}}/// <summary>/// 排序的委托函数/// </summary>/// <param name="a">节点1</param>/// <param name="b">节点2</param>/// <returns></returns>private int SortByCost(NodeInfo a, NodeInfo b){if (a.TotalWeight.CompareTo(b.TotalWeight) != 0){return (a.TotalWeight.CompareTo(b.TotalWeight));}else if (a.RemoteWeight.CompareTo(b.RemoteWeight) != 0){return (a.RemoteWeight.CompareTo(b.RemoteWeight));}else{return 1;}}/// <summary>/// 标记当前获取的路径/// </summary>public void MarkPath(){NodeInfo cd = curNode;while (cd != null){if (cd == startNode){break;}cd.Visited = true;cd = cd.Last;}}}
}

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