matlab中三维A*算法

A*算法是一种在图形搜索和路径规划中广泛应用的启发式搜索算法。它可以用于三维路径规划，但是需要对算法进行适当的修改。

在三维A*算法中，需要将搜索空间从平面扩展到立体空间。这可以通过将每个节点表示为三元组(x,y,z)，其中x、y、z分别表示节点在三个轴上的坐标来实现。

在实现A*算法时，需要确定合适的启发式函数来估计从当前节点到目标节点的距离。在三维空间中，可以使用欧几里得距离或曼哈顿距离等距离函数作为启发式函数。

另外，还需要考虑如何表示障碍物。一种常见的方法是将三维空间划分为立方体网格，并将每个网格标记为障碍或非障碍。在搜索过程中，需要避开障碍物。

以下是一个简单的三维A*算法的示例代码：

function [path, cost] = astar3d(map, start, goal)
% Three-dimensional A* algorithm
% map: 3D occupancy grid (1: free, 0: occupied)
% start: starting position (3D coordinate)
% goal: goal position (3D coordinate)

% Define heuristic function (Euclidean distance)
heuristic = @(pos) norm(pos - goal);

% Initialize open and closed lists
open = PriorityQueue();
closed = containers.Map();

% Add starting node to open list
g_score = 0;
f_score = g_score + heuristic(start);
open.insert(start, f_score);

% Loop until goal is found or open list is empty
while ~open.isempty()
    % Get node with lowest f-score from open list
    [current_pos, f_score] = open.pop();
    
    % Check if current node is goal
    if isequal(current_pos, goal)
        % Reconstruct path and return
        path = reconstruct_path(closed, start, goal);
        cost = g_score;
        return;
    end
    
    % Add current node to closed list
    closed(num2str(current_pos)) = g_score;
    
    % Expand neighbors
    neighbors = get_neighbors(map, current_pos);
    for i = 1:size(neighbors, 1)
        neighbor_pos = neighbors(i, :);
        
        % Calculate tentative g-score for neighbor
        tentative_g_score = g_score + norm(current_pos - neighbor_pos);
        
        % Check if neighbor is already in closed list
        if isKey(closed, num2str(neighbor_pos))
            % Skip neighbor if it has already been evaluated
            continue;
        end
        
        % Check if neighbor is in open list
        if open.ismember(neighbor_pos)
            % Check if tentative g-score is better than previous g-score
            if tentative_g_score < closed(num2str(neighbor_pos))
                % Update neighbor's g-score and f-score
                closed(num2str(neighbor_pos)) = tentative_g_score;
                f_score = tentative_g_score + heuristic(neighbor_pos);
                open.update(neighbor_pos, f_score);
            end
        else
            % Add neighbor to open list
            closed(num2str(neighbor_pos)) = tentative_g_score;
            f_score = tentative_g_score + heuristic(neighbor_pos);
            open.insert(neighbor_pos, f_score);
        end
    end
    
    % Update g-score
    g_score = closed(num2str(current_pos));
end

% No path found
path = [];
cost = inf;
end


function neighbors = get_neighbors(map, pos)
% Get neighboring nodes that are free and within map bounds
[x, y, z] = ind2sub(size(map), find(map));
neighbors = [x, y, z];
neighbors = neighbors(~ismember(neighbors, pos, 'rows'), :);
distances = pdist2(pos, neighbors);
neighbors(distances > sqrt(3)) = NaN; % limit to 1-neighborhood
neighbors(any(isnan(neighbors), 2), :) = [];
neighbors = neighbors(map(sub2ind(size(map), neighbors(:,1), neighbors(:,2), neighbors(:,3))) == 1, :);
end


function path = reconstruct_path(closed, start, goal)
% Reconstruct path from closed list
path = [goal];
while ~isequal(path(1,:), start)
    pos = path(1,:);
    for dx = -1:1
        for dy = -1:1
            for dz = -1:1
                neighbor_pos = pos + [dx, dy, dz];
                if isKey(closed, num2str(neighbor_pos)) && closed(num2str(neighbor_pos)) < closed(num2str(pos))
                    pos = neighbor_pos;
                end
            end
        end
    end
    path = [pos; path];
end
end


classdef PriorityQueue < handle
    % Priority queue implemented as binary heap
    
    properties (Access = private)
        heap;
        count;
    end
    
    methods
        function obj = PriorityQueue()
            obj.heap = {};
            obj.count = 0;
        end
        
        function insert(obj, item, priority)
            % Add item with given priority to queue
            obj.count = obj.count + 1;
            obj.heap{obj.count} = {item, priority};
            obj.sift_up(obj.count);
        end
        
        function [item, priority] = pop(obj)
            % Remove and return item with lowest priority from queue
            item = obj.heap{1}{1};
            priority = obj.heap{1}{2};
            obj.heap{1} = obj.heap{obj.count};
            obj.count = obj.count - 1;
            obj.sift_down(1);
        end
        
        function update(obj, item, priority)
            % Update priority of given item in queue
            for i = 1:obj.count
                if isequal(obj.heap{i}{1}, item)
                    obj.heap{i}{2} = priority;
                    obj.sift_up(i);
                    break;
                end
            end
        end
        
        function tf = isempty(obj)
            % Check if queue is empty
            tf = obj.count == 0;
        end
        
        function tf = ismember(obj, item)
            % Check if item is in queue
            tf = false;
            for i = 1:obj.count
                if isequal(obj.heap{i}{1}, item)
                    tf = true;
                    break;
                end
            end
        end
    end
    
    methods (Access = private)
        function sift_up(obj, index)
            % Move item up in heap until it satisfies heap property
            while index > 1
                parent_index = floor(index / 2);
                if obj.heap{index}{2} < obj.heap{parent_index}{2}
                    temp = obj.heap{index};
                    obj.heap{index} = obj.heap{parent_index};
                    obj.heap{parent_index} = temp;
                    index = parent_index;
                else
                    break;
                end
            end
        end
        
        function sift_down(obj, index)
            % Move item down in heap until it satisfies heap property
            while index * 2 <= obj.count
                child_index = index * 2;
                if child_index + 1 <= obj.count && obj.heap{child_index + 1}{2} < obj.heap{child_index}{2}
                    child_index = child_index + 1;
                end
                if obj.heap{child_index}{2} < obj.heap{index}{2}
                    temp = obj.heap{index};
                    obj.heap{index} = obj.heap{child_index};
                    obj.heap{child_index} = temp;
                    index = child_index;
                else
                    break;
                end
            end
        end
    end
end

该实现使用了一个基于二叉堆的优先队列来管理开放列表，并使用容器映射来管理关闭列表。搜索空间被划分为立方体网格，并使用三元组(x,y,z)表示每个节点的位置。启发式函数使用欧几里得距离，障碍物被标记为0，空闲区域被标记为1。在搜索过程中，只扩展空闲节点，并且避开障碍物。

请注意，该实现并不是最优的实现，因为它没有使用任何优化技巧，如跳跃点或平滑路径。但是，它可以作为三维A*算法的一个简单示例来帮助您开始。