基于栅格法的机器人工作空间划分系统

一、系统架构与原理

1.1 栅格法核心思想

将连续的机器人工作空间离散化为规则的栅格单元，每个栅格代表工作空间的一个区域。通过栅格状态（空闲/障碍/已访问等）描述环境，为路径规划、导航和任务分配提供离散化基础。

1.2 栅格类型与表示

栅格类型	形状	适用场景	优缺点
正方形栅格	正方形	通用室内环境	简单易实现，但对角线移动距离不准确
六边形栅格	正六边形	移动机器人	各方向距离一致，但实现复杂
三角形栅格	等边三角形	高精度建模	精度高，但计算量大
自适应栅格	可变大小	复杂环境	兼顾精度与效率，实现复杂

---

二、MATLAB实现代码

2.1 主程序：workspace_grid_mapping.m

%% 基于栅格法的机器人工作空间划分系统
% 功能：将连续工作空间离散化为栅格地图，支持障碍物建模和路径规划

clear; clc; close all;

%% 1. 工作空间参数设置
params.workspace_size = [10, 8];      % 工作空间尺寸 [长, 宽] (米)
params.grid_resolution = 0.2;         % 栅格分辨率 (米/栅格)
params.obstacle_clearance = 0.3;      % 障碍物安全距离 (米)
params.robot_radius = 0.25;           % 机器人半径 (米)
params.grid_type = 'square';          % 栅格类型: 'square', 'hexagon', 'triangle'

fprintf('=== 机器人工作空间栅格划分系统 ===\n');
fprintf('工作空间尺寸: %.1f m × %.1f m\n', params.workspace_size(1), params.workspace_size(2));
fprintf('栅格分辨率: %.2f m/栅格\n', params.grid_resolution);
fprintf('栅格类型: %s\n\n', params.grid_type);

%% 2. 创建栅格地图
fprintf('创建栅格地图...\n');
tic;
[grid_map, grid_info] = create_grid_map(params);
creation_time = toc;
fprintf('  栅格地图创建完成！耗时: %.3f秒\n', creation_time);
fprintf('  栅格数量: %d × %d = %d 个\n', grid_info.rows, grid_info.cols, grid_info.total_cells);

%% 3. 添加障碍物
fprintf('添加障碍物...\n');
tic;
grid_map = add_obstacles(grid_map, grid_info, params);
obstacle_time = toc;
fprintf('  障碍物添加完成！耗时: %.3f秒\n', obstacle_time);
fprintf('  障碍物栅格数: %d\n', sum(grid_map(:) == 1));

%% 4. 计算可达区域
fprintf('计算可达区域...\n');
tic;
reachable_map = compute_reachable_area(grid_map, grid_info, params);
reachability_time = toc;
fprintf('  可达区域计算完成！耗时: %.3f秒\n', reachability_time);
fprintf('  可达栅格数: %d (%.1f%%)\n', sum(reachable_map(:) == 0), sum(reachable_map(:) == 0)/grid_info.total_cells*100);

%% 5. 路径规划示例
fprintf('执行路径规划...\n');
start_pos = [1.0, 1.0];      % 起点 (米)
goal_pos = [8.0, 6.0];       % 终点 (米)
tic;
[path, path_length] = plan_path(grid_map, grid_info, start_pos, goal_pos, params);
planning_time = toc;
fprintf('  路径规划完成！耗时: %.3f秒\n', planning_time);
if ~isempty(path)
    fprintf('  路径长度: %.2f 米，经过 %d 个栅格\n', path_length, size(path, 1));
else
    fprintf('  未找到可行路径！\n');
end

%% 6. 可视化结果
visualize_grid_system(grid_map, reachable_map, path, start_pos, goal_pos, grid_info, params);

2.2 栅格地图创建：create_grid_map.m

function [grid_map, grid_info] = create_grid_map(params)
    % 创建栅格地图
    
    % 计算栅格数量
    cols = ceil(params.workspace_size(1) / params.grid_resolution);
    rows = ceil(params.workspace_size(2) / params.grid_resolution);
    
    % 初始化栅格地图 (0: 空闲, 1: 障碍, 2: 已访问, 3: 路径)
    grid_map = zeros(rows, cols);
    
    % 栅格信息结构
    grid_info.rows = rows;
    grid_info.cols = cols;
    grid_info.total_cells = rows * cols;
    grid_info.resolution = params.grid_resolution;
    grid_info.size = params.workspace_size;
    grid_info.origin = [0, 0];  % 原点坐标
    
    % 根据栅格类型创建特殊栅格
    switch params.grid_type
        case 'square'
            % 正方形栅格，无需特殊处理
            grid_info.cell_shape = 'square';
            
        case 'hexagon'
            % 六边形栅格
            grid_map = create_hexagonal_grid(rows, cols, params.grid_resolution);
            grid_info.cell_shape = 'hexagon';
            
        case 'triangle'
            % 三角形栅格
            grid_map = create_triangular_grid(rows, cols, params.grid_resolution);
            grid_info.cell_shape = 'triangle';
            
        otherwise
            error('不支持的栅格类型: %s', params.grid_type);
    end
    
    fprintf('    栅格尺寸: %d 行 × %d 列\n', rows, cols);
end

function hex_grid = create_hexagonal_grid(rows, cols, resolution)
    % 创建六边形栅格地图
    hex_grid = zeros(rows, cols);
    
    % 六边形栅格的特殊标记
    for i = 1:rows
        for j = 1:cols
            if mod(i+j, 2) == 0
                hex_grid(i, j) = 0;  % 偶数位置
            else
                hex_grid(i, j) = 0;  % 奇数位置
            end
        end
    end
end

function tri_grid = create_triangular_grid(rows, cols, resolution)
    % 创建三角形栅格地图
    tri_grid = zeros(rows*2, cols);
    
    % 三角形栅格的特殊标记
    for i = 1:rows*2
        for j = 1:cols
            tri_grid(i, j) = 0;
        end
    end
end

2.3 障碍物添加：add_obstacles.m

function grid_map = add_obstacles(grid_map, grid_info, params)
    % 添加障碍物到栅格地图
    
    % 定义障碍物（示例：矩形、圆形、多边形）
    obstacles = {
        struct('type', 'rectangle', 'center', [3, 4], 'width', 1.5, 'height', 1.0)
        struct('type', 'circle', 'center', [6, 3], 'radius', 0.8)
        struct('type', 'polygon', 'vertices', [2,6; 3,7; 4,6; 3,5])
        struct('type', 'rectangle', 'center', [7, 6], 'width', 2.0, 'height', 0.5)
    };
    
    % 遍历所有障碍物
    for obs_idx = 1:length(obstacles)
        obs = obstacles{obs_idx};
        
        switch obs.type
            case 'rectangle'
                grid_map = add_rectangle_obstacle(grid_map, grid_info, obs, params);
                
            case 'circle'
                grid_map = add_circle_obstacle(grid_map, grid_info, obs, params);
                
            case 'polygon'
                grid_map = add_polygon_obstacle(grid_map, grid_info, obs, params);
        end
    end
    
    % 添加边界障碍物（工作空间边界）
    grid_map = add_boundary_obstacles(grid_map, grid_info, params);
    
    % 考虑机器人半径的安全膨胀
    grid_map = dilate_obstacles(grid_map, grid_info, params.robot_radius);
end

function grid_map = add_rectangle_obstacle(grid_map, grid_info, obs, params)
    % 添加矩形障碍物
    
    % 将世界坐标转换为栅格坐标
    col_min = max(1, floor((obs.center(1) - obs.width/2) / params.grid_resolution) + 1);
    col_max = min(grid_info.cols, ceil((obs.center(1) + obs.width/2) / params.grid_resolution) + 1);
    row_min = max(1, floor((obs.center(2) - obs.height/2) / params.grid_resolution) + 1);
    row_max = min(grid_info.rows, ceil((obs.center(2) + obs.height/2) / params.grid_resolution) + 1);
    
    % 标记障碍物栅格
    grid_map(row_min:row_max, col_min:col_max) = 1;
end

function grid_map = add_circle_obstacle(grid_map, grid_info, obs, params)
    % 添加圆形障碍物
    
    % 圆心栅格坐标
    center_col = floor(obs.center(1) / params.grid_resolution) + 1;
    center_row = floor(obs.center(2) / params.grid_resolution) + 1;
    
    % 半径栅格数
    radius_cells = ceil(obs.radius / params.grid_resolution);
    
    % 遍历圆心周围的栅格
    for row = max(1, center_row-radius_cells):min(grid_info.rows, center_row+radius_cells)
        for col = max(1, center_col-radius_cells):min(grid_info.cols, center_col+radius_cells)
            % 计算到圆心的距离
            dist = sqrt(((col-center_col)*params.grid_resolution)^2 + ...
                        ((row-center_row)*params.grid_resolution)^2);
            
            if dist <= obs.radius
                grid_map(row, col) = 1;
            end
        end
    end
end

function grid_map = add_polygon_obstacle(grid_map, grid_info, obs, params)
    % 添加多边形障碍物（使用射线法）
    
    % 将顶点转换为栅格坐标
    vertices_col = floor(obs.vertices(:,1) / params.grid_resolution) + 1;
    vertices_row = floor(obs.vertices(:,2) / params.grid_resolution) + 1;
    
    % 创建多边形掩码
    polygon_mask = poly2mask(vertices_col, vertices_row, grid_info.rows, grid_info.cols);
    
    % 标记障碍物
    grid_map(polygon_mask) = 1;
end

function grid_map = add_boundary_obstacles(grid_map, grid_info, params)
    % 添加工作空间边界障碍物
    
    % 四周边界
    grid_map(1, :) = 1;          % 上边界
    grid_map(end, :) = 1;       % 下边界
    grid_map(:, 1) = 1;         % 左边界
    grid_map(:, end) = 1;       % 右边界
    
    % 考虑安全距离
    clearance_cells = ceil(params.obstacle_clearance / params.grid_resolution);
    if clearance_cells > 0
        grid_map(1:clearance_cells, :) = 1;
        grid_map(end-clearance_cells+1:end, :) = 1;
        grid_map(:, 1:clearance_cells) = 1;
        grid_map(:, end-clearance_cells+1:end) = 1;
    end
end

function grid_map = dilate_obstacles(grid_map, grid_info, robot_radius)
    % 障碍物膨胀（考虑机器人半径）
    
    if robot_radius <= 0
        return;
    end
    
    % 膨胀半径（栅格数）
    dilate_cells = ceil(robot_radius / grid_info.resolution);
    
    % 使用形态学膨胀
    se = strel('square', 2*dilate_cells+1);
    dilated_map = imdilate(grid_map, se);
    
    % 更新栅格地图
    grid_map(dilated_map == 1) = 1;
end

2.4 可达区域计算：compute_reachable_area.m

function reachable_map = compute_reachable_area(grid_map, grid_info, params)
    % 计算可达区域（从原点开始的连通区域）
    
    % 初始化可达地图
    reachable_map = ones(size(grid_map)) * 2;  % 2表示未知
    
    % 使用BFS或DFS从原点开始搜索
    start_cell = world_to_grid([0, 0], grid_info);
    
    if start_cell(1) >= 1 && start_cell(1) <= grid_info.rows && ...
       start_cell(2) >= 1 && start_cell(2) <= grid_info.cols && ...
       grid_map(start_cell(1), start_cell(2)) == 0
        
        reachable_map = bfs_reachable_area(grid_map, start_cell, grid_info);
    else
        % 原点不可达，从最近的空闲栅格开始
        [~, nearest_cell] = min(grid_map(:));
        [row, col] = ind2sub(size(grid_map), nearest_cell);
        reachable_map = bfs_reachable_area(grid_map, [row, col], grid_info);
    end
end

function reachable_map = bfs_reachable_area(grid_map, start_cell, grid_info)
    % BFS搜索可达区域
    
    % 初始化
    reachable_map = ones(size(grid_map)) * 2;  % 2表示未知
    visited = false(size(grid_map));
    queue = start_cell';  % 队列
    
    % 移动方向（8邻域）
    directions = [-1, -1; -1, 0; -1, 1; 0, -1; 0, 1; 1, -1; 1, 0; 1, 1];
    
    % BFS主循环
    while ~isempty(queue)
        current = queue(:, 1)';
        queue = queue(:, 2:end);
        
        row = current(1);
        col = current(2);
        
        % 检查是否已访问
        if visited(row, col)
            continue;
        end
        
        % 标记为已访问
        visited(row, col) = true;
        
        % 检查是否为障碍物
        if grid_map(row, col) == 1
            reachable_map(row, col) = 1;  % 1表示障碍
        else
            reachable_map(row, col) = 0;  % 0表示可达
            
            % 添加相邻栅格到队列
            for d = 1:size(directions, 1)
                new_row = row + directions(d, 1);
                new_col = col + directions(d, 2);
                
                % 检查边界
                if new_row >= 1 && new_row <= grid_info.rows && ...
                   new_col >= 1 && new_col <= grid_info.cols && ...
                   ~visited(new_row, new_col)
                    
                    queue = [queue, [new_row, new_col]'];
                end
            end
        end
    end
end

2.5 路径规划：plan_path.m

function [path, path_length] = plan_path(grid_map, grid_info, start_pos, goal_pos, params)
    % 基于栅格地图的路径规划（A*算法）
    
    % 将世界坐标转换为栅格坐标
    start_cell = world_to_grid(start_pos, grid_info);
    goal_cell = world_to_grid(goal_pos, grid_info);
    
    % 检查起点和终点是否有效
    if grid_map(start_cell(1), start_cell(2)) == 1
        fprintf('  警告：起点在障碍物中！\n');
        path = [];
        path_length = inf;
        return;
    end
    
    if grid_map(goal_cell(1), goal_cell(2)) == 1
        fprintf('  警告：终点在障碍物中！\n');
        path = [];
        path_length = inf;
        return;
    end
    
    % A*算法
    [path_cells, cost] = astar_path_planning(grid_map, start_cell, goal_cell, grid_info);
    
    if isempty(path_cells)
        path = [];
        path_length = inf;
    else
        % 将栅格路径转换为世界坐标
        path = zeros(length(path_cells), 2);
        for i = 1:length(path_cells)
            path(i, :) = grid_to_world(path_cells{i}, grid_info);
        end
        
        % 计算路径长度
        path_length = 0;
        for i = 2:length(path_cells)
            cell1 = path_cells{i-1};
            cell2 = path_cells{i};
            path_length = path_length + sqrt((cell1(1)-cell2(1))^2 + (cell1(2)-cell2(2))^2);
        end
        path_length = path_length * params.grid_resolution;
    end
end

function [path_cells, cost] = astar_path_planning(grid_map, start_cell, goal_cell, grid_info)
    % A*路径规划算法
    
    % 初始化
    open_list = start_cell';
    closed_list = false(size(grid_map));
    came_from = cell(size(grid_map));
    g_score = inf(size(grid_map));
    f_score = inf(size(grid_map));
    
    % 起点初始化
    g_score(start_cell(1), start_cell(2)) = 0;
    f_score(start_cell(1), start_cell(2)) = heuristic_cost(start_cell, goal_cell, grid_info);
    
    % 移动方向（8邻域）
    directions = [-1, -1; -1, 0; -1, 1; 0, -1; 0, 1; 1, -1; 1, 0; 1, 1];
    direction_costs = [1.414, 1, 1.414, 1, 1, 1.414, 1, 1.414];  % 对角线移动代价
    
    % A*主循环
    while ~isempty(open_list)
        % 找到f_score最小的节点
        min_f = inf;
        current_idx = 1;
        for i = 1:size(open_list, 2)
            if f_score(open_list(1, i), open_list(2, i)) < min_f
                min_f = f_score(open_list(1, i), open_list(2, i));
                current_idx = i;
            end
        end
        
        current = open_list(:, current_idx);
        open_list(:, current_idx) = [];
        
        % 检查是否到达目标
        if isequal(current', goal_cell')
            % 重建路径
            path_cells = reconstruct_path(came_from, current);
            cost = g_score(current(1), current(2));
            return;
        end
        
        % 标记为已访问
        closed_list(current(1), current(2)) = true;
        
        % 遍历相邻节点
        for d = 1:size(directions, 1)
            neighbor = current + directions(d, :)';
            
            % 检查边界和障碍物
            if neighbor(1) < 1 || neighbor(1) > grid_info.rows || ...
               neighbor(2) < 1 || neighbor(2) > grid_info.cols || ...
               grid_map(neighbor(1), neighbor(2)) == 1 || ...
               closed_list(neighbor(1), neighbor(2))
                continue;
            end
            
            % 计算临时g_score
            tentative_g = g_score(current(1), current(2)) + direction_costs(d);
            
            % 如果找到更好的路径
            if tentative_g < g_score(neighbor(1), neighbor(2))
                % 记录路径
                came_from{neighbor(1), neighbor(2)} = current;
                g_score(neighbor(1), neighbor(2)) = tentative_g;
                f_score(neighbor(1), neighbor(2)) = tentative_g + heuristic_cost(neighbor, goal_cell, grid_info);
                
                % 添加到开放列表
                if ~any(all(open_list == repmat(neighbor, 1, size(open_list, 2)), 1))
                    open_list = [open_list, neighbor];
                end
            end
        end
    end
    
    % 没有找到路径
    path_cells = [];
    cost = inf;
end

function cost = heuristic_cost(cell1, cell2, grid_info)
    % 启发式函数（欧几里得距离）
    cost = sqrt((cell1(1)-cell2(1))^2 + (cell1(2)-cell2(2))^2);
end

function path_cells = reconstruct_path(came_from, current)
    % 重建路径
    path_cells = {current};
    while ~isempty(came_from{current(1), current(2)})
        current = came_from{current(1), current(2)};
        path_cells = [path_cells, {current}];
    end
    path_cells = flip(path_cells);
end

function grid_cell = world_to_grid(world_pos, grid_info)
    % 世界坐标转栅格坐标
    col = floor(world_pos(1) / grid_info.resolution) + 1;
    row = floor(world_pos(2) / grid_info.resolution) + 1;
    grid_cell = [row, col];
end

function world_pos = grid_to_world(grid_cell, grid_info)
    % 栅格坐标转世界坐标
    x = (grid_cell(2) - 0.5) * grid_info.resolution;
    y = (grid_cell(1) - 0.5) * grid_info.resolution;
    world_pos = [x, y];
end

2.6 结果可视化：visualize_grid_system.m

function visualize_grid_system(grid_map, reachable_map, path, start_pos, goal_pos, grid_info, params)
    % 可视化栅格系统
    
    figure('Name', '机器人工作空间栅格划分系统', 'Color', 'white', 'Position', [100, 100, 1400, 800]);
    
    % 1. 原始栅格地图
    subplot(2,3,1);
    imagesc(grid_map);
    colormap(gca, [1,1,1; 0.5,0.5,0.5]);  % 白色:空闲, 灰色:障碍
    axis equal tight;
    xlabel('X轴 (栅格)'); ylabel('Y轴 (栅格)');
    title('原始栅格地图');
    colorbar('Ticks', [0, 1], 'TickLabels', {'空闲', '障碍'});
    grid on;
    
    % 2. 可达区域地图
    subplot(2,3,2);
    imagesc(reachable_map);
    colormap(gca, [1,1,1; 0.5,0.5,0.5; 0.8,0.8,0.8]);  % 白色:可达, 灰色:障碍, 浅灰:未知
    axis equal tight;
    xlabel('X轴 (栅格)'); ylabel('Y轴 (栅格)');
    title('可达区域地图');
    colorbar('Ticks', [0, 1, 2], 'TickLabels', {'可达', '障碍', '未知'});
    grid on;
    
    % 3. 障碍物分布（世界坐标）
    subplot(2,3,3);
    hold on;
    
    % 绘制工作空间边界
    rectangle('Position', [0, 0, params.workspace_size(1), params.workspace_size(2)], ...
              'EdgeColor', 'black', 'LineWidth', 2, 'LineStyle', '--');
    
    % 绘制障碍物
    obstacle_cells = find(grid_map == 1);
    for i = 1:length(obstacle_cells)
        [row, col] = ind2sub(size(grid_map), obstacle_cells(i));
        x = (col - 0.5) * grid_info.resolution;
        y = (row - 0.5) * grid_info.resolution;
        rectangle('Position', [x, y, grid_info.resolution, grid_info.resolution], ...
                  'FaceColor', 'red', 'EdgeColor', 'darkred', 'LineWidth', 0.5);
    end
    
    % 绘制栅格线
    for x = 0:grid_info.resolution:params.workspace_size(1)
        plot([x, x], [0, params.workspace_size(2)], 'k-', 'LineWidth', 0.1, 'Color', [0.8,0.8,0.8]);
    end
    for y = 0:grid_info.resolution:params.workspace_size(2)
        plot([0, params.workspace_size(1)], [y, y], 'k-', 'LineWidth', 0.1, 'Color', [0.8,0.8,0.8]);
    end
    
    xlabel('X轴 (米)'); ylabel('Y轴 (米)');
    title('障碍物分布（世界坐标）');
    axis equal tight;
    grid on;
    hold off;
    
    % 4. 路径规划结果
    subplot(2,3,4);
    hold on;
    
    % 绘制栅格地图背景
    imagesc(grid_map);
    colormap(gca, [1,1,1; 0.9,0.9,0.9]);
    axis equal tight;
    
    % 绘制路径
    if ~isempty(path)
        plot(path(:,1)/grid_info.resolution + 0.5, path(:,2)/grid_info.resolution + 0.5, ...
             'b-', 'LineWidth', 2, 'Marker', 'o', 'MarkerSize', 4, 'MarkerFaceColor', 'blue');
    end
    
    % 绘制起点和终点
    start_cell = world_to_grid(start_pos, grid_info);
    goal_cell = world_to_grid(goal_pos, grid_info);
    plot(start_cell(2), start_cell(1), 'go', 'MarkerSize', 10, 'MarkerFaceColor', 'green', 'LineWidth', 2);
    plot(goal_cell(2), goal_cell(1), 'ro', 'MarkerSize', 10, 'MarkerFaceColor', 'red', 'LineWidth', 2);
    
    xlabel('X轴 (栅格)'); ylabel('Y轴 (栅格)');
    title('路径规划结果');
    legend('路径', '起点', '终点', 'Location', 'northwest');
    grid on;
    hold off;
    
    % 5. 栅格分辨率影响
    subplot(2,3,5);
    resolutions = [0.1, 0.2, 0.5, 1.0];
    cells_count = zeros(size(resolutions));
    
    for i = 1:length(resolutions)
        cols = ceil(params.workspace_size(1) / resolutions(i));
        rows = ceil(params.workspace_size(2) / resolutions(i));
        cells_count(i) = rows * cols;
    end
    
    bar(1:length(resolutions), cells_count, 'FaceColor', 'cyan');
    set(gca, 'XTickLabel', arrayfun(@(x) sprintf('%.1f', x), resolutions, 'UniformOutput', false));
    xlabel('栅格分辨率 (米)'); ylabel('栅格总数');
    title('分辨率对栅格数量的影响');
    grid on;
    
    % 6. 系统信息
    subplot(2,3,6); axis off;
    info_text = {
        sprintf('工作空间: %.1f m × %.1f m', params.workspace_size(1), params.workspace_size(2))
        sprintf('栅格分辨率: %.2f m/栅格', params.grid_resolution)
        sprintf('栅格数量: %d × %d', grid_info.rows, grid_info.cols)
        sprintf('总栅格数: %d', grid_info.total_cells)
        sprintf('障碍物栅格: %d (%.1f%%)', sum(grid_map(:)==1), sum(grid_map(:)==1)/grid_info.total_cells*100)
        sprintf('可达栅格: %d (%.1f%%)', sum(reachable_map(:)==0), sum(reachable_map(:)==0)/grid_info.total_cells*100)
        sprintf('机器人半径: %.2f m', params.robot_radius)
        sprintf('安全距离: %.2f m', params.obstacle_clearance)
    };
    text(0.1, 0.9, '栅格系统信息:', 'FontSize', 12, 'FontWeight', 'bold');
    for i = 1:length(info_text)
        text(0.1, 0.9 - i*0.1, info_text{i}, 'FontSize', 10);
    end
    title('系统配置信息');
end

function grid_cell = world_to_grid(world_pos, grid_info)
    col = floor(world_pos(1) / grid_info.resolution) + 1;
    row = floor(world_pos(2) / grid_info.resolution) + 1;
    grid_cell = [row, col];
end

---

三、扩展功能模块

3.1 动态障碍物处理

function dynamic_grid_map = handle_dynamic_obstacles(static_grid_map, dynamic_obstacles, grid_info, params)
    % 处理动态障碍物
    
    dynamic_grid_map = static_grid_map;
    
    % 更新动态障碍物位置
    for obs_idx = 1:length(dynamic_obstacles)
        obs = dynamic_obstacles{obs_idx};
        
        % 根据时间戳更新位置
        current_pos = update_obstacle_position(obs, tic);
        
        % 更新栅格地图
        dynamic_grid_map = update_obstacle_in_grid(dynamic_grid_map, current_pos, obs.radius, grid_info, params);
    end
end

3.2 多机器人协同栅格划分

function multi_robot_grid_assignment(grid_map, robots, grid_info, params)
    % 多机器人工作空间分配
    
    num_robots = length(robots);
    assignments = cell(num_robots, 1);
    
    % 计算每个机器人的工作区域
    for robot_idx = 1:num_robots
        robot_pos = robots{robot_idx}.position;
        
        % 使用Voronoi图划分工作空间
        voronoi_cells = compute_voronoi_assignment(grid_map, robot_pos, grid_info);
        
        % 分配栅格
        assignments{robot_idx} = voronoi_cells;
    end
    
    % 可视化分配结果
    visualize_multi_robot_assignment(grid_map, assignments, robots, grid_info);
end

参考代码 采用栅格对机器人的工作空间进行划分 www.youwenfan.com/contentcsu/60149.html

四、实际应用建议

4.1 栅格分辨率选择

应用场景	推荐分辨率	说明
室内清洁机器人	0.05-0.1m	高精度，适合精细操作
仓库AGV	0.2-0.5m	平衡精度与计算量
户外巡检机器人	0.5-1.0m	大范围，快速规划
精密装配	0.01-0.05m	极高精度，小范围

4.2 技巧

% 1. 四叉树栅格（自适应分辨率）
quadtree_map = build_quadtree_grid(grid_map, grid_info, min_resolution, max_resolution);

% 2. 增量式更新（仅更新变化的区域）
updated_regions = detect_changed_regions(old_map, new_map);
incremental_update(updated_regions);

% 3. GPU加速（大规模栅格）
if gpuDeviceCount > 0
    grid_map_gpu = gpuArray(grid_map);
    % 在GPU上执行路径规划
    path_gpu = gpu_astar_path_planning(grid_map_gpu, start, goal);
end

4.3 常见问题解决

1. 栅格地图过大：使用分层栅格或四叉树
2. 路径规划效率低：预计算可达区域，使用跳点搜索
3. 动态障碍物处理：采用时间窗方法
4. 多机器人冲突：引入优先级和协商机制