利用Matlab写出路径规划的A*二次规划代码

好的，以下是一个简单的A*二次规划代码的实现，使用Matlab语言：

function [path, cost] = Astar_QP(start, goal, obs, res)

% start: 起点坐标
% goal: 终点坐标
% obs: 障碍物信息（包括障碍物位置和大小）
% res: 地图分辨率（用于计算代价）

% 初始化A*算法
open_list = [start; heuristic(start, goal)];
closed_list = [];
parent = zeros(size(obs, 1), 1);
g = zeros(size(obs, 1), 1);

% 初始化二次规划器
Q = diag([1, 1]);
f = zeros(2, 1);
A = [];
b = [];
lb = [-inf; -inf];
ub = [inf; inf];

% 执行A*算法
while ~isempty(open_list)
    
    % 选择代价最小的节点
    [~, idx] = min(open_list(:, 3));
    current = open_list(idx, 1:2);
    
    % 到达终点
    if isequal(current, goal)
        path = reconstruct_path(parent, current);
        cost = g(idx);
        return
    end
    
    % 从开启列表中移除当前节点
    open_list(idx, :) = [];
    
    % 将当前节点加入关闭列表
    closed_list(end+1, :) = [current, heuristic(current, goal)];
    
    % 扩展当前节点
    neighbors = get_neighbors(current, obs, res);
    for i = 1:size(neighbors, 1)
        
        neighbor = neighbors(i, :);
        
        % 如果邻居节点已经在关闭列表中，则跳过
        if ismember(neighbor, closed_list(:, 1:2), 'rows')
            continue
        end
        
        % 计算邻居节点代价
        g_new = g(idx) + norm(neighbor - current);
        
        % 如果邻居节点不在开启列表中，则加入
        idx_new = find(ismember(open_list(:, 1:2), neighbor, 'rows'), 1);
        if isempty(idx_new)
            h_new = heuristic(neighbor, goal);
            open_list(end+1, :) = [neighbor, g_new+h_new];
            idx_new = size(open_list, 1);
        elseif g_new >= g(idx_new)
            continue
        end
        
        % 更新邻居节点信息
        parent(idx_new) = idx;
        g(idx_new) = g_new;
        
        % 更新二次规划器信息
        Aeq = [1, 0; -1, 0; 0, 1; 0, -1];
        beq = [neighbor(1); -neighbor(1)+obs(:, 1)-obs(:, 3)/2; neighbor(2); -neighbor(2)+obs(:, 2)-obs(:, 4)/2];
        [x, cost, exitflag] = quadprog(Q, f, Aeq, beq, [], [], lb, ub);
        
        % 如果二次规划失败，则跳过
        if exitflag ~= 1
            continue
        end
        
        % 更新邻居节点代价
        open_list(idx_new, 3) = g_new + cost;
        
    end
    
end

% 如果无法找到路径，则返回空
path = [];
cost = Inf;

end

% 估价函数
function h = heuristic(current, goal)
h = norm(current - goal);
end

% 获取邻居节点
function neighbors = get_neighbors(current, obs, res)
d = res;
x = current(1);
y = current(2);
neighbors = [x-d, y; x+d, y; x, y-d; x, y+d];
idx = neighbors(:, 1) < 0 | neighbors(:, 2) < 0 | neighbors(:, 1) > 100 | neighbors(:, 2) > 100;
neighbors(idx, :) = [];
for i = 1:size(obs, 1)
    idx = neighbors(:, 1) > obs(i, 1)-obs(i, 3)/2 & neighbors(:, 1) < obs(i, 1)+obs(i, 3)/2 & neighbors(:, 2) > obs(i, 2)-obs(i, 4)/2 & neighbors(:, 2) < obs(i, 2)+obs(i, 4)/2;
    neighbors(idx, :) = [];
end
end

% 重构路径
function path = reconstruct_path(parent, current)
path = current;
while parent(current) ~= 0
    current = parent(current);
    path = [current; path];
end
end

上述代码实现了一个简单的A*二次规划算法，用于路径规划。其中，`get_neighbors`函数用于获取邻居节点，`heuristic`函数用于计算估价函数，`reconstruct_path`函数用于重构路径。在主函数`Astar_QP`中，我们使用开启列表和关闭列表来实现A*算法，同时使用二次规划器计算路径代价。