function cost = runningcosts(x, u, x_eq, u_eq, Q, R) cost = (x-x_eq)'*Q*(x-x_eq) + (u-u_eq)'*R*(u-u_eq); end

这段代码是一个计算运动学成本的函数。其中：

- x：表示当前状态向量
- u：表示当前输入向量
- x_eq：表示期望的状态向量
- u_eq：表示期望的输入向量
- Q：表示状态成本矩阵
- R：表示输入成本矩阵

函数的计算过程是将当前状态和输入向量分别与期望的状态和输入向量做差，然后分别乘以对应的成本矩阵，最后将两个部分相加得到总的成本。

相关问题

用matlab写出完整的A*算法

以下是MATLAB中实现A*算法的示例代码：

function [path, total_cost] = A_star(start_node, goal_node, map)
% A*算法实现
% 输入参数：
% start_node: 起点坐标[x,y]
% goal_node: 终点坐标[x,y]
% map: 地图矩阵，0表示可通行，1表示障碍物
% 输出参数：
% path: 路径，每个点的坐标[x,y]，包括起点和终点
% total_cost: 总代价

% 计算地图尺寸
[row, col] = size(map);

% 初始化起点和终点节点
start_node = Node(start_node(1), start_node(2), 0, 0, 0);
goal_node = Node(goal_node(1), goal_node(2), 0, 0, 0);

% 初始化open表和close表
open_list = [];
close_list = [];

% 将起点加入open表
open_list = [open_list, start_node];

% 循环直到找到终点或open表为空
while ~isempty(open_list)
    % 从open表中找到f值最小的节点
    [~, idx] = min([open_list.f]);
    current_node = open_list(idx);
    
    % 如果当前节点是终点则退出循环
    if current_node.x == goal_node.x && current_node.y == goal_node.y
        break;
    end
    
    % 将当前节点从open表中删除，加入close表
    open_list(idx) = [];
    close_list = [close_list, current_node];
    
    % 扩展当前节点的所有邻居节点
    for i = -1:1
        for j = -1:1
            % 忽略当前节点
            if i == 0 && j == 0
                continue;
            end
            
            % 计算邻居节点坐标
            x = current_node.x + i;
            y = current_node.y + j;
            
            % 判断邻居节点是否越界或是障碍物
            if x < 1 || x > row || y < 1 || y > col || map(x, y) == 1
                continue;
            end
            
            % 计算邻居节点代价
            g = current_node.g + sqrt(i^2 + j^2);
            h = sqrt((x - goal_node.x)^2 + (y - goal_node.y)^2);
            f = g + h;
            
            % 创建邻居节点
            neighbor_node = Node(x, y, f, g, h);
            
            % 如果邻居节点已经在close表中则忽略
            if ismember(neighbor_node, close_list)
                continue;
            end
            
            % 如果邻居节点已经在open表中则更新其代价
            idx = find(ismember(open_list, neighbor_node));
            if ~isempty(idx)
                if open_list(idx).g > neighbor_node.g
                    open_list(idx).g = neighbor_node.g;
                    open_list(idx).f = neighbor_node.f;
                    open_list(idx).parent = current_node;
                end
            else
                % 将邻居节点加入open表
                neighbor_node.parent = current_node;
                open_list = [open_list, neighbor_node];
            end
        end
    end
end

% 如果open表为空则无法到达终点
if isempty(open_list)
    path = [];
    total_cost = -1;
    return;
end

% 从终点回溯到起点得到路径
path = [goal_node.x, goal_node.y];
current_node = goal_node;
while ~isequal(current_node, start_node)
    current_node = current_node.parent;
    path = [current_node.x, current_node.y; path];
end

% 计算路径总代价
total_cost = path_cost(path);

end

function cost = path_cost(path)
% 计算路径总代价
cost = 0;
for i = 2:size(path, 1)
    cost = cost + sqrt((path(i,1) - path(i-1,1))^2 + (path(i,2) - path(i-1,2))^2);
end
end

classdef Node
% A*算法节点类
    properties
        x       % x坐标
        y       % y坐标
        f       % f值
        g       % g值
        h       % h值
        parent  % 父节点
    end
    
    methods
        function obj = Node(x, y, f, g, h)
            obj.x = x;
            obj.y = y;
            obj.f = f;
            obj.g = g;
            obj.h = h;
            obj.parent = [];
        end
        
        function tf = eq(obj1, obj2)
            tf = obj1.x == obj2.x && obj1.y == obj2.y;
        end
    end
end

使用示例：

% 定义地图
map = [0 0 0 0 0 0 0 0;
       0 1 1 1 0 0 0 0;
       0 0 0 0 0 1 1 0;
       0 0 0 0 0 1 1 0;
       0 0 0 0 0 1 1 0;
       0 0 0 0 0 0 0 0];

% 执行A*算法
[start, goal] = [1,1;6,8];
[path, cost] = A_star(start, goal, map);

% 绘制地图和路径
figure;
imagesc(map);
hold on;
plot(path(:,2), path(:,1), 'r');
hold off;

其中，`map`是地图矩阵，0表示可通行，1表示障碍物；`start`和`goal`是起点和终点坐标；`path`是路径，每个点的坐标[x,y]，包括起点和终点；`cost`是路径总代价。

A*三维路径规划MATLAB

A*算法是一种常用的路径规划算法，可以用于三维路径规划。以下是使用MATLAB实现A*算法的基本步骤：

1. 构建三维地图：将三维空间离散化为网格，每个网格表示一个状态，状态可以是障碍物或自由空间。

2. 定义启发式函数：启发式函数用于估计从当前状态到目标状态的距离，可以使用欧几里得距离或曼哈顿距离等。

3. 定义开放列表和关闭列表：开放列表存储待探索的状态，关闭列表存储已经探索过的状态。

4. 初始化：将起点加入开放列表，并将起点的启发式函数值设置为0。

5. 迭代：每次从开放列表中选取启发式函数值最小的状态作为当前状态，将当前状态加入关闭列表，并检查其周围的状态是否可行。如果某个周围的状态未被探索过，将其加入开放列表，并更新其启发式函数值和父节点。

6. 回溯路径：当目标状态被加入关闭列表时，可以通过回溯其父节点来得到路径。

以下是一个示例代码：

function [path, cost] = A_star(start, goal, map)
% A* algorithm for 3D path planning
% Input:
%   start: 1x3 vector, start position [x, y, z]
%   goal: 1x3 vector, goal position [x, y, z]
%   map: nxnxn binary array, 1 indicates free space, 0 indicates obstacle
% Output:
%   path: mx3 matrix, path from start to goal
%   cost: scalar, cost of the path

% Initialize
[nx, ny, nz] = size(map);
start_node = Node(start, 0, heuristic(start, goal));
goal_node = Node(goal, Inf, 0);
open_list = [start_node];
closed_list = [];

% A* loop
while ~isempty(open_list)
    % Select node with lowest f value
    current_node = open_list(1);
    for i = 2:length(open_list)
        if open_list(i).f < current_node.f
            current_node = open_list(i);
        end
    end
    
    % Move current node to closed list
    open_list(open_list == current_node) = [];
    closed_list = [closed_list, current_node];
    
    % Check if goal is reached
    if current_node == goal_node
        path = backtrack_path(current_node);
        cost = current_node.g;
        return
    end
    
    % Expand current node
    for i = -1:1
        for j = -1:1
            for k = -1:1
                % Skip current node
                if i == 0 && j == 0 && k == 0
                    continue
                end
                
                % Get neighbor node
                neighbor_pos = current_node.pos + [i, j, k];
                if neighbor_pos(1) < 1 || neighbor_pos(1) > nx || ...
                        neighbor_pos(2) < 1 || neighbor_pos(2) > ny || ...
                        neighbor_pos(3) < 1 || neighbor_pos(3) > nz
                    continue
                end
                if map(neighbor_pos(1), neighbor_pos(2), neighbor_pos(3)) == 0
                    continue
                end
                neighbor_node = Node(neighbor_pos, Inf, Inf);
                
                % Check if neighbor node is in closed list
                if any(closed_list == neighbor_node)
                    continue
                end
                
                % Update neighbor node
                tentative_g = current_node.g + heuristic(current_node.pos, neighbor_pos);
                if any(open_list == neighbor_node)
                    neighbor_node = open_list(open_list == neighbor_node);
                    if tentative_g >= neighbor_node.g
                        continue
                    end
                end
                neighbor_node.g = tentative_g;
                neighbor_node.h = heuristic(neighbor_pos, goal);
                neighbor_node.f = neighbor_node.g + neighbor_node.h;
                neighbor_node.parent = current_node;
                
                % Add neighbor node to open list
                if ~any(open_list == neighbor_node)
                    open_list = [open_list, neighbor_node];
                end
            end
        end
    end
end

% No path found
path = [];
cost = Inf;

end

function h = heuristic(pos1, pos2)
% Euclidean distance heuristic
h = norm(pos1 - pos2);
end

function path = backtrack_path(node)
% Backtrack path from goal to start
path = [];
while ~isempty(node.parent)
    path = [node.pos; path];
    node = node.parent;
end
path = [node.pos; path];
end

classdef Node
    % Node class for A* algorithm
    
    properties
        pos % position [x, y, z]
        g % cost from start
        h % heuristic cost to goal
        f % total cost
        parent % parent node
    end
    
    methods
        function obj = Node(pos, g, h)
            obj.pos = pos;
            obj.g = g;
            obj.h = h;
            obj.f = g + h;
        end
        
        function bool = eq(obj1, obj2)
            bool = isequal(obj1.pos, obj2.pos);
        end
    end
    
end

注意：以上代码仅供参考，具体实现可能需要根据具体情况进行修改和优化。