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1 A Star算法及其应用现状
进行搜索任务时提取的有助于简化搜索过程的信息被称为启发信息.启发信息经过文字提炼和公式化后转变为启发函数.启发函数可以表示自起始顶点至目标顶点间的估算距离, 也可以表示自起始顶点至目标顶点间的估算时间等.描述不同的情境、解决不同的问题所采用的启发函数各不相同.我们默认将启发函数命名为H (n) .以启发函数为策略支持的搜索方式我们称之为启发型搜索算法.在救援机器人的路径规划中, A Star算法能结合搜索任务中的环境情况, 缩小搜索范围, 提高搜索效率, 使搜索过程更具方向性、智能性, 所以A Star算法能较好地应用于机器人路径规划相关领域.
2 A Star算法流程
承接2.1节, A Star算法的启发函数是用来估算起始点到目标点的距离, 从而缩小搜索范围, 提高搜索效率.A Star算法的数学公式为:F (n) =G (n) +H (n) , 其中F (n) 是从起始点经由节点n到目标点的估计函数, G (n) 表示从起点移动到方格n的实际移动代价, H (n) 表示从方格n移动到目标点的估算移动代价.
function varargout = astar_jw(varargin)
end
function [path, directions] = search(grid, init, goal, delta, printDebugInfo)
% This function implements the A* algorithm
end
function A = deleteRows(A, rows)
% The following way to delete rows was taken from the mathworks website
% that compared multiple ways to do it. The following appeared to be the
% fastest.
index = true(1, size(A,1));
index(rows) = false;
A = A(index, 😃;
end
function A = addRow(A, row)
A(end+1,:) = row;
end
function [open, closed, expanded] = expand(grid, open, closed, delta, expanded, h)
% This function expands the open list by taking the coordinate (row) with
% the smallest f value (path cost) and adds its neighbors to the open list.
end
function h = computeHeuristic(varargin)
% This function is used to compute the distance heuristic, h. By default
% this function computes the Euclidean distance from each grid space to the
% goal. The calling sequence for this function is as follows:
% h = computeHeuristic(grid, goal[, distanceType])
% where distanceType may be one of the following:
% ‘euclidean’ (default value)
% ‘city-block’
% ‘empty’ (returns all zeros for heuristic function)
grid = varargin{1};
goal = varargin{2};
if nargin==3
distanceType = varargin{3};
else
distanceType = ‘euclidean’;
end
[m n] = size(grid);
[x y] = meshgrid(1:n,1:m);
if strcmp(distanceType, ‘euclidean’)
h = sqrt((x-goal(2)).^2 + (y-goal(1)).^2);
elseif strcmp(distanceType, ‘city-block’)
h = abs(x-goal(2)) + abs(y-goal(1));
elseif strcmp(distanceType, ‘empty’)
h = zeros(m,n);
else
warning(‘Unknown distanceType for determining heuristic, h!’)
h = [];
end
end
function neighbors = findNeighbors(grid, open, row, delta)
% This function takes the desired row in the open list to expand and finds
% all potential neighbors (neighbors reachable through legal moves, as
% defined in the delta list).
end
function neighbors = removeListedNeighbors(neighbors, open, closed)
% This function removes any neighbors that are on the open or closed lists
end
function goalRow = checkForGoal(closed, goal)
% This function looks for the final goal destination on the closed list.
% Note, you could check the open list instead (and find the goal faster);
% however, we want to have a chance to expand the goal location itself, so
% we wait until it is on the closed list.
[~, goalRow] = ismember(goal, closed(:,1:2), ‘rows’);
end
function displayDebugInfo(grid, init, goal, open, closed, h)
% Display the open and closed lists in the command window, and display an
% image of the current search of the grid.
home
disp('Open: ‘)
disp(open)
disp(’ ')
disp('Closed: ')
disp(closed)
end
function displaySearchStatus(grid, init, goal, open, closed, h)
% This function displays a graphical grid and search status to make
% visualization easier.
grid = double(~grid);
grid(init(1),init(2)) = 0.66;
grid(goal(1),goal(2)) = 0.33;
end
function displayPath(grid, path, h)
grid = double(~grid);
end
1 matlab版本
2014a
2 参考文献
[1]钱程,许映秋,谈英姿.A Star算法在RoboCup救援仿真中路径规划的应用[J].指挥与控制学报. 2017,3(03)
3 备注
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