RRT* (matlab)

本文详细介绍了快速随机树算法RRT*的MATLAB实现过程,包括路径规划的基本思想、关键步骤及代码解析,帮助读者理解并掌握RRT*在机器人路径规划中的应用。

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%%------------------------
%%2022/06/05
%%matlab
%%rrt star
%%------------------------

clc;
clear all;
close all;

%加载地图
ImpRgb = imread("map.png");
Imp = rgb2gray(ImpRgb);
imshow(Imp);
hold on;
x_l = size(Imp,1)  %row
y_l = size(Imp,2)  %col

% Imp(120,129)
% plot(120,120,'r*');
% hold on;

%参数初始化
start = [1,1];
goal = [450,800];
threshold = 30;
step = 30;
r = 70;
MaxIter = 3000;

T.v(1).x = start(1);
T.v(1).y = start(2);
T.v(1).xPre = start(1);
T.v(1).yPre = start(2);
T.v(1).cost = 0;
T.v(1).indPre = -1;

plot(start(2),start(1),'mo','MarkerSize',10,'MarkerFaceColor','m');
plot(goal(2),goal(1),'go','MarkerSize',10,'MarkerFaceColor','g');

%开始主循环
for iter = 1:MaxIter
   %step1.生成随机点
   n = rand();
   if n < 0.5
        Prand = [unifrnd(0,x_l),unifrnd(0,y_l)];
   else
       Prand = goal;
   en
### RRT* Algorithm Implementation in MATLAB The Rapidly-exploring Random Tree (RRT*) algorithm is an extension of the original RRT method, designed to provide asymptotically optimal solutions over time. In MATLAB, implementing this involves several key components including initialization, node expansion, rewiring for optimality, and ensuring connectivity. #### Initialization Phase Initialization sets up necessary parameters such as start position, goal region, environment boundaries, obstacle locations, step size (`delta`), and a threshold distance (`r`) used during neighbor searches[^1]. ```matlab % Define initial conditions startPosition = [0; 0]; % Start point coordinates goalRegion = [9; 9]; % Goal point coordinates environmentLimits = [-5 15;-5 15]; obstacles = []; % List of obstacles defined by their vertices stepSize = 0.5; searchRadius = 1; rrtStarTree = struct('position', startPosition,'cost', 0); nodes = {rrtStarTree}; ``` #### Node Expansion Process During each iteration, new nodes are added based on random sampling within free space while considering Dubins paths when applicable: ```matlab function newNode = expandNode(rrtStarTree, environmentLimits, obstacles) randPoint = generateRandomFreePoint(environmentLimits, obstacles); nearestNeighborIndex = findNearestNeighbor(rrtStarTree, randPoint); proposedNewPosition = moveTowards(rrtStarTree(nearestNeighborIndex).position, ... randPoint, stepSize); if checkCollision(proposedNewPosition, obstacles) == false costToCome = computeCost(rrtStarTree(nearestNeighborIndex).position,... proposedNewPosition); newNode.position = proposedNewPosition; newNode.cost = rrtStarTree(nearestNeighborIndex).cost + costToCome; end end ``` #### Rewiring Mechanism After adding a new node, nearby existing nodes may be reconnected through it if doing so reduces total path costs: ```matlab function updateConnections(newNode, allNodes, searchRadius) closeByIndices = getNearbyNodes(allNodes, newNode.position, searchRadius); betterParentFound = false; for i = 1:length(closeByIndices) potentialParentIdx = closeByIndices(i); alternativePathCost = allNodes(potentialParentIdx).cost +... computeCost(allNodes(potentialParentIdx).position,... newNode.position); if alternativePathCost < newNode.cost && ~checkCollision(... lineSegmentBetweenPoints(allNodes(potentialParentIdx).position,... newNode.position)) betterParentFound = true; break; end end if betterParentFound newNode.parentIndex = potentialParentIdx; newNode.cost = alternativePathCost; else addAsChildOfClosestNeighbor(newNode, allNodes, closeByIndices); end end ``` This iterative process continues until either reaching maximum iterations or finding a feasible solution connecting start and goal positions via optimized tree structure. --related questions-- 1. How does one define custom environments with specific boundary constraints? 2. What modifications would need to apply for non-holonomic systems like cars using Dubin's curves? 3. Can you explain how collision detection works between sampled points and predefined polygonal obstacles? 4. Is there any way to visualize intermediate steps of growing trees graphically inside MATLAB GUIs?
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