Matlab实现比较分析PRM&RRT-puma560完整源码+项目介绍操作说明.zip资源-CSDN文库

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puma560

rrt路径规划

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Matlab实现比较分析PRM&RRT_puma560完整源码+项目介绍操作说明.zip （7个子文件）

Matlab实现比较分析PRM&RRT_puma560完整源码+项目介绍操作说明

Project Report.pdf 362KB

RapidRandomTree.m 6KB

projectStartup.m 5KB

robotCollision.m 1KB

项目程序操作说明.doc 16KB

PRMap.m 5KB

lineCollision.m 636B

  A Comparative Analysis Between Probabilistic Roadmaps and Rapidly

Exploring Random Trees for Puma 560

Prasanth Murali, Himtanaya Bhadada, Robert Platt

Northeastern University

ABSTRACT

This work explores motion planning algorithms

for the puma 560 robot in a high dimensional

configuration space. We illustrate the two

popular sampling algorithms (Probabilistic

Roadmaps (PRM*) and Rapidly Exploring

Random Trees (RRT*) ) and present a

comparative analysis for convergence of the

algorithms in finding a collision free path from

start to end position in the workspace.

INTRODUCTION

Sampling-based planners create possible paths

by randomly adding points to a tree until some

solution is found or time expires instead of

evaluating all possible solutions. They are hence

probabilistic complete since a path will be found

if times goes to infinity.

RRTs can be thought of as creating a tree from a

robot’s starting point until one of its branches

reaches the goal. On the other hand,

probabilistic road-maps create a tree by

randomly sampling points in the configuration

space, keeping only those points that are

collision free, connecting them with nearby points

using paths that depend on the kinematics of a

robot, and then using graph shortest search

algorithms to find shortest paths on the resulting

tree.

Such probabilistic roadmaps have to be created

only once (assuming the environment is not

changing) and can then be used for multiple

queries. This is a particular advantage that the

PRM presents, over the RRT algorithm. In

contrast, RRT’s are known as single query

path-planning algorithms. Thus, for the same

workspace, running a RRT for the robot can lead

to different solutions each time while PRM is

more consistent in this way.

But, it should be noticed that there is no gold

standard or heuristic and even their

parameter-sets are highly problem-specific.

Figure 1: Workspace representing the Puma 560

robot and the obstacles

In this project, we are studying the application of

PRM and RRT to the puma 560 robot, provided

by Peter Corke’s Robotics Toolbox. The puma

560 is modeled as a Serial Link object having 6

DOF. The script creates the workspace variable

p560 which describes the kinematic and dynamic

attributes of a Unimation Puma 560 manipulator

using standard DH conventions.

The configuration space consists of five

spherical, four hemispherical and two cylindrical

obstacles as shown in Figure 1. The goal of the

robot is to traverse from the current joint

configuration to [-0.3;0.5;0.5] (marked as blue

circle).

We will now have an overview of the PRM and

RRT algorithms implemented to achieve the

above task.

PROBABILISTIC ROADMAP

Probabilistic Roadmaps are processed in two

phases, the preprocessing phase to construct

the roadmap; and the query phrase to connect

the initial (qStart) and final (qGoal) configurations

to this map and find a path between them.

The preprocessing stage involves building the

probabilistic roadmap,which is an undirected

graph G = (N, E). The nodes in N correspond to

configurations of the robot in the collision free

C-space. The edges of the graph in E denote the

feasible straight-line paths. In the query phase,

given a starting configuration (qStart) and a goal

configuration (qGoal), the algorithm will search

the roadmap for a path joining these two points

together.

Figure 2: PRM pseudocode

The above figure details the pseudocode behind

the PRM algorithm. It starts with an empty graph:

G(Vertex, Edge). Assuming we are generating N

random points, a sample configuration is

generated for every point. We now run the

collision detector to find out whether the point is

in collision. Post this, we need to find out all the

edges that this point is able to connect to. This

set of neighbourhood is made of nodes within a

certain distance of R from this point. If there is no

obstacle in the configuration space within the

straight line, we add the edge to the graph G.

Otherwise, we do not retain the edge. This

process is repeated for all the points.

RAPIDLY EXPLORING RANDOM TREES

We use a baseline Rapidly Exploring Random

Tree (RRT) searching for a path from the initial to

the goal configuration to compare the

performance of PRM against it.

For each step, the algorithm determines a target

configuration and expands the tree towards it.

During expanding, the algorithm only needs to

verify whether each step is collision free but does

not need to avoid obstacles. A pseudocode of

the RRT algorithm is described in Figure 3.

During the search process, the target can either

be a random configuration or the goal

configuration itself, depends on the probability

value defined by the user. This bias is introduced

into the algorithm, since the algorithm might not

converge otherwise. Introducing the goal

configuration as a sampling point helps the

algorithm sample and move towards the goal in

shorter time.

Figure 3: RRT algorithm

From the above descriptions, it is evident that the

collision checks comprise of the most important

parts of both the algorithms. We will have an

overview of the collision check algorithms used

in this project.

COLLISION CHECK

From figure 1, it is clear that our workspace

consists of five spherical, four hemispherical and

two cylindrical obstacles. The collision check

involves calculating the cartesian coordinates for

each joint of the robot using Forward Kinematics

for the current joint configuration and checking

for the presence of these points inside or on the

boundary of the obstacles. The serial links each

of the joints are checked for collision by dividing

the line joining the joints into various points and

checking those for collision. The manipulator is

also checked for self collision at all points.

For the sphere with center at (x0,y0,z0) and

radius (r) , a point (x,y,z) is on/inside the sphere

if the following equation is satisfied :

x x0)² (y y0)² (z z0)² = r²( − + − + − <

The hemisphere is checked for collision in a

similar way. The hemisphere is essentially the

intersection of a half space and a sphere. Thus,

the point is checked for presence in both the

cases and the intersection is taken as as the

result.

For a cylinder with center at (x0,y0,z0) and

height ‘h’ (parallel to z axis), the process to

check if a random point (x,y,z) is on/inside the

cylinder is as follows:

1. Check if the point is within the cylinder on the

x-y plane, checking for presence of the point

inside a circle denoted by center at (x0,y0) and

radius (r) using the following equation:

x x0)² (y y0)² = r²( − + − <

If the inequality is false, the point is outside,

otherwise continue.

2. Check if the z coordinate of the point is with

the z coordinates of the top and bottom surfaces

of the cylinder.

top 0 h/2z = z +

bottom z0 h/2z = −

Thus, for each random joint configuration of the

robot, the coordinates of each of the joints

calculated using FK is checked for presence

inside the obstacles using the above equations.

The point is said to be collision free only if it is

outside all the obstacles (thereby satisfying all of

the equations).

Now, while calculating the edges of the graphs,

we must ensure that the line is collision free. This

is done by dividing an edge joining two nodes

with a step size of ten and checking for collision

for each of those ten points. The path is said to

be collision free only if all the points are collision

free.

After setting up the environment and

implementing the algorithm, we conducted

several experiments to compare the performance

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