Robotics Coordinates, position, orientation kinematics. HTML5 reading file. Homework: Prepare for lab. Postings

Robotics

Coordinates, position, orientation kinematics. HTML5 reading file.

Homework: Prepare for lab. Postings

Coordinate system

• Method of providing system for specifying points / positions / vectors in a given N-dimensional space.

• This space, typically, is a line (1D), plane (2D), or space (3D).

• The most common coordinate system is Cartesian: 3 orthogonal, linear dimensions; fixed origin– Position of origin needs to be specified– Orientation of axes needs to be defined

• Right-hand rule is convention involving relationship of x, y and z

• Another common system for the plane is polar (angle and distance), cylindrical (polar + height) or spherical (3D vector + distance) for space.

Polar

d

a

x

y

x = d * cos(a)

y = d * sin (a)

a= atan(y/x)

need to specify quadrant—computer atan function may do this.

d = sqr(x*x+y*y)

Note

• May be easier to collect positions in polar coordinates and then convert them, as needed, to something else.

• REPEAT: critical issue is defining the origin.

Addition (of moves)

Robot moved … and moved again.

• Adding [cartesian] vectors– (x1, y1) + (x2,y2) IS (x1+x2, y1+y2)

• Need to be aware of when something is a position and when it is a displacement

• Adding polar coordinates– Convert to cartesian and convert back!

Position

• … of what?

• Robot wheel base

• Robot ultrasonic sensor

• Robot bumper or touch sensor itself

• Robot light sensor

Orientation

• Where is robot facing?

• Plane: 2 positional degrees of freedom and 1 angle

• Space: 3 positional degrees of freedom and 3 angles.

Reference

• Neat Flash animation on vectors– Ocean, bottle, current

http://ephysics.physics.ucla.edu/newkin/html/position_velocity_ship.htm

http://ephysics.physics.ucla.edu/newkin/html/position_velocity_ship.htm

Kinematics

• For linked/jointed structures, calculating the position of the end-point, given the position/angle of each joint.

• Easy (easier) problem

Inverse kinematics

• Given jointed/linked structure, what are positions of joints/angles to make endpoint be at a given point?– May be no answer or multiple answers

• Easy for IBM Box frame robot: links were not coupled.

• For articulated mechanisms, various approaches, often requiring iterative techniques.

Challenge: mapping

• Program the robot to provide map of the room– More precisely, provide coordinates of positions of

walls/barriers/lines (points)(think about connecting points later)

• Upload using Mindstorms to Desktop. HTML5 program draws points.

• (Later) send file (single position is 2 numbers) to other robot using Bluetooth

• (Later) automatically upload file to computer

HTML5 JavaScript• reads in whole file

– HTML5 file API. More general / more features than used for this example.

– Note: asynchronous action. Set up function for the event of indicating the file AND set up function for the event of reading in the text data.

– program detects line breaks– program converts from text to number

• draws on canvas– blue dot is the center– red dots are calculated positions

• Note: draws based on standard, not upside down!, coordinates.

testpairs.txt file

0502060120352006030040

HTML5 program drawing positions

• http://faculty.purchase.edu/jeanine.meyer/robotics/mapdata.html

• Works in Firefox

• Two sample files:– textpairs.txt– textpairs3.txt

http://faculty.purchase.edu/jeanine.meyer/robotics/mapdata.html

http://faculty.purchase.edu/jeanine.meyer/robotics/mapdata.html

HTML5 functions

• init

• readInData

• receivedText

• drawpositions

• drawdot

HTML5 outline

<html><head><script>….</script></head><body onload="init();">Name the file:<input type="file" id="fileinput" " /><canvas id="canvas" width="900" height="600">The browser does not recognize canvas.</canvas></body></html>

global data and init function

var ctx;var center = [450,300];var rad = 5;var data;function init() {

ctx = document.getElementById("canvas").getContext("2d");drawdot(center[0],center[1],"blue");

document.getElementById("fileinput").addEventListener('change',readInData,false);

}

function readInData(ev) {var input = document.getElementById("fileinput");

if (!input.files) {alert("browser doesn't seem to support files ");return;

}else if (!input.files[0]) {

alert("please select a file");return;

}else {file = input.files[0];fr = new FileReader();

fr.onload = receivedText; fr.readAsText(file); }}

function receivedText() {

var i;

data = fr.result.split("\n");

for (i=0;i<data.length;i++) {

data[i] = Number(data[i]);

}

drawpositions();

}

function drawpositions() {//uses info in data arrayvar i;var angle;var dist;var x;var y;for(i=0;i<data.length;i=i+2) {

angle = (data[i]/180)*Math.PI;dist = data[i+1];x = center[0]+dist*Math.cos(angle);y = center[1]-dist*Math.sin(angle);drawdot(x,y,"red");

}}

function drawdot(x,y,color) {

ctx.fillStyle = color;

ctx.beginPath();

ctx.arc(x,y,rad,0,2* Math.PI,true);

ctx.fill();

ctx.closePath();

}

Lab: Mapping

• One group of strategies is to generate any number of points along walls.– Leave it to other program to connect dots

• Another strategy is to measure walls– Walk along walls, mark points or lengths

• You can make assumptions (constraints) on shape of room

• "Build" room using books or other obstacles.

Homework

• Postings

• Start/Continue work on mapping strategy / strategies– What sensor(s)?– How to specify origin?

– Amount of travel versus walls versus ????

Documents

Robotics Coordinates, position, orientation kinematics. HTML5 reading file. Homework: Prepare for lab. Postings