calculating position using follower wheels

[Ether]

Originally Posted by flameout

It is at the origin, facing 15 degrees clockwise from the +Y axis.

EDIT: 120 deg/sec * 3 sec = 360 degrees -- it just goes in a circle.

Nice work. That was quick.

Question 2: What's the radius of the circle?

[flameout]

Spoiler for solution:

Speed = sqrt(4^2+5^2), which approximately equals 6.4 ft/s

6.4 ft/s * 3 sec = 19.2 feet (circumference of the circle).

Thus the radius is 19.2 feet / (2*pi), or approximately 3.06 feet

EDIT: Perfectly matched text color w/ background color.
EDIT2: Oops, it's 5 ft/s forward and 4 ft/s strafing, not 4 ft/s and 3 ft/s
EDIT3: Changed colored text to a spoiler -- thank you EricH

[Ether]

Originally Posted by flameout

Text made the same color as the background so as not to give it away for others -- highlight to read.

Good job. I see this is too easy.

This one is quite a bit more difficult:

Question 3: Exactly the same as Question 1, except the FWD speed is a function of time, as follows: FWD = 5.0 + 1.0*T. In other words, FWD starts with the value 5.0 at T=0, and increases smoothly and linearly at a rate of 1 ft/sec/sec. The STR and RCW remain constant at 4 ft/sec and 120 deg/sec respectively.

[maths222]

Spoiler for Solution:

(1.3836,-0.3707); 15 degrees clockwise

Can this be done without integrals?

[RyanCahoon]

Originally Posted by Ether

Question 3:

Spoiler for Question 3:

T=0: (0,0) pi/12 (from +Y axis)

FWD = (5.0 + 1.0*T) ft/s
STR = 4 ft/sec
RCW = 120 degrees/sec

T=3:
x = Integrate[(5 + t)*Sin[(2*Pi/3)*t + Pi/12] + 4*Cos[(2*Pi/3)*t + Pi/12], t, 0, 3]
= -1.3836

y = Integrate[(5 + t)*Cos[(2*Pi/3)*t + Pi/12] - 4*Sin[(2*Pi/3)*t + Pi/12], t, 0, 3]
= 0.3707

angle = (2*Pi/3)*3 + Pi/12 = Pi/12 = 15 degrees

Originally Posted by maths222

...

maths222, what coordinate orientation did you use? If X x Y is out of the page (like axes are usually drawn), I think you got your angle sign wrong (the strafe movement cancels out. rotation is clockwise, so the robot's forward movement is toward +X for most of the first half of the movement, and -X for the second half. since the robot moves faster during the second half, a negative result makes sense)

[flameout]

Originally Posted by RyanCahoon

maths222, what coordinate orientation did you use? If X x Y is out of the page (like axes are usually drawn), I think you got your angle sign wrong (the strafe movement cancels out. rotation is clockwise, so the robot's forward movement is toward +X for most of the first half of the movement, and -X for the second half. since the robot moves faster during the second half, a negative result makes sense)

I think he's just reporting the angular orientation of the robot. Since the angular rate does not depend on the location (in the XY plane), it is still facing 15 degrees clockwise from the Y axis.

[EricH]

Not answering the math questions... just this one.

Originally Posted by flameout

Text made the same color as the background so as not to give it away for others -- highlight to read. (Is there a way to spoiler tag text here?)

A spoiler tag looks like [ spoiler=yourspoilernamehere] what the spoiler is[/spoiler] (without the space in the first bracket) and ends up looking like:

Spoiler for This is a spoiler:

I warned you this was a spoiler.

And now back to the math...