solving matrices in terms of variables with matlab

nsrbb5 · **Posted:** Mon 03-21-2005 11:42PM

so i'm taking ME349 robotic manipulators this semester, and it involves a shitload of matrix multiplication. not like 3x3*3x1 or anything, i'm talking 6 4x4 matrices multiplied together, each with sine theta cosine theta a and d terms in them. i COULD do this in my TI89, but you can imagine how long it takes to type this shit out on a fucking calculator. i can't figure out how to get matlab to solve a matrix in terms of variables, i just get "d is not a defined variable" does anyone know if there is a way to get matlab to crank all these matricies out to get a 4x4 matrix with 902348 fucking terms in it? (because i know it will be that big, despite how many zeroes and ones are in it)

Paradigm · **Posted:** Tue 03-22-2005 12:24AM

I really have no idea what you just said.

But Matlab <3's matrices. It's what it's built for. It will multiply the matrices no problem, so then you just get a 4X4 matrix. If you're looking to solve with row reductions, try the command rref (i think).

Ex:

You have matrices A, B, C, and D (all 4x4, or other such multipliable)
And you have an answer matrix which is 4 rows by 1 column of the desired answers.

E=A*B;
E=E*C;
E=E*D;
E=[E [ans_matrix]];
Ans=rref(E);

This will get you the values of the variables that will get you the answer matrix. Not sure if this is what you were looking for, but we'll see.

nsrbb5 · **Posted:** Tue 03-22-2005 1:27AM

yeah, but that is for a matrix of say [1,2;3,4]. i'm looking for a matrix of [cos(t1),-sin(t1);a1,d1]*[-cos(t2),sin(t2);a2,0]=ANS, where ANS is in terms of t1, t2, a1, a2, and d1.

Paradigm · **Posted:** Tue 03-22-2005 3:19AM

Ahhh, I got you now. But can't think of how to help you. Sorry, not sure how to make Matlab deal with uninitialized variables.

bsiever · **Posted:** Tue 03-22-2005 8:15AM

Matlab can work with symbolic variables, but you need to declare them first:
<ul>syms a b c;
[a 2 sin(b)]*c</ul>

There are some handy commands to work with expressions
(simplify, subs, int (integrate), diff (differentiate), factor, expand, sym, etc.).

Mathworks has decent documentation on-line (and as a PDF):
<ul>http://www.mathworks.com/access/helpdesk/help/toolbox/symbolic/</ul>

Or you can get the basics from Matlab's on-line help
(I.e. "help simple", "help syms", ...).

Bill

tansir1 · **Posted:** Tue 03-22-2005 10:32AM

>> syms t1 a1 d1 t2 a2
>> [cos(t1),-sin(t1);a1,d1]*[-cos(t2),sin(t2);a2,0]

ans =

[ -cos(t1)*cos(t2)-sin(t1)*a2, cos(t1)*sin(t2);
-a1*cos(t2)+d1*a2, a1*sin(t2)]

nsrbb5 · **Posted:** Tue 03-22-2005 2:08PM

BAM! thanks guys. i had tried using "global variables" but they were being defined as 1x1 matrices of empty value, causing a vert_cat error. i had searched help for "variables" but hadn't found any of this symbolic shit. i'm definatl going to give it a try though!

its just too bad that my syms are going to be th1-6, a1-6 and d2-5

nsrbb5 · **Posted:** Tue 03-22-2005 2:29PM

HAHAHAHHAHAHAHAHAHAH

what was tha command for simplifying, again?

Quote:

>> T60=A1*A2*A3*A4*A5*A6

T60 =

[ (((cos(t1)*cos(t2)*cos(t3)-cos(t1)*sin(t2)*sin(t3))*cos(t4)-sin(t1)*sin(t4))*cos(t5)+(cos(t1)*cos(t2)*sin(t3)-cos(t1)*sin(t2)*cos(t3))*sin(t5))*cos(t6)+(-(cos(t1)*cos(t2)*cos(t3)-cos(t1)*sin(t2)*sin(t3))*sin(t4)-sin(t1)*cos(t4))*sin(t6), -(((cos(t1)*cos(t2)*cos(t3)-cos(t1)*sin(t2)*sin(t3))*cos(t4)-sin(t1)*sin(t4))*cos(t5)+(cos(t1)*cos(t2)*sin(t3)-cos(t1)*sin(t2)*cos(t3))*sin(t5))*sin(t6)+(-(cos(t1)*cos(t2)*cos(t3)-cos(t1)*sin(t2)*sin(t3))*sin(t4)-sin(t1)*cos(t4))*cos(t6), -((cos(t1)*cos(t2)*cos(t3)-cos(t1)*sin(t2)*sin(t3))*cos(t4)-sin(t1)*sin(t4))*sin(t5)+(cos(t1)*cos(t2)*sin(t3)-cos(t1)*sin(t2)*cos(t3))*cos(t5), (cos(t1)*cos(t2)*sin(t3)-cos(t1)*sin(t2)*cos(t3))*d4+cos(t1)*a2*cos(t2)+sin(t1)*d2]
[ (((sin(t1)*cos(t2)*cos(t3)-sin(t1)*sin(t2)*sin(t3))*cos(t4)+cos(t1)*sin(t4))*cos(t5)+(sin(t1)*cos(t2)*sin(t3)-sin(t1)*sin(t2)*cos(t3))*sin(t5))*cos(t6)+(-(sin(t1)*cos(t2)*cos(t3)-sin(t1)*sin(t2)*sin(t3))*sin(t4)+cos(t1)*cos(t4))*sin(t6), -(((sin(t1)*cos(t2)*cos(t3)-sin(t1)*sin(t2)*sin(t3))*cos(t4)+cos(t1)*sin(t4))*cos(t5)+(sin(t1)*cos(t2)*sin(t3)-sin(t1)*sin(t2)*cos(t3))*sin(t5))*sin(t6)+(-(sin(t1)*cos(t2)*cos(t3)-sin(t1)*sin(t2)*sin(t3))*sin(t4)+cos(t1)*cos(t4))*cos(t6), -((sin(t1)*cos(t2)*cos(t3)-sin(t1)*sin(t2)*sin(t3))*cos(t4)+cos(t1)*sin(t4))*sin(t5)+(sin(t1)*cos(t2)*sin(t3)-sin(t1)*sin(t2)*cos(t3))*cos(t5), (sin(t1)*cos(t2)*sin(t3)-sin(t1)*sin(t2)*cos(t3))*d4+sin(t1)*a2*cos(t2)-cos(t1)*d2]
[ ((sin(t2)*cos(t3)+cos(t2)*sin(t3))*cos(t4)*cos(t5)+(sin(t2)*sin(t3)+cos(t2)*cos(t3))*sin(t5))*cos(t6)-(sin(t2)*cos(t3)+cos(t2)*sin(t3))*sin(t4)*sin(t6), -((sin(t2)*cos(t3)+cos(t2)*sin(t3))*cos(t4)*cos(t5)+(sin(t2)*sin(t3)+cos(t2)*cos(t3))*sin(t5))*sin(t6)-(sin(t2)*cos(t3)+cos(t2)*sin(t3))*sin(t4)*cos(t6), -(sin(t2)*cos(t3)+cos(t2)*sin(t3))*cos(t4)*sin(t5)+(sin(t2)*sin(t3)+cos(t2)*cos(t3))*cos(t5), (sin(t2)*sin(t3)+cos(t2)*cos(t3))*d4+a2*sin(t2)+d1]
[ 0, 0, 0, 1]

bagvwf · **Posted:** Tue 03-22-2005 4:28PM

Aside from all THIS, though, how you liking the Robotic Manipulators class? It's one I'm half thinking about taking when I get up there.

bsiever · **Posted:** Tue 03-22-2005 6:04PM

nsrbb5 wrote:

HAHAHAHHAHAHAHAHAHAH

what was tha command for simplifying, again?

Quote:

>> T60=A1*A2*A3*A4*A5*A6

T60 =

[ (((cos(t1)*cos(t2)*cos(t3)-cos(t1)*sin(t2)*sin(t3))*cos(t4)-sin(t1)*sin(t4))*cos(t5)+(cos(t1)*cos(t2)*sin(t3)-cos(t1)*sin(t2)*cos(t3))*sin(t5))*cos(t6)+(-(cos(t1)*cos(t2)*cos(t3)-cos(t1)*sin(t2)*sin(t3))*sin(t4)-sin(t1)*cos(t4))*sin(t6),
...
]

Well, there's only so much you can expect it to do.
You might try simplifying each individual step:
<ul>
tmp1=simplify(A1*A2);
tmp2=simplify(tmp1*A3);
...
etc.
</ul>
It might not be any better, but it's worth a try.

simplify and simple are different commands.
Take a look at the help on simple and it lists the
different techniques that it uses. It might be helpfull
to call them directly (collect, combine, convert, etc.)

Bill

nsrbb5 · **Posted:** Tue 03-22-2005 6:46PM

bagvwf wrote:

Aside from all THIS, though, how you liking the Robotic Manipulators class? It's one I'm half thinking about taking when I get up there.

i like it, but there are some things in the class that straight up get on my nerves (like this shit, for example). the lab is fun at first, but then a pain. programming a robot to pick up blocks from one pallet and place them in another is fun. then you program it to pick up from a conveyor, and from arbitrary locations using a camera to detect the blocks. but writing the labs is a pain in the butt because you have to describe every damn part of the program and what it does "; this line asks the user if he wants to proceed" yeah no shit. the test was redic. easy (72/75) but the homework is a lot like dalton's 279 homework-- you spend 3 hours on it and get 10/40 points on it. and then some shit like this... i don't even know how this is physically possible to do. not only is this hard, but i have to mutiply it by each of the inverses and solve for thetas. yes, i have to solve this monster for theta1-6.

that mechatronics class sounds cool, but they are just NOW offering it...

tansir1 · **Posted:** Tue 03-22-2005 6:59PM

What class is the mechatronics one? Is it a special topics or something? That sounds like fun to me.

nsrbb5 · **Posted:** Tue 03-22-2005 7:43PM

i heard its about integration between mechanical, electronicics, control systems and some other stuff. i think anyone in MAEEM can enroll in it, it's going to be ME301.... what i gathered from an email i read.

is there anyway matlab can convert this shit into like cos(t1+t2+t3) or whatever? i think if i did that it might help..... but that's a whole lot of trig that i don't know how to do / am not willing to do by hand

solving matrices in terms of variables with matlab

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