Subject:
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Re: Trigonometry and NQC
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Newsgroups:
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lugnet.robotics.rcx.nqc
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Date:
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Fri, 14 Dec 2001 14:35:00 GMT
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Viewed:
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6349 times
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Thank you for these posts! This idea of creating a table of arctangents is
just what I need. I'll let everyone know how it works after I redesign the
racer. (The prototype, designed for speed, experienced a significant
mechanical shock when it smashed into the first wall. The sensor response
time was not sufficient to allow the robot to stop. : )
Rich
In lugnet.robotics.rcx.nqc, Rainer Balzerowski writes:
> In lugnet.robotics.rcx.nqc, Richard Jenkins writes:
> > Hi!
> >
> > I'm working on a project where a robot needs to travel a right triangle with
> > unkown side lengths. Basically, the robot starts at a point in a room,
> > travels perpendicularly toward a wall, turns 90 degrees left when it hits,
> > and when it gets to the corner needs to return to the starting point in the
> > room (somewhere). No marks or other guides are provided to help the robot
> > find the starting point, but it can obviously measure the distance (or the
> > time) of the two perpendicular legs. I could complete the course making a
> > square instead of a triangle, but that's not very elegant.
> >
> > I prefer NQC as my Mindstorms programming tool, but it isn't apparent to me
> > that it supports trig functions.
> >
> > Can anyone offer any suggestions?
> >
> > Thanks,
> >
> > Rich
>
> Hi Rich,
>
> there are no trig functions, because there's no float.
> I had the same problem and was able to approximate these values.
>
> I created two tables with the necessary values.
> The first table includes the values of the tangens of a angle. This values
> are times 100, because there's no float available.
> What you need in fact is the arcustangens. But it's not avbailable. So i
> check the values i want to calculate the arcustanges for with my table and
> can see the resulting angle +/- 5 degree. (It's not easy to explain in
> english, i'm from germany)
>
> So, if the result of the following equation
> degree_to_goal = (abs(delta_y)*100)/abs(delta_x);
> is 74 (0.74*100) , then the resulting angle is between 35° and 40°
>
> The second table is a table of squares. It's the same priciple as before.
> You need a square-root for Pythagoras. But there is no square-root in NQC.
> So look in the table to get an approximation of the square-root.
>
> Pay attention, that the values for sqr(x-direction) + sqr(y-direction) do
> not exceed 32.767 (because all values in NQC are signed integer (-32768 ->
> 32767) and you will get wrong results)
>
> It works well. Try it and let me know what you think.
>
> Rainer
>
> **************************************************************************
>
> #define degree5 9 // -> tan(5°) = 0.0875 // *100 because no float
> #define degree10 18 // -> tan(10°) = 0.1763 // *100 because no float
> #define degree15 27 // -> tan(15°) = 0.2679 // *100 because no float
> #define degree20 36 // -> tan(20°) = 0.364 // *100 because no float
> #define degree25 47 // -> tan(25°) = 0.4663 // *100 because no float
> #define degree30 58 // -> tan(30°) = 0.5774 // *100 because no float
> #define degree35 70 // -> tan(35°) = 0.7002 // *100 because no float
> #define degree40 84 // -> tan(40°) = 0.8391 // *100 because no float
> #define degree45 100 // -> tan(45°) = 1 // *100 because no float
> #define degree50 119 // -> tan(50°) = 1.1918 // *100 because no float
> #define degree55 143 // -> tan(55°) = 1.4281 // *100 because no float
> #define degree60 173 // -> tan(60°) = 1.7321 // *100 because no float
> #define degree65 214 // -> tan(65°) = 2.1445 // *100 because no float
> #define degree70 275 // -> tan(70°) = 2.7475 // *100 because no float
> #define degree75 373 // -> tan(75°) = 3.7321 // *100 because no float
> #define degree80 567 // -> tan(80°) = 5.6713 // *100 because no float
> #define degree85 1143 // -> tan(85°) = 11.4301 // *100 because no float
>
> #define Square10 100 // square-root 100 = 10
> #define Square20 400 // square-root 400 = 20
> #define Square30 900 // square-root 900 = 30
> #define Square40 1600 // square-root 1600 = 40
> #define Square50 2500 // square-root 2500 = 50
> #define Square60 3600 // square-root 3600 = 60
> #define Square70 4900 // square-root 4900 = 70
> #define Square80 6400 // square-root 6400 = 80
> #define Square90 8100 // square-root 8100 = 90
> #define Square100 10000 // square-root 10000 = 100
> #define Square110 12100 // square-root 12100 = 110
> #define Square120 14400 // square-root 14400 = 120
> #define Square130 16900 // square-root 16900 = 130
> #define Square140 19600 // square-root 19600 = 140
> #define Square150 22500 // square-root 22500 = 150
> #define Square160 25600 // square-root 25600 = 160
> #define Square170 28900 // square-root 28900 = 170
> #define Square180 32400 // square-root 32400 = 180
>
>
> // Approximate angle to destination !
>
> degree_to_goal = (abs(delta_y)*100)/abs(delta_x); // times 100,
> //because no float
> if (degree_to_goal < degree5){
> degree_to_goal = 5;
> }
> else if (degree_to_goal < degree10){
> degree_to_goal = 10;
> }else if (degree_to_goal < degree15){
> degree_to_goal = 15;
> }else if (degree_to_goal < degree20){
> degree_to_goal = 20;
> }else if (degree_to_goal < degree25){
> degree_to_goal = 25;
> }else if (degree_to_goal < degree30){
> degree_to_goal = 30;
> }else if (degree_to_goal < degree35){
> degree_to_goal = 35;
> }else if (degree_to_goal < degree40){
> degree_to_goal = 40;
> }else if (degree_to_goal < degree45){
> degree_to_goal = 45;
> }else if (degree_to_goal < degree50){
> degree_to_goal = 50;
> }else if (degree_to_goal < degree55){
> degree_to_goal = 55;
> }else if (degree_to_goal < degree60){
> degree_to_goal = 60;
> }else if (degree_to_goal < degree65){
> degree_to_goal = 65;
> }else if (degree_to_goal < degree70){
> degree_to_goal = 70;
> }else if (degree_to_goal < degree75){
> degree_to_goal = 75;
> }else if (degree_to_goal < degree80){
> degree_to_goal = 80;
> }else if (degree_to_goal < degree85){
> degree_to_goal = 85;
> }else{
> degree_to_goal = 90;
> }
>
> // Approximate distance to destination !
>
> distance = (delta_x*delta_x)+(delta_y*delta_y); // nearly Pythagoras,
> // except of the square-root
> if (distance >= Square180){
> distance = 180;
> } else if (distance >= Square170){
> distance = 170;
> } else if (distance >= Square160){
> distance = 160;
> } else if (distance >= Square150){
> distance = 150;
> } else if (distance >= Square140){
> distance = 140;
> } else if (distance >= Square130){
> distance = 130;
> } else if (distance >= Square120){
> distance = 120;
> } else if (distance >= Square110){
> distance = 110;
> } else if (distance >= Square100){
> distance = 100;
> } else if (distance >= Square90){
> distance = 90;
> } else if (distance >= Square80){
> distance = 80;
> } else if (distance >= Square70){
> distance = 70;
> } else if (distance >= Square60){
> distance = 60;
> } else if (distance >= Square50){
> distance = 50;
> } else if (distance >= Square40){
> distance = 40;
> } else if (distance >= Square30){
> distance = 30;
> } else if (distance >= Square20){
> distance = 20;
> } else if (distance >= Square10){
> distance = 10;
> } else {
> distance = 0;
> }
> *******************************************************************
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Message is in Reply To:
 | | Re: Trigonometry and NQC
|
| (...) Hi Rich, there are no trig functions, because there's no float. I had the same problem and was able to approximate these values. I created two tables with the necessary values. The first table includes the values of the tangens of a angle. (...) (25 years ago, 13-Dec-01, to lugnet.robotics.rcx.nqc)
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