Re: Re: Problem with Euler Angles

Frans,

The problem with the mixing of the X and Z angles is probably because you
are using one of my older getAngles( ) functions.  The most current
getAngles( ) function is at
http://www.mikejost.com/cyberbotics/RotationMatrix/Judoka0_AngleTest.zip
The function will return X=0 and Z=0 when the robot is standing vertical.

The previous functions were based on the two rotation matrix compositions:
     R = Rx * Rz * Ry  and
     R = Rx * Ry * Rz
Both of these compositions mix the X and Z angles, since they are not the
way the controller actually calculates the composition.
The lastest getAngles( ) function uses a composition based on the heirarchy
of the robot from the judo.wbt VRML file(see previous post Nov. 30, 2003).
This composition is
    R = Ry * Rx * Rz
This function returns correct X and Z angles with no mixing for -90 < X <
90.  For X angles beyond +/-90 the Z angle is locked at +/- PI.  The Y angle
is not correct.
This function will work as an inclinometer, but cannot be used to determine
the correct X,Y, and Z angles all the time.  There is a problem with using
Euler angles for rotation composition because the order of the composition
determines the final matrix and is not unique.  This has the effect of
mapping a rototion axis onto another axis (the mixing problem) and for
intermediate elementary rotations of +/-Pi/2 it will be impossible to rotate
around the final elementary axis (the locking problem).

Mike Jost


----- Original Message ----- 
From: "fransklip" <[email protected]>
To: <[email protected]>
Sent: Monday, December 15, 2003 18:20 PM
Subject: [webots-contest] Re: Problem with Euler Angles


> Hi Mike,
>
> I tried your angle calculation routines in my Kimaita robot for fall
> detection. That seemed to work at first, with the initial dive-attack.
> But later on in the match it went wrong: falls were detected when
> there was none.
>
> This weekend I logged sensor data every 64 msec while the robot was
> walking a small circle, and doing some body rotations after every
> (about) 90 degrees: tilt forward/back, tilt left/right and rotate ,
> each + and -10 degrees.
>
> Near the Z-axis, the angles routines return values that can be related
> to the actual robot posture. But when moving away from the Z-axis, I
> cannot relate the returned angles to the robot anymore.
>
> I have made a summary of the test rotation values (angletest 01
> summaray.txt). You can donwload this file from
> www.van-der-klip.demon.nl/webots/angletest01.zip. It also contains the
>  sensor data for each of the 4 test movements in the walk (set 1, 2,
> 3, 4.txt) and the complete sensor and action log files).
>
> You can download the webview file of the test walk from:
> www.van-der-klip.demon.nl/webots/angletest01.wva
>
> Are the calculated angles something else then a rotation of the robot
> body around its center? If so, could you please axplain what they are?
>
> Regards,  Frans / Kimaita
>
> --- In [email protected], "Mike Jost"
> <webotsContest@m...> wrote:
> > Olivier,
> >
> > I found some problems with the Euler angle calculations this
> weekend.  I tested the previous equations by rotating the robot with
> the mouse, since I did not have a robot controller capable of turning
> on its own.   Apparently the rotation composition used by the mouse in
> the Webots program is different than the rotation composition used
> when a robot actually moves itself.  The current gps_euler( ) function
> in Webots 4.0.17 also returns wrong X and Z angles for some Y
> orientations of a robot.
> >
> > Solution:
> > I looked at the VRML file and used a rotation composition based on
> the heirarchy of the robot.
> >    Judoka_Robot {
> >       rotation 0 1 0 0 (rot about Y)
> >       children {
> >          back_1 servo {
> >             rotation 1 0 0 0 (rot about X)
> >             children {
> >                back_2 servo {
> >                   rotation 0 0 1 0 (rot about Z)
> >                }
> >             }
> >          }
> >          gps_device
> >       }
> >    }
> >
> > The resulting composition should be  Rgeneral = Ry * Rx * Rz instead
> of the previous  Rx * Ry * Rz.
> >
> > The routine to compute the euler angles based on this composition is:
> >    public static float[] getAngles(float matrix[]) {
> >
> >       float[] angles = new float[3];
> >       double cosX;
> >
> >       angles[0] = (float)Math.asin(-1*matrix[9]); // find X angle
> >
> >       cosX = Math.cos(angles[0]);
> >       angles[1] = (float)Math.atan2( -1*matrix[8]/cosX,
> matrix[10]/cosX  );  // find Y angle
> >       angles[2] = (float)Math.atan2( matrix[1]/cosX, matrix[5]/cosX
> );       // find Z angle
> >
> >       return angles;
> >    } // end of getAngles()
> >
> >
> > I have generated a Judoka0 test robot that will rotate itself about
> Y and stop at 45 Degree intervals and bend forward,backward, left, and
> right, and display the computed angles from this new routine.
> > The back_1 and back_2 servos are set to a rotation of +/- 0.5 rad at
> each test point.
> > Hopefully, this routine will work in all cases, such as after Coyote
> does a summersalt and rotates X around a full 2*pi radians.
> >
> >
> > Judoka0 Test Robot:
> >
> http://www.mikejost.com/cyberbotics/RotationMatrix/Judoka0_AngleTest.zip
> >
> > HTML version of Maple worksheet of General Rotation Matrix for
> R=Ry*Rx*Rz:
> >
> http://www.mikejost.com/cyberbotics/RotationMatrix/RotationMatrix.html
> >
> >
> > Mike Jost (FreeTIme)
>
>
>
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>
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>
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>



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