[Dprglist] Assisting PID odometry with an IMU

Carl Ott carl.ott.jr at gmail.com
Sat Jan 23 05:57:05 PST 2021

Hi Murray,

regarding PID tuning of your heading loop -

have you tried to examine the heading loop step response?

For example - what happens if you place your robot on that turntable at
your desk -
turn on the PID loop so that the robot tries to maintain a constant
heading, without any forward motion -
then give the turntable various disturbances - especially abrupt
step-function changes - where you slew the table 30 or 40 degrees, with the
slew-rate change in table rotation speed as high as possible (ie. zero to
max turn-rate as quickly as possible, then max turn-rate to zero as quickly
as possible).

If you had a super-beefy motor you could automate turn-table rotation to
make a repeatable test-bed.  Otherwise you could just do it by hand.

The robot should try to re-orient itself to maintain the same heading even
as you rotate the table underneath it.

As you observe the robot response - look to see if the heading correction
overshoots and rings before it settles on the correct heading, or if it
just takes 'forever' to finally creep to the right heading / if it ever
even reaches the right heading.

OR - on a stable surface without the turntable complication -
perhaps you could do an even better step-response test by adding a tiny bit
of code...

what about adding a software motor drive enable/disable switch, one that
you could toggle wirelessly from your laptop?

   1. Give the robot a 'zero' heading set-point with the PID loop and motor
   drive on -
      - let it settle on that heading.
   2. Then turn the motor drive off,
      - *but leave the PID loop on*.
   3. Then manually turn the robot something like 45 degrees and take your
   hands off of it.
      - At this point, you have introduced a large step error -
      - and you're about to ask for the maximum possible slew rate response
      - a step response
   4. Then turn the motor drive back on,
      - and watch the robot's 'return-to-zero' behavior.
   5. At first you could iterate steps 1..4 and dial-in PID values just by
   eyeballing the step-response.
      - Your goal is to have the robot 'return-to-zero' as quickly as
      possible, without overshooting
   6. But to really dial things in, you could use a video to accurately
   look for overshoot and measure timing.

- Carl

On Sat, Jan 23, 2021 at 1:28 AM Murray Altheim via DPRGlist <
dprglist at lists.dprg.org> wrote:

> Hi Doug,
> My initial question was asking what might be the algorithm for
> handling the rug bumps. Finding a Python library that handles this
> is great, but I must admit I was still a bit adrift as to how to
> actually incorporate it into my robot's behaviour. It'll take me a
> bit of time to digest what you've written, and try it out in code
> on my robot, but you've actually answered that question, i.e., how
> to work out how to take that IMU error and incorporate it into the
> robot's motor outputs.
> Thanks very much for that!
> One of the things I keep getting reminded of is that while there's
> a lot of focus on fancy sensors and such (but of course!), some of
> the more "basic" stuff in robotics is actually pretty tricky to get
> right. Precise navigation and odometry is quite difficult, which is
> what makes it all the more impressive to see done well.
> Cheers,
> Murray
> On 23/01/21 7:17 pm, secretary at dprg.org wrote:
> > Murray,
> >
> > One approach is to take the theta value from the IMU instead
> > of calculating it from the encoders, and then adding the
> > heading error to the summing node of the negative feedback loop.
> >
> > Taking the theta value form the IMU:
> >
> > /* accumulate total rotation around our center */
> > /*theta += (left_inches - right_inches) / WHEEL_BASE; */
> >
> > /* replace theta value with IMU yaw value */
> > theta = read_IMU_yaw();  /* make sure that the units and orientation are
> correct */
> >
> > /* and clip the rotation to plus or minus 360 degrees */
> > theta -= (float)((int)(theta/TWOPI))*TWOPI;
> >
> > Now the theta value is from the IMU and should show the impact of
> > your rug/floor disturbance.
> >
> > The next part is to add the heading error (heading error = heading
> > target – theta) to the input summing node of your negative feedback
> > loop. The heading error is zero when you are going in the right
> > direction, elsewise it will have either a negative or positive
> > value. It will be summed in with your reference value (desired
> > speed in this case) and the -feedback value (PID error). If you
> > view it in terms of your PID error, it is like you are changing
> > the reference value.
> >
> > I hope this helps.
> ...........................................................................
> Murray Altheim <murray18 at altheim dot com>                       = =  ===
> http://www.altheim.com/murray/                                     ===
> ===
>                                                                     = =
> ===
>      In the evening
>      The rice leaves in the garden
>      Rustle in the autumn wind
>      That blows through my reed hut.
>             -- Minamoto no Tsunenobu
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