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    <p>PS, forgot to mention.  Since the bottom end of his pendulum is
      fixed, an IMU is not really needed.  A simple low-friction pot
      will do to deduce the angle.   That's how I began my balancing
      robot experiments back in the before time:
      <a class="moz-txt-link-freetext" href="http://www.geology.smu.edu/dpa-www/robo/nbot/polebot.mpg">http://www.geology.smu.edu/dpa-www/robo/nbot/polebot.mpg</a><br>
    </p>
    <p>cheers!</p>
    <p>dpa</p>
    <p><br>
    </p>
    <div class="moz-cite-prefix">On 8/21/22 7:03 PM, David P. Anderson
      via DPRGlist wrote:<br>
    </div>
    <blockquote type="cite"
      cite="mid:35a09750-1d15-2fba-4fba-062cebff663a@smu.edu">
      <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
      <p>Cool experiment.   <br>
      </p>
      <p>Accelerometers don't help that much because when you are
        falling, they are in free fall -- as it were -- and therefore
        don't have any useful information to impart.  However, gyros
        tell when the body is rotating.  That and the speed of rotation
        are all that's needed.  <br>
      </p>
      <p>If the inverted pendulum has a moveable bottom end, like a
        wheel for example, rather than fixed in place like the example,
        then the gyro and wheel feedback together totally constrain the
        movement of the plant.   Same with the classic printer carriage
        inverted pendulum, like for example this one: <a
          class="moz-txt-link-freetext"
href="https://secure-web.cisco.com/1g7ebb1_wK9t-D5bNCuP4C6VZZxAWhxSmwXEA80v1rBMyxz45grwCKHTrltpsnplE2uZK-aD0gOw3T_QDBoodfGQF7iN9JB7Yb08AmFOl5MtHtkdMGsIMRceB7ZMOnD0VflGDxW9tX0iRAFRHBQ3R--12pQi8S7sqm7FFzqBUoEOQcBg_QHM1f4-ByM_D81qg5HvnfWy8bt_ZIrLLb4oVdH9T4XhkoODMSSL-hPSqT8K9Vo-hqu6Y9XVsQeLHmk877Ev7wAnKvkf_afrqtBxgMpOvh7OhhIMOIDnmGIjj918/https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DNdbODkTNvp4"
          moz-do-not-send="true">https://www.youtube.com/watch?v=NdbODkTNvp4</a><br>
      </p>
      <p>The lego experiment does seem to have to deal with lots of edge
        cases, which always raises some red flags for me.  Simpler is
        usually more robust, as a general rule.</p>
      <p>And speaking of PID, found this great article, very complete,
        with some nifty history:</p>
      <p><a
href="https://secure-web.cisco.com/1eofDntL9pzGQ8zQ2siZtPMyQiqYcM-lHUy9mesofY7rIWDRHBE4IS1-05YFxe4Dh6IgKuRjsjPkwyuonHubPuciNVCoD3ckiBXGkAJ8Xq6nHfUquR_MVAPm-rY7Pis7OfeTFr0f_NJ_zS4T83ac0sOgKR4fkREQNRP-5aE4wO5DpvFAEHeyxHBm2MEn7t9kysciN-TZjKO5fXsPJfWFYOqBl6XshnZgsV6OE_IcriUykrHS0xj2YJuRFQTNNVB3UQ7nwYthVnAW1RiHgMkvB8YVPczcJRtnyTZpDopHDgYI/https%3A%2F%2Fwww.wikiwand.com%2Fen%2FPID_controller"
          target="_blank" rel="nofollow"
data-saferedirecturl="https://www.google.com/url?hl=en-US&q=https://www.wikiwand.com/en/PID_controller&source=gmail&ust=1661212316294000&usg=AOvVaw1q7lmzx9uyvlbs7uRQYYRt"
          moz-do-not-send="true">https://www.wikiwand.com/en/PID_controller</a></p>
      <p>thanks Karim!</p>
      <p>dpa</p>
      <p><br>
      </p>
      <div class="moz-cite-prefix">On 8/21/22 6:33 PM, Karim Virani via
        DPRGlist wrote:<br>
      </div>
      <blockquote type="cite"
cite="mid:CAKtnkiy91Wjd3Sa+Kgi2NMPuXaRkdegmvRiai28rRhB_bLy2zg@mail.gmail.com">
        <p style="background-color: #f4eaa5;color: #000000
          ;margin:5px;padding: 2px;text-align: left !important;
          align-content: center; display: block; border: 1px solid
          #000000; font-size: large; font-family: sans-serif;"><strong><em
              style="font-size: 11px;"> [EXTERNAL SENDER]</em></strong></p>
        <div dir="ltr"><a
href="https://secure-web.cisco.com/16B_Ej4RXqIrh14ouP6NBo6mR_R4YDFOjBp9ZRQrDroxM9mYDkppWw8HBFDb8IRHvKuMa4GHn3IinBk2kHgEIGLz_7vBowU3xS11L2MQ-mXk0KPmX--LlwRq8dZTdicAw8oaqBoX8f4FEaxCNITE5k8HzNRPefFM-mS8jIQ7jSJt9Q5eLOnRIzyv_Yhfwm5IzExp3pW33v1cOAEjkF_krlxS6ZoTx0o0s1Jha1jHr9XXjZJvfBu_tkdppwm_ahsAenUpKi7hDBTlcXfj3S5-cDKIYpPLgsyER3SJ1favI-Lo/https%3A%2F%2Fyoutu.be%2FWObG2LoSEwQ"
            moz-do-not-send="true">https://youtu.be/WObG2LoSEwQ</a><br>
          <div><br>
          </div>
          <div>Just wanted to share this very nice example of deliberate
            and experimental improvement of real world control of an
            inverted pendulum (like walking) in this case using a
            reaction wheel.<br>
          </div>
          <div><br>
          </div>
          <div>The number of configurations and variations tested is
            very cool.</div>
          <div><br>
          </div>
          <div>It also helps to clarify some concepts
            around dynamic balance. Like accelerometers don't really
            help because you are not actually chasing where up is, you
            are only chasing the orientation where the gyro tends to
            flip direction and change the slowest, and gyro drift
            doesn't really matter.  This is well demonstrated at 11:25.<br>
            <br>
            I'm tempted to say some things about their usage of Angle
            Fix Rate and whether they really got the optimal PID values,
            but I've had my fill of PID discussions for a while.</div>
          <div><br>
          </div>
          <div>I just appreciate the thoroughness of the approach they
            took and how well it was documented and communicated in the
            video edit.</div>
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