Inverse Kinematics: Part 2

I have since implemented the maths in my previous post. After a little debugging, I had the expected joint angles returned by the code, which could then be sent to Hexy. Necessarily it didn't all work perfectly first time...

The Python code is as follows:

Here's a video of Hexy trying to move its leg on a vertical path (e.g. constant x, stepped y):

Two problems with the motion as seen in this video:

  1. The motion is very jerky.
  2. The motion isn't purely vertical.

Apart from these two minor issues, it really was rather a success. So I went onto try a horizontal path:

To get a better understanding of the paths that the legs follow during these movements, I slowed the movement right down and took a few photos of the leg positions. These composite images are shown below.


So it appears that the vertical path really wasn't that, but the horizontal path was pretty close to correct. Given that the maths is of closed form the remaining sources of error is the physical implementation, e.g. the servos. Given that this is a low-cost hexapod kit, the servos are very low cost. This suggests that when you ask for x-degress you don't always get x-degrees.

A non-linear response from robot actuators is bad news for precise positioning. Hopefully some range of the positioners will be close enough to linear, or the servos will have a predictable response which can be measured and then compensated for. Although the complication here is that if you have to evaluate each servos' non-linear response, you'll spend all your time calibrating. This is a problem for another day.

Now to revisit that jerky motion. During the vertical IK movement, this effect is particularly strong. I'm told that these servos do not allow any modification to their closed-loop feedback parameters, so all one can do is pass a sensible set of demand positions at a sensible rate. The controller code (PoMoCo) run in python and sends commands via a serial link to the Servotor32 PCB in Hexy, which in turn sets the demand position on the individual servos.

Perhaps a future Servotor32 firmware might be able to handle paths rather than just absolute positions, which would make performing complex movements smoother, with less stress on the serial link between controller and Hexy... I must suggest this to the developers (I'm aware that I could do this myself as the whole thing's open source, but hey: collaboration and what-not).

3 thoughts on “Inverse Kinematics: Part 2

  1. I've integrated your code into my 'port' of PoMoCo to a different set of electronics:

    https://github.com/koenkooi/Adafruit-Raspberry-Pi-Python-Code/commits/beaglebone-hexapod

    It works as expected for a wide range of moves, but not for all.

    The problem I'm having is that the calculation doesn't take in account the boundaries of the servo, -90 and 90. I've added instrumentation to my setAngle() method:

    Angle smaller than -92: -100.031798066 for channel 8
    Angle smaller than -92: -96.5824257192 for channel 0
    Angle smaller than -92: -103.481170413 for channel 10
    Angle smaller than -92: -100.031798066 for channel 6
    Angle smaller than -92: -96.5824257192 for channel 2
    Angle smaller than -92: -93.1330533721 for channel 4
    Angle smaller than -92: -103.481170413 for channel 8
    Angle smaller than -92: -100.031798066 for channel 0
    Angle smaller than -92: -106.930542761 for channel 10
    Angle smaller than -92: -103.481170413 for channel 6
    Angle smaller than -92: -100.031798066 for channel 2
    Angle smaller than -92: -96.5824257192 for channel 4

    I haven't googled around to check if there's an easy solution for this, but I thought I'd let you know :)

    • That's very true, it doesn't deal with the real world at all. Thanks for highlighting this shortcoming.

      I'll try to include some more intelligent error checking in a later revision. NB it seems to me that whilst the servos will accept angles of \pm 90^{\circ}, during movements if you ask to start at these extreme angles the servo will "hang" during the beginning of this move. I'll try and document if I get the chance.

      • I haven't checked how far the servos will safely go, but robotalchemist mentioned that the metal gear servos will tend to stick at the extreme ends. Time to schedule some tests tomorrow :)

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