Do Robots get the “Twisties”?

In watching some of the Olympic events and the Paralympic events, you can’t help but be amazed at the human body.  There has been a lot of discussion about Simone Biles experiencing the “twisties” and how that  danger puts an athlete in danger..  While my own experience as a gymnast didn’t get much past cartwheels, I am acutely aware of what this phenomena can do.  Humans utilize proprioception, which is the awareness of the position of the body, to control our bodies.  When that awareness is altered, we can have trouble with a host of things such as reaching, balance, and walking (not to mention executing multiple aerial flips).  Robots also have a concept of proprioception through sensors and calculations.  Exoskeletons aren’t doing backflips (though you can see some impressive gymnastics from Boston Dynamics’ Atlas here: https://www.bostondynamics.com/atlas), but accuracy and control of the motion they are executing is still important.  When I design the gait trajectory of an exoskeleton, the placement of the foot in space throughout the gait is very important.  If it is too high and the human cannot match the awkward high-step gait; too low and the human will trip when their foot does not clear the ground.   Toe clearance can be as low as about ½”, so there is not a lot of room for mistakes.

If we want to know where the exo’s toe is, there are a number of ways to do this.  One is to directly measure the distance from the ground.  To do this while walking, you need something like a laser range sensor or sonar sensor.  These can be difficult to ensure that your measurements are accurate on a variety of surfaces. 

You can also use IMUs (inertial measurement units).  These utilize accelerometers and gyroscopes to calculate orientation and acceleration and these measurements can be integrated to determine position.  These sensors are subject to drift, though there is extensive research on how to mitigate this problem which I will not cover here (but it’s worth a Google search if you’re interested!).

One of the most common ways to measure toe location uses forward kinematics.  Forward kinematics takes the known position of one link of an object and calculates the end position using the known lengths and angles of each.  

Take for example, a 2-link robot arm.  The base is fixed on the ground, so we’ll call that (0,0).   Each of the links have an angle and a length associated with them.  If we want to calculate the position of the end of the robot, we use trigonometry to calculate the X and Y component of each link and then add them together.

A 2-link arm

    \[x = l_1cos(\theta_1) + l_2cos(\theta_1+\theta_2)\]

    \[y = l_1sin(\theta_1) + l_2sin(\theta_1 + \theta_2)\]

But what if the robot has the “twisties” and the measurement of the first angle is off by just a little bit?  Maybe the sensor calibration wasn’t quite right or the mechanism got loose and slipped a bit or the beam isn’t perfectly stiff and so it sags a bit through the length?  Let’s a assume an error of just 5°.  It may not look like much to our eye, but it can mean the difference between successfully picking up an object or colliding with it.

Let’s put some numbers in just to see what difference a mere 5 degrees makes. Let:

    \[l_1 = 12 in\]

    \[l_2 = 10 in\]

    \[\theta_1 = 30^{\circ} \]

    \[\theta_2 = 15^{\circ} \]

In our original calculation, y = 13.07 inches.

However, if sensor is off by 5°, we have to adjust the measured angles…

    \[\theta_1 = 25^{\circ}\]

    \[\theta_2 = 15^{\circ}\]

Now y = 11.5 in.

When we look at the kinematics of a body, we usually start from a foot that we know is on the ground and work our way up that leg and down the other to determine the foot position.  Over this many links, small errors in our perception can cause big problems.  5° is as simple as not measuring the flexibility of a link or accumulated small errors due to the inaccuracy of sensors.  Given this, I am constantly amazed by our bodies and our ability to do things as seemingly simple as walk across a room to as complex as flips on the balance beam.  We engineers have quite a challenge ahead of us!

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