Due to the number of inquiries I get from my YouTube videos of Gizmo, I wanted to post here some of the frequently asked questions.

Q: I am an engineering student, and I’m trying to create a balancing robot for my (senior project, lab course, party butler, etc.). Please send me the list of parts you used and all of your code.

I’m glad you’re studying to be an engineer. It can be an extremely fun, challenging, and rewarding career. However, it’s important that you learn something before you take another single derivative. Using Google to find someone to give you all the answers to your project really cripples the purpose of doing the project in the first place. Sure, someone else may have already done what you’re trying to do. Sure, I learned from others and you will too. However, I firmly believe the best way you can help out yourself and your education is to step in there and try something. The first try will likely be wrong, and that’s why we as engineers do design analysis before we cut metal. With the prevalence of great tools like Matlab and Simulink (usually with Student versions available at a huge discount), as well as the low cost of cheap robotics parts, do a little math, run a few simulations, and then build something. You’ll learn something from each step. When you find yourself completely stuck and have specific questions to ask about why your solutions might not be working, then hit up the vast knowledge of the internet.

Posing questions to me before you have done any of this doesn’t help either of us. I’ve responded to hundreds of questions about Gizmo, but I generally only respond to those that are asking questions based on the results of whatever they’ve already tried. Please don’t ask me to do your project for you, and please don’t ask me to just give you my code. The code is extremely simple, the core of it is only a handful of lines. It’s all that you’ll learn getting to those few lines that is the real reward for doing the project in the first place.

Q: What motors did you use?

I was lucky enough to purchase them from a co-worker that had them on hand. They are 24V Pittman DC gear motors, 19.1:1 gearing ratio, with very high count encoders on the motors. The part number is GM9236S021. For the 6” wheels that I have, this allows the robot to “cruise” at about 1.3 m/s (intentionally close to human walking speed) and still have enough velocity to accelerate to overcome most disturbances. The actual speed itself isn’t important as long as the motors have enough torque to accelerate, and the peak speed is fast enough to overcome disturbances the robot might encounter.

Backlash in the gearbox IS extremely important. Cheap motors will have a lot of backlash. Backlash will directly impact how smoothly the robot balances and how far it will oscillate back and forth when standing still.

My general suggestions on motors are:

1) If you’re going to put your money anywhere, get good geared motors with high quality gearboxes.

2) Don’t drive directly off an output shaft that uses a bushing (or drive one with a tensioned belt).

3) Encoders, either on the motor, output shaft, or wheels are desirable, if not absolutely necessary.

Q: How did you choose the motors/sensors/wheels/etc?”

I generally chose what I had on hand or could purchase locally at low cost.

Wheels – The wheels are model airplane wheels from a hobby shop. I chose these wheels because they are very lightweight and thus have very low inertia. They were also the right size. They have fine traction on hard surfaces or carpet, but poor traction on gravel or sand.

Hubs – The hubs were custom turned a lathe using a large bolt as a starting piece. The hubs are less than optimal – the set screws that hold them to the shafts tend to work themselves out over time as the robot balances. This could be improved by using two set screws at an angle to each other, but I’ve just never gotten around to doing this.

Gyroscope – Analog Devices ADXRS150 single axis gyroscope. These are available already soldered to a board from a number of suppliers around the net. I used a custom board at the time. These days, just about any gyro will work, and I would probably use a digital variety. The rate range needs to be above about 50 degrees per second, but if you use more than about 300 degrees per second you’ll likely start loosing resolution that will be necessary for proper state estimation.

Accelerometers – Analog devices ADXL202 dual axis analog accelerometer. These are also readily available, although these days digital versions are probably easier to use. It can be done with one axis, but it’s more robust with two.

Microcontroller – STR710 microcontroller development board. I had one, so it was free. I also have access to a rather expensive toolchain for this part, but there are free options out there. The choice isn’t that important, there’s no reason you can’t make it work on a moderate 8-bit micro-controller. If you have no bias, the STM32 series of processors is really nice and you can get a very cheap development board for <20USD from ST as well as free development tools and software.

Q: Will you share you design or code with me?

This page attempts to share the design, but this page is also as far as I’ll go. I won’t share the actual code because it’s very straightforward and I feel like it’s creation is one of the more rewarding parts of the endeavor.

Q: Do you have a mathematical/matlab/simulink model of the pendulum that you will send me?

Yes, I have one somewhere. No, I won’t send it to you. There is a simple reason for this: it’s a classic design problem for engineering students, and you should take the time to go through the process yourself. However, if you’re not an engineering student, know that you don’t really need a complicated model to have a working robot. The control laws described below can be easily coded and tuned by hand through trial and error. The state space model is also readily available (see Google, or Ogata, Modern Control Engineering). I found Simulink to be the most helpful tool in the design process, and used it to validate the control laws I wanted to try before coding them.

Q: What control method did you use?

I’m fairly certain this problem can be solved via just about any reasonable control law. I know it’s been solved using PID, fuzzy logic, LRQ, State Space, analog controllers and likely many more. I used basic linear PID controllers and tuned them by hand.

I use two cascaded loops, one for velocity control, the output of which is a commanded angle which becomes the reference input of the angle control. Note that this is possible without a direct-coupling or “feedforward” term because the commanded angle is zero for a steady state velocity. Non-zero angles will always result in vehicle acceleration.

The inner loop uses as it’s feedback term the angle estimate and controls via a Proportional-Derivative controller. Since the angle derivative is the output of the gyroscope, we shouldn’t have noise issues related to taking a simple numerical derivative. If you’re starting out, do this part as soon as you have a working state estimator. You should be able to get this working and basically balancing without any other controls and the vehicle should basically balance, although it will probably wander with a steady state error and may slowly accelerate smoothly until it’s going to fast to fall over. This happens because the state estimate isn’t perfect and may not register the slow acceleration relative to the very small gyroscope rates.

The outer loop control is a Proportional-Integral controller which outputs a commanded angle into the inner loop controller. The velocity command comes from the (wireless) control link via a joystick. The integral term compensates for trying to balance at the wrong setpoint, since balancing at a non-zero angle will result in a constant acceleration and increasing velocity. In this way the robot can handle changes in the balance point due to loads.

There is also some dead-band compensation in the PWM controller which helps to reduce the non-linearity in the PWM due to shaft and rolling friction. This is required since there is some small PWM value which should be the minimum to turn the wheels under load, and that value will very likely be non-zero. I don’t have any backlash compensation, but I have good motors with low gearbox slop.

Q: How do you sense the angle? Kalman Filter, rangefinder?

The orientation of the robot is sensed through the use of a single axis Analog Devices (ADI) analog gyroscope (ADXRS150) and a dual axis ADI analog accelerometer. None of these sensors alone is sufficient to measure the tilt angle of the robot.

However, we can use the fact that the accelrometers, over the long term, can be used to estimate the average tilt (plus the high-frequency platform acceleration), while the gyroscope will measure the instantaneous tilt rate of the robot. Since the gyroscope isn’t perfect and has some amount of bias (it reads a value even when sitting still), simply integrating the gyroscope will result in an estimation of tilt that will “drift” over time.

If we use the arc-tangent function to derive an angle from the X (forward) and Z(down) accelerometers, we will have one estimate of our tilt angle. However, while this angle will be correct when the vehicle is still (or more precisely, not accelerating), it will be corrupted when the vehicle is accelerating (e.g the motors drive the wheels causing the robot to move). However, we can use this as one measurement of the vehicle tilt, one that we know may be inaccurate in the short term (meaning we can’t trust any one measurement).

Gyroscopes, as good as they have become recently, are also not perfect. When sitting perfectly still, they may measure a value which is non-zero. This is called bias, and is due to effects within the device as well as environmental effects such as temperature and (in poor gyroscopes) vibration. If we integrate the gyroscope measurement, we will integrate the bias along with the sensor measurement. This means that the integrated gyro value will drift over time. This can be seen by integrating a gyroscope which is stationary and observing the integrated value over a few minutes. The value will not stay at zero, but will instead have random angular walk plus constant drift due to bias.

The solution I use is a Kalman filter to optimally combine the accelerometer’s measurement of angle with the gyroscope’s measurement of angle. The nice thing about the Kalman filter is that in the process of crunching the numbers, one output is a measurement of the gyro bias, and this can be measured along with the robot’s angle.

However, a Kalman filter is actually overkill for this problem. The reason is that a Kalman filter actually changes how much it ‘trusts’ the accelerometers versus how much it ‘trusts’ the gyroscope over time. However, we don’t really need that ‘trust index’ to change over time in order to get a usable measurement of angle. The simple answer is a complimentary filter. Instead of explaining that here, check out this paper that does a nice job of explaining it.

I took my inverted pendulum balancing robot, added a camera and wireless transmitter, and let everyone around the office take a spin. The event was not without mishap, but it’s a lot of fun to watch people interact with the robot, and not so much fun when they try to block it’s view, or just don’t get out of it’s way. Or they kick volleyballs at it. That’s just mean.

I remember seeing the mock-up of this on my old dos-based astronomy program when I was in 5th grade. The computer program made it out to be the most important thing that would happen in the sky for hundreds of years, and let you ”watch” the transit from different viewing points around the earth. So what’s all the fuss about anyway?

Well, I’ll let you read the whole story on your own time, but the general idea is that these transits occur only twice in anyone’s lifetime, spaced 8 years apart. This morning’s transit is the first one that any living human has seen, so we’re all seeing something new together. The last recorded transit occured in the late 19th century, and the Brits sent people out all over the world to record the times of the ”contacts.” These times represent the times when the disk of Venus makes contact with the edges of the sun. However, just like during our own sunrise and sunset, the atmosphere of Venus will refract the sunlight slightly, creating a slight distortion between Venus and the sun’s edge that makes it very difficult to record the exact contact times. Had these times been recorded a bit more accurately in the 1800’s, the astronomers could have very precisely calculated the size of the solar system. However, the actual times recorded by the various watchers around the earth were off by 20-40 seconds, making the actual calculated size of the solar system incorrect. However, even with the problems, the Brits gave a pretty good try at deploying a global array of telescopes all pointed in the same direction in a time when communication was by horse courier and long distance travel was by sail.

Between episodes of 24 the game around here lately has been Communications Systems.  A midterm tomorrow that I almost have to get an A on has kept me away from much else, but I have done a little work on the website that I am working freelance on.  Another Solar Flare yesterday was an X20+, actually overloading the sensors that measure flares for a full 11 minutes.  Looks like that one will be the largest ever recorded.  If the flare had been pointing at Earth, and not off into space, we’d probably be seeing Aurora farther south than last week, but of course, if a flare of that magnitude hit us broadside, the Aurora would be the least of our worries.  Folks in commercial airliners at high latitudes would be getting radiation doses 100 times that of a normal X-Ray.  Not fun stuff. 

It was a busy weekend, and has been a busy week so far.  Over the weekend, we finished up CQ World Wide with 1112 contacts, up 103 over last year, even amidst some fairly strong solar flares that caused radio blackouts for a few hours.  Tuesday morning we saw the third-strongest flare on record, an X17, which caused aurora as far south as Houston Tuesday night.  So last night, I took off north to see what I could see.  It was well worth it, and I got a fairly good show.  Being about 10 miles from nowhere, OK without any city lights to be seen helps.  It was also a nice drive, 250 miles and all after sunset.  Made it back here about 2, after being followed for awhile by some hick kids trying to mess with me.  It was an interesting evening.

Upcoming highlights:  Maybe more aurora tonight as a result of an X11 flare yesterday afternoon.  If the Kp index gets up to 8 or 9 there will be a pretty good chance.  Right now its back down to 5.  See spaceweather.com for more about aurora forecasting.

This is a pretty interesting story about a paper that I definitely agree with, although I would like to see some of the mathematics behind it. The jist is that time doesn’t exist as a series of moments, but as a continuous flow; in this case it becomes paradoxial and cannot exist at all. For all the theoretical physics buffs out there.