Inverse Pendulum Balancing Robot

Stick balancing

IPBAR side view

The small cart will move forward and backwards in order to balance the stick with the weight on the end.  I am using this to eventually being able to create a similar balancing robot with only two wheels placed side by side.
The Angle is sensed with this encoder attached to the long stick.
I used a pid controller with the angle as the input and the the motor controller PWM value as the output.  The microcontroller board is an Arduino (see arduino.cc).  I made the motor controller myself and used a wheel/motor assembly based around this.

Currently, it is able to balance itself with some assistance via a dial.

I still need to improve my control algorithm.


The controller is basically a PID based on the angle of the stick.  I initially used the following:

PWM_{out} = k_{1}e+k_2\int_{0}^{t}e\,dt+k_3\frac{d e}{d t}

where e is the angle error (angle from vertical).

However, I realized that this didn’t work. Since the I term didn’t seem to do anything, I removed it and added a manually adjusted bias to the angle:

PWM_{out} = k_{1}(e-b)+k_2\frac{d e}{d t}

where b is the manually adjusted angle bias.  By constantly adjusting the angle bias, I was able to balance the stick as is seen below.

Next, I will add the wheel encoders to the control equation. Using this, I might be able to get it to balance unassisted.

Source Code

A subversion repository with my code for some test programs, the microcontroller firmware, and a simulator is available here:  http://keegan.webhop.net/svn/tipsybot/.  The microcontroller firmware uses Arduino and the arduino IDE, while the programs that run on the computer use Processing which is Java with additional libraries and some preprocessing and a minimalistic IDE.


The simulator itself is available as a java applet here: http://keegan.webhop.net/applets/tipsybot_e_sim/

The mathematical model is based on an explanation here.


First successful assisted balance:


IPBAR side view



Back side of the bx housing the dials and power supply.

Serial data stream waveform with annotations

A supplies power and houses some dials for tuning the pid.

Encoder waveform with annotations.

Here it is with the LCD mounted. I later changed the card stock to plastic.

The general setup


2 Responses to IPBAR

  1. Mark Paynter says:


    That’s so cool. I’m glad you got your robot working. Can you post videos?

    If it’s not balancing perfectly, I can think of a few possible reasons. You said that you were using an encoder to sense the angle. If the encoder is low resolution, that could be an issue. You could try using a low friction potentiometer and reading with the ADC. Another possible issue could be gearbox backlash. That said, yours works, and mine doesn’t. Hope to see it in person soon.



    • Keegan says:

      Although it moves in the right direction when you bump the stick, it doesn’t get close to actually balancing it successfully. I have the encoder set to 4096 steps per revolution which is more than what I’d get out of a potentiometer.

      One problem might be that I have trouble setting the exact center point exactly so I’m going to add a dial to adjust that. I also might be able to add a little bit more voltage to the motor power supply because of the voltage drop associated with the motor controller.

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