nBot Balancing Robot
David P. Anderson

nBot: 27 January 2003

nBot6 right rear
Update: 14 Sept 2013: nBot Rev 6.0.

nBot completely rebuilt as Version 6.0 after the disastrous LiPo Fire of 2012.
nBot sensors
Update: 14 June 2012: nBot finally has some avoidance and navigation sensors, two PING))) ultrasonic sonar sensors, and five SHARP IR distance detectors, in addition to the MicroStrain FAS-G IMU.

Here is a video of nBot doing perimeter following (72M mpeg) in the basement of the building where I work.

I've been working on a two-wheeled balancing robot, nBot .

This robot was featured as NASA's Cool Robot of the Week for 19 May 2003. Thereafter Scientific American's online website, SCI/Tech Web Awards, honored the NASA page as one of the top 10 engineering and technical web sites for 2003, referencing nBot in its text. nBot is also featured in a new O'Reilly book spun off from Make Magazine in 2006, called The Makers.

The basic idea for a two-wheeled dynamically balancing robot is pretty simple: drive the wheels in the direction that the upper part of the robot is falling. If the wheels can be driven in such a way as to stay under the robot's center of gravity, the robot remains balanced. In practice this requires two feedback sensors: a tilt or angle sensor to measure the tilt of the robot with respect to gravity, and wheel encoders to measure the position of the base of the robot. Four terms are sufficient to define the motion and position of this "inverted pendulum" and thereby balance the robot. These are 1) the tilt angle and 2) its first derivative, the angle velocity, and 3) the platform position and 4) its first derivative, the platform velocity. These four measurements are summed and fed back to the platform as a motor voltage, which is proportional to torque, to balance and drive the robot. Here is a diagram of the algoithm with some code and implementation notes.

nBot trucks The robot hardware was built in my home machine shop. Here as some exploded views of the motor platform and drive components, as well as the castering tailwheel, now removed, which was used for testing and calibrating the motors and encoders before nBot was able to balance on two wheels. The robot uses the HC11 robot controller developed for the M.I.T. 6.270 Robotics Course, the same robot controller used on the LegoBot and SR04.

Polebot Rev 1. This began as an experiment to learn to control an inverted pendulum. I began with a three wheeled robot with a ball-bearing pivot used to attach a 3 foot wooden pole topped with an orange Nerf Ball. The pivot has a low-friction 5k potentiometer used for measuring the tilt angle of the pole. I moved the battery pack over the rear wheel to give more stability. Here is an mpeg movie (10 Meg) of the robot balancing the pole in my office. Here (3.3 Meg) is a shorter version, and here (3.7) is another.

Pole bot nBot

Rev 2. After learning to balance the pole, the robot was re-built as a two-wheel version, with the battery mounted directly above the wheels. The ball-bearing pivot was attached to the bottom of the robot with a short aluminium feeler touching the floor. In this way the robot can sense it's angle to the floor and, assuming the floor is level, to gravity as well. The aluminium feeler has a teflon pad on the end to help it ride over cracks and joints in the floor.

nBot with feeler Rev 3. For the third version a third deck was added and the batteries moved to the top deck. This allows the robot to generate more torque without having to tilt over as far. The side view of the platform shows the battery and user interface on the top deck, the microcontroller and h-bridge on the middle deck, and the motors and axles on the lowest deck.

nBot rev 3. The ball-bearing pivot and angle sensor were replaced by a piezo-electric gyroscope and ADXL202 accelerometer mounted just above the motor deck. Those sensors were eventually replaced by a commerical inclinometer, the FAS-G from MicroStrain, also consisting of an ADXL202 accelerometer and a rate gyro, similar to the boards and kits available from rotomotion. This rear view shows the complete stack.

nBot with IMU Rev 4. New base and motors for nBot, using the Pittman GM8712 DC gearhead motors with home-brew shaft encoders. These are powered by 18 NiMH 1800 mAh rechargeable AA cells, at about 24 volts. They have a lot more torque at very low rpm than the previous 12 volt motors, as well as higher maximum rpm. The result is that the robot is more stable and can respond more quickly.

nBot rev 4 Additional detail pictures of the Rev4 modifications are available here.


The gyroscope and accelerometer are combined with complementary filters to provide an inertial reference sensor. The ADXL202 accelerometer provides accurate static tilt information, when the robot is not accelerating. The gyroscope can be integrated to provide accurate dynamic tilt information, but the integration tends to drift over time. Combining the two sensors provides a robust inertial measurement. The FAS-G IMU implements a "Weiner" filter to combine the two sensors into a single measurement. The sourceforge autopilot project. and the boards available from rotomotion.com use a "Kalman" filter. Some really good information on inertial measurement units is available from the sourceforge autopilot project.

nBot being shoved Here is a video of the robot balancing. (2.2M .mpg), (2.3M .wmv), (1.4M .rm) It shows nBot being shoved and regaining its balance, and being pushed off center and resisting.

Steering. If a constant offset voltage is added to one wheel and subtracted from the other wheel, the robot balance is not altered. In this way the robot can be steered while maintaining its balance.

nBot spins Here is a video (2.1M .mpg), (1M .wmv), (280K .rm). of the robot spinning in place while balancing. I'm using a knob on the robot to add a voltage offset to one motor and subtract it from the other.


If a small offset is added to the tilt angle the robot must remain in motion to stay balanced. This combined with a voltage offset added to one wheel and subtracted from the other will cause the robot to drive in a circle.

nBot circling This dark mpeg (2.9 Meg) shows the robot circling smoothly on a tile floor, until it runs into my foot. Because of the PWM wheel offsets, it pivots away from the collsion and continues; sort of a built in "bumper" behavior without an actual physical bumper. (It's really too dark to see what's going on. I'll try to make a better one soon.)

nBot circles Here's a better video (5.2M .mpg), (2.7M .wmv), (1.2M .rm), of the robot circling smoothly and bouncing off my leg, the walls and the furniture.

nBot on gravel nbot on gravel (1.3 Meg) shows the robot circling on a gravel driverway. You can see the platform rock fore and aft as it tries to get enough torque to climb over rocks and maintain its balance on the uneven surface.


Like my other robots (except the camera car), this is an autonomous robot. That is, it is not radio controlled by a human and there is no R/C link. Instead it has an onboard computer (MIT 6.270) that makes all of its behavior decisions, in addition to balancing the robot.

In the following mpeg videos, the robot is running a simple navigation program that uses wheel odometry to go forward 24 feet (or some arbitrary distance) and turn around and come back, looping endlessly.

nBot parking lot Here is a video (5.0M .mpg), (2.5M .wmv), (1.1M .rm), of the robot running that program in a parking lot.

Most of the following videos are of the robot running this odometry program in different environments, indoors and outdoors, etc.

nBot on the driveway Here is a video (7.8M .mpg), (3.4M .wmv), (1.4M .rm), of the robot running the same program on an inclined driveway. Note the "pirouette" required to keep its balance while turning around on the incline. The cicadas singing in nearby trees provide the soundtrack for a hot Texas afternoon.

nBot outdoors For outdoors perfomance in general, the robot's balance seems to be unaffected by uneven and irregular surfaces, as this outdoor mpeg (2.7 Meg) demonstrates.

nBot at Ilse Dubois Here is the Rev4 robot running on uneven and rocky ground at Ilse DuBois State Park: (4.4M .mpg), (2.3M .wmv), (1.0M .rm)

I think the two-wheel balancing robot will turn out to be more stable than my other three-wheeled robots. Here is an mpeg movie (3.3 Meg) of the balancing robot going up and down a loading ramp. Notice how it leans backward as it goes down the ramp, and forward is it goes back up.

Notice also that it takes several trys to overcome the bump at the start of the ramp. The robot initially bounces away, leaning further forward to get enough torque to climb over the bump and start up the ramp. nBot on a ramp At the top of the ramp the robot touches the left wall. At this stage in development it has no sensors to detect collisions. The balance algorithm bounces it along the wall until it is finally free at the corner. In its final version it will have sensors and behaviors to avoid running into things, but note that the robot does not lose its balance and fall over when it does collide.

nBot on a ramp Here is a video (5.2 Meg) that shows what happens when you try to run down-hill too fast without wearing your helmet. In order to slow down the robot must first speed up, to get the wheels underneath and eventually out ahead of the center of gravity. If the robot is going too fast, it is unable to speed up, and hence unable to slow down. Also includes some successful attempts.

So I started the robot at the bottom of the ramp further away from the wall, hoping that the odometery errors would be small enough that the 'bot could made several runs up and down. Instead, it climbed the ramp smoothly and then fell off the side (2.8 Meg mpeg) coming back down. Ouch! Time to think about installing those sensors...


nBot bounce Update Rev 4: The two-wheel robot is indeed able to handle much more agressive slopes than my other robots. Here (3.6 Mb mpeg) , (800K .wmv) , (400K .rm) , is the Rev 4 robot descending a very steep uneven grassy slope on the campus of UNT. Note the bounce and recovery as it hits the concrete at the bottom. Here (3.2 Mb mpeg) is another, with a more graceful dismount. This one (2.7 Mb mpeg) got going too fast and took a tumble.

nBot first step nBot's first step. I think it's possible that the two-wheel balancing robot may eventually be able to descend stairs, even if it can never go up them. Here (1.5 Meg) is nBot successfully negotiating a step. One small step for a robot, one giant leap... Here (1.6 Meg) is another attempt.

nBot on the steps Here is an mpeg (5.3 M) of the robot obliquely descending a set of canted stairs. Leaning left and right does not affect the robot's balance, unless the tilt angle is great enough for the center of gravity to be outside of the base. Watch that last step!

nBot on the path Here is a video (5.9M .mpg), (3.0M .wmv), (1.2M .rm), of the robot set to go in a straight line cross country, traversing the campus of UNT and more-or-less following a footpath.

nBot in the courtyard This mpeg (5.3 M) is of the robot doing a 24 foot looping pattern in a sloping couryard over a drain and some broken concrete.

nBot at Ptarmigan MeadowRocky Mountains: Here is video (7.6M .mpg) (3.6M .wmv) (2.1M .rm) of the robot navigating down a steep 4wheel drive access road in Ptarmigan Meadows in the Colorado Rocky Mountains.

nBot at Ptarmigan Meadow Here is another video (2.4M .mpg) of the same descent from another angle which may give a better sense of the steepness of the slope.

nBot limit of the envelope Limit of the Envelope!.

Here is a video (1.4M .mpg) (730K .wmv) (340K .rm) of the robot attempting to to descend a gravel road that is too steep/rough for it to handle. That's my mother in the background talking encouragingly to the robot like she does to all small creatures.

nBot in SeattlenBot in Seattle

A tour of the Seattle Fairgrounds with nBot during the Seattle Robotics Society Robothon 2003.

Other two-wheel inverted pendulum balancing robots:

Here is Joe le pendule, a radio-controlled 2 wheel robot that seems to work very well. Included are some cool mpeg movies and documentation. They have a pdf document in English which describes their project. They seem to be getting all their sensor data from only 2 wheel encoders and a rate gyro. Here is a local copy I've downloaded.

Steve Hassenplug has built a two-wheeled balancing robot from Legos he calls LegWay that uses IR proximity detectors to balance and also do line following. Pretty cool.

Ted Larson is working on a two-wheel balancer with Bob Allen. The web page includes some videos of their robot in action (always the best!) as well as a link to their recent appearance on TechTV.

Bram Stolk is working on a two-wheel robot using the sourceforge autopilot IMU sensor.

BaliBot is a two-wheel inverted pendulum robot built by Bill and Mark Sherman.

Matt Cross is working on a two-wheeled firefighting robot for the Trinty College Firefighting Contest. Matt uses the 68332 Mini Robo Minds controller board running the RTEMS realtime multitasking operating system.

Larry Barello of the Seattle Robotics Society has done some excellent work on GyroBot, a gyroscopically stablized robot.

Duane Gustavus is working on a balancing robot with the weight distribuition arranged so that it can drive on three wheels or tip forward and balance on two. Very cool. Duane uses the MRM board running RTEMS

Dan Piponi has a clever balancing robot Equibot that uses a Sharp infrared sensor to measure the distance to the floor and uses that information to deduce tilt angle.

Juan Pablo Angulo has developed a similar balancing robot using IR to measure floor angle. There is a nice writeup of his work on the Parallax website.

Ron Grant of the Dallas Personal Robotics Group is working on a nifty balancing robot. He is currently using a "floor feeler" to determine tilt angle, a potentiometer driven by a lever and ping pong ball that rests on the floor. Ron uses a home-brew CPU board with an ATMEL controller and on-board H-bridge. [Ron, where did your site go?]

Jack Wu and Jim Bal at Carnegie Mellon University have constructed BBot as a semester design project for the Fall of 2003, "a self-balancing two-wheeled robot." Based on their 68 Meg mpeg video, it doesn't appear to actually be balancing yet... (Note: link no longer working as of 07 July 04. I guess school's out)

Lee Magnusson at MIT is working on a self-balancing unicycle. His page has links to some videos and a pdf report. From the videos it looks like the human rider still has to do the side-to-side balancing. Cool nonetheless! (This link also not working as of 07 July 04. The college sites must go down at the end of the semester.)

The Technology Department of the Bolton School in Manchester, England, has built this nifty single wheel cycling robot which they call the Loony-Cycle. I believe this design has to stay in motion in order to maintain balance. It is steered with propellers that are arranged at 90 degrees to the direction of travel.

Jormungand.net has a very nice two-wheel balancing robot design called crunch along with a few other robot projects.

Francisco Lobo de la Garza has an on-going development project for a two-wheel balancing robot named Spider. Web page includes photos, video, and some software.

Roderick Lee Mann is working on ichibot, a two wheel balancer inspired, I believe, by the nBot project. Way to go Roderick!

Sanghyuk Park, a recent graduate of M.I.T., has a fascinating group of robot control/navigation/guidance projects including a two-wheel balancing robot named Balance-bot I. Sanghyuk writes that he was "deeply impressed" with the nBot website, which pleases me greatly! Be sure and check out his unmanned air vehicles projects as well. Very intriquing. [But, as of 04 Feb 2005, Mr. Park and all his nifty robots seemed to have vanished from the Internet.]

Four members of the The University of West Florida's Institute for Human and Machine Cognition have built a self-described Joe le Pendule look-alike as a testing platform for autonomous agent software. Real-time Linux and wireless ehternet! Some video and lots of links. Their robot and a several others (including nBot) have been gathered together as Joe's Relatives on the Joe le Pendule website.

Joris Maervoet and friends have built a Balancing LEGO Robot using Java and standard LEGO parts, including the LEGO light sensor, that can balance while standing on a mirror. Very nice web page: graphics, charts, graphs, and code.

Alistair Sutherland and Thomas Bräunl are working on a couple of two wheel balancing robots they call ballybots based around the excellent eyebot robot controller.

Edwin Dertien has among his many other robots a design for a LEGO two-wheel balancer using a home-brew light sensor.

Blind Man is a fuzzy logic-based two wheel balancer that appears to be a class project of the University of Alberta. The robot uses a floor feeler to sense it's angle, like a blind man's cane, hence the name.

uBot from UMASS, Amherst, by Patrick Deegan and Robert Grupen, appears to be an R/C controlled 2-wheel balancing platform using a Rotomotion IMU and custom software. Nice site with descriptions and mpeg videos. Check out uBot standing up on its own from leaning on its kick stand in the 3rd movie. Update: 03 March 2007: Patrick sends a new web page with more work completed on several new two-wheel balancers including some with grippers and manipulators. Includes videos of various lifting and pushing tasks while balancing.

Ballbot from the Microdynamic Systems Laboratory at Carnegie Mellon University balances on a single wheel, actually a ball. Press release includes links to videos of the robot recovering from a disturbance and navigating across a room.

BBot, a balancing robot by Brody Radford, uses ADXL202 accelerometers and ENC-03J gyroscopes from Murata to create a nice platform, inspired by nBot and Joe le Pendule. Nice work.

Nuts_and_volts Magazine for November and December 2006 have a two-part Personal Robotics article by Phil Davis and Brandon Heller, titled "Building a Balancing Bot on a Budget." Their design is based around a SparkFun 5DOF IMU and modified R/C servos, and the article includes a link to their Kalman filter and balancing code on the Nuts_and_Volts ftp server.

Brian Kuschak has a very nicely implemented home-brew balancing robot based around an ARM7 processor and custom inertial measurement sensor. Lots of good information and details, very nice webpage.

Dirk Uffmann from Munich, Germany, has developed a two-wheel balancing robot based on fischertechnik components, named ARTIST, with home-brew electonics and tilt sensor. Nice web-page with lots of links and videos.

Frits van Evert and colleagues at the Wageningen University and Research Center in the Netherlands have built a two-wheel balancing "field robot" to compete in the field robot competition in June of 2007. Their web site has photos and videos of the robot in action navigating autonomously through rows of corn, and they have sent along a very nice note thanking nbot for "inspiration and lots of practical information." Great job!

Kazuo Yamafuji, Professor Emeritus at the University of Electro-Communications in Tokyo, built the first two-wheel inverted pendulum robot in 1986, according to this article in the Japan Times.

Here are some related links:

The source forge autopilot group is working on a home-brew three axis inertial measurement unit for an autonomous helicopter. They have a single axis version suitable for a two-wheel balancing robot.

Carnegie Mellon University has some online documentation and matlab code for balancing an inverted pendulum.

Some researchers at the Max Planck Institute in Germany can balance three inverted pendulums, one on top of another. Amazing!

Fuzzy logic tutorials seem to like inverted pendulum problems. Here's one for a two stage inverted pendulum and the fuzzy code used to solve it.

Here is an appnote (pdf) from Microchip on using a pic chip to balance an inverted pendulum.

Dean Kamen's Segway Human Transport Vehicle patent application describes the algorithm he is using for a of similar inverted pendulum type of platform.

Trevor Blackwell has built a home-brew balancing scooter out of the Rotomotion single axis IMU and other off-the-shelf-parts. Nice webpage with pictures and videos. He has also built an very nice unicycle version of the inverted pendulum.

The UBC Electric Bike Club have designed and built a very cool senior project, a two-wheel balancing skateboard using sonar and IR sensors to measure angle. Website includes text, illustrations, photos, and videos of the platform in action.

This company has a nice pdf document on building a two wheel balancing robot like Steve's "Legway" using LEGO parts and a couple of photo reflector sensors for measuring the angle to the floor.

These people from a company called "Balbots" offer a kit for a photo-reflective type balancer. Looks pretty nifty, lots of good documentation and a nice design.

Ted Larson has also developed some nice balancing robot components listed on his CTG robotics website. I don't see any prices listed yet. He show a very nice looking 3-axis inertial measurement unit, somewhat like the ones offered by Rotomotion.

Stumpy is an inverted pendulum walker, or more accurately an inverted pendulum hopper.

The 1932 Dynasphere was a two-person single wheel vehicle that could cruise at speeds of 30 mph. Ok, it's not really the same thing as a two-wheel dynamic balancer, but it's a very cool picture! I especially like the 1930's geek driver, complete with suit and tie.

nBot and Segway nBot and friend nBot and a friend hanging out together in the hallway of the SMU Heroy Building.

nBot tries to convince the Segway to go for a spin without its clumsy human occupant (2M mpeg).

Back to my robots homepage.

last update: 14 Sep 2013 dpa
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