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{{short description|Mobile robot design}}
[[File:Ballbot CMU 2008.jpg|thumb|The CMU Ballbot,<ref name="CMU Ballbot">[http://www.msl.ri.cmu.edu/projects/ballbot/ CMU Ballbot]</ref> the first successful ballbot, built by Prof. Ralph Hollis<ref>[https://www.cs.cmu.edu/afs/cs/user/rhollis/www/home.html Prof. Ralph Hollis]</ref> (not in picture) at [[Carnegie Mellon University]], USA in 2005]]
[[File:BallIP 2008.jpg|thumb|The BallIP, developed by Prof. Masaaki Kumagai<ref name="Kumagai">[http://www.mech.tohoku-gakuin.ac.jp/rde/members/kumagai/index_e.html Prof. Masaaki Kumagai]</ref> at [[Tohoku Gakuin University]], Japan in 2008]]
[[Image:Ballbot Rezero 2010.jpg|thumb|The Rezero<ref name="Rezero1">{{Cite web|url=https://spectrum.ieee.org/project-rezero-ball-balancing-elegance |author=Markus Waibel|title=Project Rezero: Ball Balancing Robot With Style |website=[[IEEE]]|date=June 2010}}</ref> developed at [[ETH Zurich]], Switzerland in 2010]]
[[Image:Kugle ballbot.jpg|thumb|The Kugle ballbot<ref name="Kugle1">[https://github.com/mindthomas/kugle-matlab Kugle - Modelling and Control of a Ball-balancing]</ref> developed at Aalborg University, Denmark in 2019]]
[[File:Ballbot CMU Arms 2011.jpg|thumb|The CMU Ballbot<ref name="CMU Ballbot" /> with a pair of 2-[[degrees of freedom (mechanics)|DOF]] arms (2011). It is the first – and currently the only – ballbot with arms.]]
A ball balancing robot also known as a '''ballbot''' is a dynamically-stable [[mobile robot]] designed to balance on a single spherical wheel (''i.e.'', a ball). Through its single contact point with the ground, a ballbot is omnidirectional and thus exceptionally agile, maneuverable and organic in motion compared to other ground vehicles. Its ''dynamic stability'' enables improved navigability in narrow, crowded and dynamic environments. The ballbot works on the same principle as that of an [[inverted pendulum]].
==History==
The first successful ballbot was developed in 2005<ref name="Lauwers05">{{cite web|url=http://www.msl.ri.cmu.edu/publications/pdfs/isrr05.pdf |title=One is Enough! |author=Tom Lauwers |author2=George Kantor|author3=Ralph Hollis |date=October 2005 |work=12th International Symposium on Robotics Research }}</ref><ref name="Lauwers06">{{cite web|url=http://www.msl.ri.cmu.edu/publications/pdfs/ballbot_ICRA06_web.pdf |title=A Dynamically Stable Single-Wheeled Mobile Robot with Inverse Mouse-Ball Drive |author=Tom Lauwers |author2=George Kantor|author3=Ralph Hollis |date=May 2006 |work=IEEE International Conference on Robotics and Automation |pages=2884–2889 }}</ref><ref name="Hollis06">{{cite web|url=http://www.scientificamerican.com/article.cfm?id=ballbots |title=Ballbots |author=Ralph Hollis |date=October 2006 |work=Scientific American |pages=72–78 }}</ref> by Prof. Ralph Hollis of the Robotics Institute at [[Carnegie Mellon University]] (CMU), Pittsburgh, USA and it was patented in 2010.<ref name="BallbotPatent">{{cite web|url=https://patents.google.com/patent/US7847504 |title=Dynamic balancing mobile robot |author=Ralph Hollis |date=Dec 7, 2010 |work=US Patent #7847504 }}</ref> The  CMU Ballbot<ref name="Hollis06" /><ref name="DailyPlanet">{{cite web|url=https://www.youtube.com/watch?v=aq9G5Yg09Qw |title=CMU Ballbot on Discovery Channel's Daily Planet |website=[[YouTube]] |date=June 2007 |type=VIDEO}}</ref><ref name="Roborama">{{cite web|url=https://www.youtube.com/watch?v=5le0tQBrGJU  |archive-url=https://ghostarchive.org/varchive/youtube/20211219/5le0tQBrGJU |archive-date=2021-12-19 |url-status=live|title=CMU Ballbot on ROBORAMA |website=[[YouTube]] |date=August 2006 |type=VIDEO}}{{cbignore}}</ref><ref name="GadgetShow">{{cite web|url=https://www.youtube.com/watch?v=aq9G5Yg09Qw |title=CMU Ballbot on UK's Gadget Show |website=[[YouTube]] |date=January 2010 |type=VIDEO }}</ref> is built to be of human size, both in height and footprint. Prof. Hollis and his group at CMU demonstrated that the ballbot can be robust to disturbances including kicks and shoves, and can also handle collisions with furniture and walls.<ref name="UmaICRA09a">{{cite web|url=http://www.msl.ri.cmu.edu/publications/pdfs/BallbotTransition_ICRA._2009.pdf |title=State Transition, Balancing, Station Keeping and Yaw Control for a Dynamically Stable Single Spherical Wheel Mobile Robot |author=Umashankar Nagarajan |author2=Anish Mampetta|author3=George Kantor|author4=Ralph Hollis |date=May 2009 |work=IEEE International Conference on Robotics and Automation |location=Kobe, Japan |pages=998–1003 }}</ref><ref name="UmaICRA09b">{{cite web|url=http://www.msl.ri.cmu.edu/publications/pdfs/Ballbot_TrajectoryPlanning_ICRA_2009.pdf |title=Trajectory Planning and Control of a Dynamically Stable Single Spherical Wheel Mobile Robot |author=Umashankar Nagarajan |author2=George Kantor|author3=Ralph Hollis |date=May 2009 |work=IEEE International Conference on Robotics and Automation |location=Kobe, Japan |pages=3743–3748 }}</ref><ref name="BallbotIntroVideo">{{cite web|url=https://www.youtube.com/watch?v=39zeZwlVaN0  |archive-url=https://ghostarchive.org/varchive/youtube/20211219/39zeZwlVaN0 |archive-date=2021-12-19 |url-status=live|title=CMU Ballbot: Overview |website=[[YouTube]] |date=December 2008 |type=VIDEO }}{{cbignore}}</ref>
They showed that a variety of interesting human-robot physical interaction behaviors can be developed with the ballbot,<ref name="UmaHRI09">{{cite web|url=http://www.msl.ri.cmu.edu/publications/pdfs/BallbotPhysicalInteraction_HRI_2009.pdf |title=Human-Robot Physical Interaction with Dynamically Stable Mobile Robots |author=Umashankar Nagarajan |author2=George Kantor|author3=Ralph Hollis |date=March 2009 |work=IEEE International Conference on Robotics and Automation |location=San Diego, USA |pages=3743–3748 }}</ref><ref name="BallbotHRIVideo">{{cite web|url=https://www.youtube.com/watch?v=miZ_ebjoiFY  |archive-url=https://ghostarchive.org/varchive/youtube/20211219/miZ_ebjoiFY |archive-date=2021-12-19 |url-status=live|title=CMU Ballbot: Human-Robot Physical Interaction |website=[[YouTube]] |date=December 2008 |type=VIDEO }}{{cbignore}}</ref> and presented planning and control algorithms to achieve fast, dynamic and graceful motions using the ballbot.<ref name="UmaRSS10">{{cite web|url=http://www.roboticsproceedings.org/rss06/p31.pdf |title=Dynamic Constraint-based Optimal Shape Trajectory Planner for Shape-Accelerated Underactuated Balancing Systems |author=Umashankar Nagarajan |date=June 2010 |work=Robotics: Science and Systems |location=Zaragoza, Spain }}</ref><ref name="BallbotFast1">{{cite web|url=https://www.youtube.com/watch?v=Wd03f_6utA8  |archive-url=https://ghostarchive.org/varchive/youtube/20211219/Wd03f_6utA8 |archive-date=2021-12-19 |url-status=live|title=CMU Ballbot: Fast Motions |website=[[YouTube]] |date=June 2010 |type=VIDEO }}{{cbignore}}</ref><ref name="BallbotFast2">{{cite web|url=https://www.youtube.com/watch?v=VWAF3jTZLgw  |archive-url=https://ghostarchive.org/varchive/youtube/20211219/VWAF3jTZLgw |archive-date=2021-12-19 |url-status=live|title=CMU Ballbot: Fast, Graceful Maneuvers |website=[[YouTube]] |date=December 2010 |type=VIDEO }}{{cbignore}}</ref> They also demonstrated the ballbot's capability to autonomously navigate human environments to achieve point-point and surveillance tasks.<ref name="UmaCDC10">{{cite web|url=https://www.cs.cmu.edu/~unagaraj/Ballbot_HybridControl_CDC.pdf |title=Hybrid Control for Navigation of Shape-Accelerated Underactuated Balancing Systems |author=Umashankar Nagarajan |author2=George Kantor|author3=Ralph Hollis |date=December 2010 |work=IEEE Conference on Decision and Control |location=Atlanta, USA |pages=3566–3571}}</ref><ref name="UmaICRA12a">{{cite web|url=https://www.cs.cmu.edu/~unagaraj/Ballbot_GracefulNavigation_ICRA.pdf |title=Integrated Planning and Control for Graceful Navigation of Shape-Accelerated Underactuated Balancing Mobile Robots |author=Umashankar Nagarajan |author2=George Kantor|author3=Ralph Hollis |date=May 2012 |work=IEEE Conference on Decision and Control |location=St. Paul, USA}}</ref><ref name="BallbotNavigation">{{cite web|url=https://www.youtube.com/watch?v=tzNKiGq5oaA  |archive-url=https://ghostarchive.org/varchive/youtube/20211219/tzNKiGq5oaA |archive-date=2021-12-19 |url-status=live|title=CMU Ballbot: Autonomous Graceful Navigation |website=[[YouTube]] |date=September 2011 }}{{cbignore}}</ref> A pair of two [[degrees of freedom (mechanics)|degrees of freedom]] (DOF) arms was added to the CMU Ballbot<ref name="Hollis06" /> in 2011, making it the first and currently, the only ballbot in the world with arms.<ref name="UmaICRA12b">{{cite web|url=https://www.cs.cmu.edu/~unagaraj/Ballbot_HighDimShapePlanner_ICRA.pdf |title=Planning in High-dimensional Shape Space for a Single-wheeled Balancing Mobile Robot with Arms |author=Umashankar Nagarajan |author2=Byungjun Kim|author3=Ralph Hollis |date=May 2012 |work=IEEE Conference on Decision and Control |location=St. Paul, USA}}</ref><ref name="BallbotArms1">{{cite web|url=https://www.youtube.com/watch?v=YX3DuIA9FLo  |archive-url=https://ghostarchive.org/varchive/youtube/20211219/YX3DuIA9FLo |archive-date=2021-12-19 |url-status=live|title=CMU Ballbot: Motion with Arms |website=[[YouTube]] |date=April 2011 |type=VIDEO }}{{cbignore}}</ref><ref name="BallbotArms2">{{cite web|url=https://www.youtube.com/watch?v=BW78KmmB9IU  |archive-url=https://ghostarchive.org/varchive/youtube/20211219/BW78KmmB9IU |archive-date=2021-12-19 |url-status=live|title=CMU Ballbot: Motions with Constraints on Arms |website=[[YouTube]] |date=October 2011 |type=VIDEO }}{{cbignore}}</ref>
In 2005, around the same time when CMU Ballbot<ref name="Hollis06" /> was introduced, a group of researchers at [[University of Tokyo]] independently presented the design for a human-ridable ballbot wheelchair that balances on a basketball named "B. B. Rider".<ref name="B.B. Rider">{{cite journal |title=An Omnidirectional Vehicle on a Basketball |author1=Tatsuro Endo |author2=Yoshihiko Nakamura |journal=12th International Conference on Advanced Robotics |date=July 2005 |pages=573–578 |type = PDF}}</ref> However, they reported only the design and never presented any experimental results.<ref name="B.B. Rider" /> Around the same time, László Havasi from Hungary independently introduced another ballbot called ''ERROSphere''.<ref name="ERROS">{{cite journal |title=ERROSphere: an Equilibrator Robot |author=László Havasi |journal=International Conference on Control and Automation |date=June 2005 |type = PDF |location=Budapest, Hungary |pages=971–976}}</ref>
The robot did not reliably balance and no further work was presented.
Since the introduction of CMU Ballbot<ref name="Hollis06" /> in 2005, several other groups around the world have developed ballbots. Prof. Masaaki Kumagai developed ''BallIP'' in 2008<ref name="BallIP">{{cite journal |title=Development of a Robot Balancing on a Ball |author1=M Kumagai |author2=T Ochiai |journal=International Conference on Control |publisher=Automation and Systems |date=October 2008 |location=Seoul, Korea |pages=433–438}}</ref> at [[Tohoku Gakuin University]], Japan. Prof. Kumagai and his group demonstrated the capability of ballbots to carry loads and be used for cooperative transportation.<ref name="BallIP2">{{cite journal |title=Development of a Robot Balanced on a Ball: Application of passive motion to transport |author1=M Kumagai |author2=T Ochiai |journal=International Conference on Robotics and Automation |date=May 2009 |location=Kobe, Japan |pages=4106–4111}}</ref> They developed a number of small ballbots and demonstrated cooperative transportation using them.<ref name="BallIP2" /><ref name="BallIPIEEE">{{cite web|url=https://spectrum.ieee.org/042910-a-robot-that-balances-on-a-ball |title=BallIP on IEEE Spectrum |date=April 2010 }}</ref> A group of mechanical engineering students at [[ETH Zurich]], Switzerland developed Rezero in 2010.<ref name="Rezero">{{cite web |url=http://www.rezero.ethz.ch/content/press/20101022-Maxon-Motor-AG-EN.pdf |title=Rezero, Focus Project Report |author1=Simon Doessegger |author2=Peter Fankhauser |author3=Corsin Gwerder |author4=Jonathan Huessy |author5=Jerome Kaeser |author6=Thomas Kammermann |author7=Lukas Limacher |author8=Michael Neunert |website=Autonomous Systems Lab, ETH Zurich Institute of Technology|date=June 2010 |type = PDF|url-status=dead|archive-url=https://web.archive.org/web/20130730144120/http://www.rezero.ethz.ch/content/press/20101022-Maxon-Motor-AG-EN.pdf|archive-date=30 July 2013}}</ref> Rezero re-emphasized the fast and graceful motions that can be achieved using ballbots.<ref name="RezeroTed">{{cite web|url=http://www.ted.com/talks/peter_fankhauser_meet_rezero_the_dancing_ballbot.html |title=Rezero on TED Talks |date=July 2011 |type=VIDEO }}</ref>
Tomás Arribas (Spain) developed the first ballbot using LEGO Mindstorms NXT in 2008 as the Master Project at University of Alcala.<ref>Tomás Arribas (August 2008). https://www.youtube.com/watch?v=FZ5K0tZ2ZOk</ref><ref>{{cite web|url=https://www.youtube.com/watch?v=5Eau8y-yhPc |archive-url=https://ghostarchive.org/varchive/youtube/20211219/5Eau8y-yhPc |archive-date=2021-12-19 |url-status=live|title=NXT BallBot: Balancing Robot Omnidirectional Trajectory correction|last=Tomás Arribas|date=30 December 2010|via=YouTube}}{{cbignore}}</ref> He developed a simulation project with Microsoft Excel to easily simulate the system.<ref>{{cite web|url=http://ballbotexcel.blogspot.com.es/2011/01/nxt-ballbot-simulation-with-microsoft.html|title=NXTBallbot balancing robot Simulation with Microsoft Excel: NXT Ballbot Simulation with Microsoft Excel|first=Tomás|last=Arribas|date=5 January 2011 }}</ref> As part of the research carried out inside the Space Research Group of the University of Alcalá (SRG-UAH), Spain, the work team, specialised in optimal control and planning applied to non-linear dynamic systems, published in 2012 the article called "A Monoball Robot Based on LEGO Mindstorms"<ref>( S. Sánchez, T. Arribas, M. Gómez and O. Polo, “A Monoball Robot Based on LEGO Mindstorms,” IEEE Control Systems Magazine, vol. 32, no. 2, pp. 71–83, 2012.)</ref> This article describes the math model and trajectory control as a baseline to unstable and non-linear control systems.
Yorihisa Yamamoto (Japan) inspired by Tomás Arribas's project, developed a ballbot using LEGO Mindstorms NXT in 2009.<ref name="nxt1">{{cite web|url=http://www.mathworks.com/matlabcentral/fileexchange/23931 |title=NXT Ballbot Model-Based Design.pdf |author= Yorihisa Yamamoto |date=April 2009 |format = PDF |pages=47}}</ref><ref name="nxt1a">{{cite web|url=https://www.youtube.com/watch?v=f8jxGsg3p0Y  |archive-url=https://ghostarchive.org/varchive/youtube/20211219/f8jxGsg3p0Y |archive-date=2021-12-19 |url-status=live|title=LEGO NXT Ballbot |website=[[YouTube]] |date=January 2009 |type=VIDEO }}{{cbignore}}</ref>
He created a detailed demo to build, model and create controllers using [[MATLAB]].<ref name="nxt1" />
A group of mechanical engineering students at [[University of Adelaide]] (Australia) developed both a LEGO ballbot and a full-scale ballbot in 2009.<ref name="nxt2">{{cite web|url=https://www.youtube.com/watch?v=H2e7f30ljH8  |archive-url=https://ghostarchive.org/varchive/youtube/20211219/H2e7f30ljH8 |archive-date=2021-12-19 |url-status=live|title=Ballbot at University of Adelaide |website=[[YouTube]] |date=October 2009  |type=VIDEO}}{{cbignore}}</ref> A group of students from [[Saint Petersburg State University of Information Technologies, Mechanics and Optics|ITMO University]] (Russia) introduced an algorithm and constructed a ballbot based on LegoNXT robotics kit which performed stability with only two actuators used.<ref>{{cite journal|title=Ballbot stabilization algorithm|url=http://ntv.ifmo.ru/en/article/858/sistema_i_algoritmy_stabilizacii_bolbota.htm|journal=Journal Scientific and Technical of Information Technologies, Mechanics and Optics |date=28 September 2011 |volume=75 |issue=5 |page=58 |last1=S |first1=Borgul Alexander |last2=S |first2=Gromov Vladislav |last3=A |first3=Zimenko Konstantin |last4=Maklashevich |first4=Sergey }}</ref> Videos on [[YouTube]] present ballbots developed around the world. Some of them have been developed using LEGO Mindstorms NXT.<ref name="nxt3">{{cite web|url=https://www.youtube.com/watch?v=gKMl8G44U4E |archive-url=https://ghostarchive.org/varchive/youtube/20211219/gKMl8G44U4E |archive-date=2021-12-19 |url-status=live|title=Ballbot - A dynamically stable inverted pendulum balancing on a bowling ball|last=Samuel Jackson|date=13 August 2011|via=YouTube}}{{cbignore}}</ref><ref name="nxt4">{{cite web|url=https://www.youtube.com/watch?v=F7k9p1sOfEE |archive-url=https://ghostarchive.org/varchive/youtube/20211219/F7k9p1sOfEE |archive-date=2021-12-19 |url-status=live|title=2-Dimension Inverted Pendulum|last=double051|date=14 March 2011|via=YouTube}}{{cbignore}}</ref><ref name="nxt5">{{cite web|url=https://www.youtube.com/watch?v=-r3xxI4yQ9A|title=YouTube|website=[[YouTube]] }}</ref><ref name="nxt6">{{cite web|url=https://www.youtube.com/watch?v=OAc1ipVpn3k |title=YouTube|website=[[YouTube]] }}{{deadlink|date=February 2022}}</ref><ref name="nxt7">{{cite web|url=https://www.youtube.com/watch?v=L-J7zymXuxI|title=YouTube|website=[[YouTube]] }}</ref> Other custom designs use omni-wheels to actuate the ball.<ref name="omni1">{{cite web|url=https://www.youtube.com/watch?v=a94z9p3vU-c |archive-url=https://ghostarchive.org/varchive/youtube/20211219/a94z9p3vU-c |archive-date=2021-12-19 |url-status=live|title=Ballbot - prima versione|last=antonio88m|date=11 February 2011|via=YouTube}}{{cbignore}}</ref><ref name="omni2">{{cite web|url=https://www.youtube.com/watch?v=7Ib3l9KYbBM |archive-url=https://ghostarchive.org/varchive/youtube/20211219/7Ib3l9KYbBM |archive-date=2021-12-19 |url-status=live|title=AST Ballbot - G1|last=StAstRobotics|date=1 March 2011|via=YouTube}}{{cbignore}}</ref><ref name="omni3">{{cite web|url=https://www.youtube.com/watch?v=uSKhixP-d-Y |archive-url=https://ghostarchive.org/varchive/youtube/20211219/uSKhixP-d-Y |archive-date=2021-12-19 |url-status=live|title=玉乗りロボット1号|last=aoki2001|date=14 November 2010|via=YouTube}}{{cbignore}}</ref><ref name="omni4">{{cite web|url=https://www.youtube.com/watch?v=J0PnIyyydPE |archive-url=https://ghostarchive.org/varchive/youtube/20211219/J0PnIyyydPE |archive-date=2021-12-19 |url-status=live|title=Self-balancing Arduino Ballbot - SPSU senior design project|last=Jeroen Waning|date=2 December 2011|via=YouTube}}{{cbignore}}</ref>
Thomas Kølbæk Jespersen (Denmark) developed the Kugle ballbot as his final master thesis in 2019.<ref name=":0">{{Cite book|url=https://github.com/mindThomas/Kugle-MATLAB/blob/master/Kugle%20-%20Modelling%20and%20Control%20of%20a%20Ball-balancing%20Robot.pdf|title=Kugle - Modelling and Control of a Ball-balancing|last=Jespersen|first=Thomas Kølbæk|publisher=Master Thesis, AAU|date=April 2019}}</ref> The Kugle ballbot is a human-sized ballbot developed as part of an ongoing Human Robot Interaction research project at [[Aalborg University]]. Equipped with three motors and [[Omni wheel|omniwheels]], an onboard Intel NUC, two SICK LiDARs, an ARM microprocessor and a tablet on the top, the robot is capable of maneuvering autonomously in indoor environments and guide people around. The master thesis takes a different approach to the system modelling by deriving a non-linear quaternion-based dynamic model which is used to derive a non-linear sliding mode controller to stabilize the balance and a path-following model predictive controller to plan and execute smooth trajectories. The complete master thesis and all material including MATLAB source code and C++ controller implementations are publicly available on GitHub.<ref>{{Cite web|url=https://github.com/mindthomas/kugle-matlab|title=Kugle ballbot repository|last=Jespersen|first=Thomas Kølbæk|website=GitHub}}</ref>
Ballbots have also appeared in the science fiction world. [[Pixar]]'s 2008 movie ''[[Wall-E]]'' featured "M-O" (Microbe Obliterator), a ballbot cleaning robot. [[Syfy]]'s 2010 TV series ''[[Caprica (TV series)|Caprica]]'' featured "Serge", a ballbot butler robot.<ref name="Serge">{{cite web|url=http://en.battlestarwiki.org/wiki/Serge|title=Serge - Battlestar Wiki|access-date=2010-05-04|archive-url=https://web.archive.org/web/20100402112945/http://en.battlestarwiki.org/wiki/Serge|archive-date=2010-04-02|url-status=dead}}</ref>
==Motivation and characteristics==
Historically, mobile robots have been designed to be statically stable, which results in the robot not needing to expend energy while standing still. This is typically achieved through the use of three or more wheels on a base. In order to avoid tipping, these statically-stable mobile robots have a wide base for a large polygon of support, and a lot of dead weight in the base to lower the [[center of gravity]]. They also tend to have low acceleration or deceleration to avoid tipping. The wide base makes it difficult for statically-stable mobile robots to navigate cluttered human environments. Moreover, these robots have several other limitations that make them poorly suited to a constantly changing human environment. They can neither roll in any direction, nor can they turn in place.<ref name="Hollis06" />
The desire to build tall and narrow mobile robots that do not tip over led to development of balancing mobile robots like the ballbot. A ballbot generally has a body that balances on top of a single spherical wheel (ball). It forms an [[underactuation|underactuated]] system, ''i.e.'', there are more [[degrees of freedom (mechanics)|degrees of freedom]] (DOF) than there are independent control inputs. The ball is directly controlled using [[actuators]], whereas the body has no direct control. The body is kept upright about its [[mechanical equilibrium|unstable equilibrium]] point by controlling the ball, much like the control of an [[inverted pendulum]].<ref name="Hollis06" /> This leads to limited but perpetual position displacements of the ballbot. The counter-intuitive aspect of the ballbot motion is that in order to move forward, the body has to lean forward and in order to lean forward, the ball must roll backwards. All these characteristics make planning to achieve desired motions for the ballbot a challenging task. In order to achieve a forward straight line motion, the ballbot has to lean forward to accelerate and lean backward to decelerate.<ref name="UmaICRA09b" /><ref name="UmaRSS10" /><ref name="UmaICRA12b" /><ref name="Rezero"/> Further, the ballbot has to lean into curves in order to compensate for [[centripetal force]]s, which results in elegant and graceful motions.<ref name="UmaRSS10" /><ref name="UmaICRA12a" /><ref name="UmaICRA12b" /><ref name="Rezero"/>
Unlike two-wheeled balancing mobile robots like [[Segway PT|Segway]] that balance in one direction but cannot move in the lateral direction, the ballbot is omni-directional and hence, can roll in any direction. It has no minimal turning radius and does not have to [[Yaw angle#Tait–Bryan angles|yaw]] in order to change direction.
==System description==
===Major design parameters===
The most fundamental design parameters of a ballbot are its height, mass, its center of gravity and the maximum torque its actuators can provide. The choice of those parameters determine the robot's moment of inertia, the maximum pitch angle and thus its dynamic and acceleration performance and agility. The maximum velocity is a function of actuator power and its characteristics. Besides the maximum torque, the pitch angle is additionally upper bounded by the maximum force which can be transmitted from the actuators to the ground. Therefore, [[friction]] coefficients of all parts involved in force transmission also play a major role in system design. Also, close attention has to be paid to the ratio of the moment of inertia of the robot body and its ball in order to prevent undesired ball spin, especially while yawing.<ref name="Rezero" />
===Ball and actuation===
The ball is the core element of a ballbot, it has to transmit and bear all arising forces and withstand mechanical [[wear]] caused by rough contact surfaces. A high friction coefficient of its surface and a low inertia are essential. The CMU Ballbot,<ref name="Hollis06" /> Rezero<ref name="Rezero" /> and Kugle<ref name=":0" /> used a hollow metal sphere with poly-urethane coating. B.B. Rider<ref name="B.B. Rider" /> used a basketball, while BallIP<ref name="BallIP" /> and Adelaide Ballbot<ref name="nxt2" /> used bowling balls coated with a thin layer of rubber.
In order to solve the rather complex problem of actuating a sphere, a variety of different actuation mechanisms have been introduced.
The CMU Ballbot<ref name="Hollis06" /> used an inverse mouse-ball drive mechanism. Unlike the traditional mouse ball that drives the mouse rollers to provide computer input, the inverse mouse-ball drive uses rollers to drive the ball producing motion. The inverse mouse-ball drive uses four rollers to drive the ball and each roller is actuated by an independent electric motor. In order to achieve yaw motion, the CMU Ballbot uses a bearing, slip-ring assembly and a separate motor to spin the body on top of the ball.<ref name="UmaICRA09b" /> The LEGO Ballbot<ref name="nxt1" /> also used an inverse mouse-ball drive, but used normal wheels to drive the ball instead of rollers.
Unlike CMU Ballbot<ref name="UmaICRA09b" /> both BallIP,<ref name="BallIP" /> Rezero<ref name="Rezero" /> and Kugle<ref name=":0" /> use omni-wheels to drive the ball. This drive mechanism does not require a separate yaw drive mechanism and allows direct control of the yaw rotation of the ball. Unlike CMU Ballbot<ref name="UmaICRA09b" /> that uses four motors for driving the ball and one motor for yaw rotation, BallIP,<ref name="BallIP" /> Rezero<ref name="Rezero" /> and Kugle<ref name=":0" /> use only three motors for both the operations. Moreover, they only have three force transmission points compared to four points on CMU Ballbot. Since the contact between an omni-wheel and the ball should be reduced to a single point, most available omni-wheels are not properly suitable for this task because of the gaps between the individual smaller wheels that result in an unsteady rolling motion. Therefore, the BallIP<ref name="BallIP" /> project introduced a more complex omni-wheel with a continuous circumferential contact line. The Rezero<ref name="Rezero" /> team equipped this omni-wheel design with roller bearings and a high-friction coating.<ref name="Rezero" /> They also additionally fitted a mechanical ball arrester that presses the ball against the actuators in order to further increase friction forces and a [[Suspension (vehicle)|suspension]] to dampen vibrations.<ref name="Rezero" /> The Kugle robot is equipped with a skirt which holds the ball in place to avoid that the ball gets pushed out during large inclinations. The Adelaide Ballbot<ref name="nxt2" /> uses wheels for its LEGO version and traditional omni-wheels for its full-scale version.
Prof. Masaaki Kumagai,<ref name="Kumagai" /> who developed BallIP<ref name="BallIP" /> introduced another ball drive mechanism that uses partially sliding rollers.<ref name="PSR">{{cite book|author=Masaaki Kumagai |title=2010 IEEE/RSJ International Conference on Intelligent Robots and Systems |chapter=Development of a ball drive unit using partially sliding rollers &mdash; an alternative mechanism for semi-omnidirectional motion &#x2014 |date=October 2010 |location=Taipei,Taiwan|pages=3353–3357 |chapter-url=https://www.researchgate.net/publication/221063469 |chapter-url-access=subscription|doi=10.1109/IROS.2010.5651007|isbn=978-1-4244-6674-0 |s2cid=15901355 }}</ref>
<ref name="PSR1">{{cite web|url=https://www.youtube.com/watch?v=HbKvtivAx8A  |archive-url=https://ghostarchive.org/varchive/youtube/20211219/HbKvtivAx8A |archive-date=2021-12-19 |url-status=live|title=Ball Actuation using Partial Sliding Rollers |website=[[YouTube]] |date=October 2010 }}{{cbignore}}</ref> The objective of this design was to develop 3-[[degrees of freedom (mechanics)|DOF]] actuation on the ball using a low cost mechanism.
===Sensors===
In order to actively control the position and body orientation of a ballbot by a sensor-computer-actuator framework, beside a suitable [[microprocessor]] or some sort of other computing unit to run the necessary control loops, a ballbot fundamentally requires a series of sensors which allow to measure the orientation of the ball and the ballbot body as a function of time. To keep track of the motions of the ball, [[rotary encoder]]s (CMU Ballbot,<ref name="Hollis06" /> BallIP,<ref name="BallIP" /> Rezero,<ref name="Rezero" /> Kugle<ref name=":0" />) are usually used. Measuring the body orientation is more complicated and is often done by the use of [[gyroscope]]s (NXT Ballbots<ref name="nxt1" /><ref name="nxt2" />) or, more generally, an [[Inertial Measurement Unit]] (CMU Ballbot,<ref name="Hollis06" /> BallIP,<ref name="BallIP" /> Rezero,<ref name="Rezero" /> Kugle<ref name=":0" />) which includes an [[accelerometer]], [[gyroscope]] and possibly [[magnetometer]] whose measurements are fused into the body orientation through [[Attitude and heading reference system|AHRS]] algorithms.
The CMU Ballbot<ref name="Hollis06" /> uses a Hokuyo URG-04LX [[Laser rangefinder|Laser Range Finder]] to localize itself in a 2D map of the environment.<ref name="UmaICRA12a" /><ref name="BallbotNavigation" /> It also uses the laser range finder for detecting obstacles and avoiding them.<ref name="UmaICRA12a" /><ref name="BallbotNavigation" /> Conversely the Kugle robot<ref name=":0" /> uses two SICK TiM571 2D [[Laser rangefinder|LiDAR]] to localize itself, perform obstacle avoidance and detect people for guidance.
===Arms===
The CMU Ballbot<ref name="Hollis06" /> is the first and currently, the only ballbot to have arms.<ref name="UmaICRA12b" /><ref name="BallbotArms1" /><ref name="BallbotArms2" /> It has a pair of 2-[[degrees of freedom (mechanics)|DOF]] arms that are driven by series-elastic actuators. The arms are hollow aluminium tubes with a provision to add dummy weights at their ends. In their present state, the arms cannot be used for any significant manipulation, but are used to study their effects on the dynamics of ballbot.<ref name="UmaICRA12b" /><ref name="BallbotArms1" /><ref name="BallbotArms2" />
===System modeling, planning and control===
The mathematical MIMO-model which is needed in order to simulate a ballbot and to design a sufficient [[Controller (control theory)|controller]] which stabilizes the system, is very similar to an [[inverted pendulum|inverted pendulum on a cart]]. The LEGO NXT Ballbot,<ref name="nxt1" /> Adelaide Ballbot,<ref name="nxt2" /> Rezero<ref name="Rezero" /> and Kugle<ref name=":0" /> include actuator models in their robot models, whereas CMU Ballbot<ref name="Hollis06" /> neglects the actuator models and models the Ballbot as a body on top of a ball. Initially, CMU Ballbot<ref name="Hollis06" /> used two 2D planar models in perpendicular planes to model the ballbot<ref name="UmaICRA09a" /><ref name="UmaICRA09b" /> and at present, uses 3D models without yaw motion for both the ballbot without arms<ref name="UmaRSS10" /><ref name="UmaCDC10" /><ref name="UmaICRA12a" /> and the ballbot with arms.<ref name="UmaICRA12b" /> BallIP<ref name="BallIP" /> uses a model that describes the dependence of the ball position on the wheel velocities and the body motion.
Rezero<ref name="Rezero" /> uses a full 3D model that includes yaw motion too. Kugle<ref name=":0" /> uses a fully coupled [[Quaternions and spatial rotation|quaternion]]-based 3D model which couples the motion of all axes.
The ballbots (CMU Ballbot,<ref name="Hollis06" /> BallIP,<ref name="BallIP" /> NXT Ballbot,<ref name="nxt1" /> Adelaide Ballbot,<ref name="nxt2" /> Rezero<ref name="Rezero" />) use linear feedback control approaches to maintain balance and achieve motion. The CMU Ballbot<ref name="Hollis06" /> uses an inner balancing control loop that maintains the body at desired body angles and an outer loop controller that achieves desired ball motions by commanding body angles to the balancing controller.<ref name="UmaICRA09a" /><ref name="UmaICRA09b" /><ref name="UmaRSS10" /><ref name="UmaCDC10" /><ref name="UmaICRA12a" /><ref name="UmaICRA12b" /> The Kugle robot is tested with both linear feedback controllers ([[Linear–quadratic regulator|LQR]]) and non-linear [[Sliding mode control|sliding mode controllers]] to show the benefit of its coupled dynamic quaternion model.<ref name=":0" />
A ballbot is a shape-accelerated underactuated system. The inclination angles of a ballbot is thus dynamically linked to the resulting accelerations of the ball and robot leading to an underactuated system. The CMU Ballbot plans motions in the space of body lean angles in order to achieve fast, dynamic and graceful ball motions.<ref name="UmaRSS10" /><ref name="UmaCDC10" /><ref name="UmaICRA12a" /><ref name="UmaICRA12b" /> With the introduction of arms, CMU Ballbot uses its planning procedure to plan in the space of both body lean angles and arm angles to achieve desired ball motions.<ref name="UmaICRA12a" /><ref name="UmaICRA12b" /><ref name="BallbotArms1" />   Moreover, it can also account for cases where the arms are constrained to certain specific motions and only body angles have to be used to achieve desired ball motions.<ref name="BallbotArms2" /> The CMU Ballbot uses an integrated planning and control framework to autonomously navigate human environments.<ref name="UmaICRA12a" /><ref name="BallbotNavigation" /> Its motion planner plans in the space of controllers to produce graceful navigation, and achieves point-point and surveillance tasks. It uses the laser range finder to actively detect and avoid both static and dynamic obstacles in its environment.<ref name="UmaICRA12a" /><ref name="BallbotNavigation" />
For Kugle a path-planning model predictive controller (MPC) is designed to control the inclination angles of the ballbot to follow a given path. A path-following strategy is chosen over common trajectory or reference tracking controllers to accommodate for the temporally lacking behaviour of ballbots due to the underactuated nature. The path is parameterized as a polynomial and included into the cost-function of the MPC. A set of soft-constraints ensures that obstacles are avoided and that progress is made with a desired speed.<ref name=":0" />
===Safety features===
The biggest concern with a ballbot is its safety in case of a system failure. There have been several attempts in addressing this concern. The CMU Ballbot<ref name="Hollis06" /> introduced three retractable landing legs that allow the robot to remain standing (statically-stable) after being powered down. It is also capable of automatically transitioning from this statically-stable state to the dynamically-stable, balancing state and vice versa.<ref name="UmaICRA09a" /><ref name="BallbotIntroVideo" /> Rezero featured a roll-over safety mechanism in order to prevent serious damage in case of a system failure.<ref name="Rezero" />
==Possible applications==
Due to its dynamic stability, a ballbot can be tall and narrow, and can also be physically interactive, making it an ideal candidate for a personal mobile robot.<ref name="Hollis06" /> It can act as an effective service robot at homes and offices and offer guidance to people in e.g. malls and airports.<ref name=":0" /> The present day ballbots<ref name="Hollis06" /><ref name="BallIP" /><ref name="Rezero" /> are restricted to smooth surfaces. The concept of the ballbot has attracted a lot of media attention,<ref name="DailyPlanet" /><ref name="Roborama" /><ref name="GadgetShow" /><ref name="BallIPIEEE" /><ref name="RezeroTed" />
and several ballbot characters have appeared in Hollywood movies.<ref name="WallE">[[WALL-E]]</ref><ref name="Serge" /> Hence, the ballbot has a variety of applications in the entertainment industry, including toys.
== Notable Ballbot projects ==
* Academic projects:
** The Ballbot Research Platform at [[Carnegie Mellon University]] (CMU) (2005)<ref name="CMU Ballbot" />
** BallIP at [[Tohoku Gakuin University]] (2007)<ref name="Kumagai" />
** Rezero at [[ETH Zurich]] (2010)<ref name="Rezero1" />
** Kugle at [[Aalborg University]] (AAU) (2018)<ref name="Kugle1" />
** Ballbot-based [[wheelchair]] prototype at [[University of Illinois Urbana-Champaign]] (2023)<ref>[https://healtheng.illinois.edu/news/hands-free-wheelchair-prototype-achieves-major-milestone Hands-free wheelchair prototype achieves major milestone]</ref>
* Industrial projects:
** mObi by Bossa Nova Robotics (2012)<ref>[https://spectrum.ieee.org/bossa-nova-introduces-mobi-research-ballbot Bossa Nova Robotics Launches Mobi Research Ballbot]</ref>
** BionicMobileAssistant by [[Festo]] (2015)<ref>[https://www.festo.com/us/en/e/about-festo/research-and-development/bionic-learning-network/highlights-from-2015-to-2017/bionicmobileassistant-id_326923/ BionicMobileAssistant: Mobile Robot System with Pneumatic Gripper Hand]</ref>
==References==
{{reflist|30em}}
{{Commons category|Ballbot}}
[[Category:One-wheeled balancing robots| ]]