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rotation, BallIP, Rezero and Kugle 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 project introduced a more complex omni-wheel with a continuous circumferential contact line. The Rezero team equipped this omni-wheel design with roller bearings and a high-friction coating. They also additionally fitted a mechanical ball arrester that presses the ball against the actuators in order to further increase friction forces and a
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dynamic and graceful ball motions. 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. 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. The CMU Ballbot uses an integrated planning and control framework to autonomously navigate human environments. 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.
107:(CMU), Pittsburgh, USA and it was patented in 2010. The CMU Ballbot 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. They showed that a variety of interesting human-robot physical interaction behaviors can be developed with the ballbot, and presented planning and control algorithms to achieve fast, dynamic and graceful motions using the ballbot. They also demonstrated the ballbot's capability to autonomously navigate human environments to achieve point-point and surveillance tasks. A pair of two
173:, 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.
385:. The LEGO NXT Ballbot, Adelaide Ballbot, Rezero and Kugle include actuator models in their robot models, whereas CMU Ballbot neglects the actuator models and models the Ballbot as a body on top of a ball. Initially, CMU Ballbot used two 2D planar models in perpendicular planes to model the ballbot and at present, uses 3D models without yaw motion for both the ballbot without arms and the ballbot with arms. BallIP uses a model that describes the dependence of the ball position on the wheel velocities and the body motion. Rezero uses a full 3D model that includes yaw motion too. Kugle uses a fully coupled
237:. 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. Further, the ballbot has to lean into curves in order to compensate for
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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. The LEGO Ballbot also used an inverse mouse-ball drive, but used normal wheels to drive the ball instead of rollers.
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209:. 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.
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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" This article describes the math model and trajectory control as a baseline to unstable and non-linear control systems.
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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 introduced three retractable landing legs that allow the robot to remain standing (statically-stable) after being powered down. It is also capable
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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
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caused by rough contact surfaces. A high friction coefficient of its surface and a low inertia are essential. The CMU Ballbot, Rezero and Kugle used a hollow metal sphere with poly-urethane coating. B.B. Rider used a basketball, while BallIP and
Adelaide Ballbot used bowling balls coated with a thin
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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
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independently presented the design for a human-ridable ballbot wheelchair that balances on a basketball named "B. B. Rider". However, they reported only the design and never presented any experimental results. Around the same time, László Havasi from
Hungary independently introduced another ballbot
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In order to solve the rather complex problem of actuating a sphere, a variety of different actuation mechanisms have been introduced. The CMU Ballbot used an inverse mouse-ball drive mechanism. Unlike the traditional mouse ball that drives the mouse rollers to provide computer input, the inverse
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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. It can act as an effective service robot at homes and offices and offer guidance to people in e.g. malls and airports. The present day
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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,
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The ballbots (CMU Ballbot, BallIP, NXT Ballbot, Adelaide
Ballbot, Rezero) use linear feedback control approaches to maintain balance and achieve motion. The CMU Ballbot uses an inner balancing control loop that maintains the body at desired body angles and an outer loop controller that achieves
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Unlike CMU Ballbot both BallIP, Rezero and Kugle 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 that uses four motors for driving the ball and one motor for yaw
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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
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Tomás
Arribas (Spain) developed the first ballbot using LEGO Mindstorms NXT in 2008 as the Master Project at University of Alcala. He developed a simulation project with Microsoft Excel to easily simulate the system. As part of the research carried out inside the Space Research Group of the
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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.
134:, Japan. Prof. Kumagai and his group demonstrated the capability of ballbots to carry loads and be used for cooperative transportation. They developed a number of small ballbots and demonstrated cooperative transportation using them. A group of mechanical engineering students at
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ballbots are restricted to smooth surfaces. The concept of the ballbot has attracted a lot of media attention, and several ballbot characters have appeared in
Hollywood movies. Hence, the ballbot has a variety of applications in the entertainment industry, including toys.
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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.
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to dampen vibrations. 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 uses wheels for its LEGO version and traditional omni-wheels for its full-scale version.
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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,
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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,
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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
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of automatically transitioning from this statically-stable state to the dynamically-stable, balancing state and vice versa. Rezero featured a roll-over safety mechanism in order to prevent serious damage in case of a system failure.
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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.
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Thomas Kølbæk
Jespersen (Denmark) developed the Kugle ballbot as his final master thesis in 2019. The Kugle ballbot is a human-sized ballbot developed as part of an ongoing Human Robot Interaction research project at
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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
87:, 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
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Yorihisa
Yamamoto (Japan) inspired by Tomás Arribas's project, developed a ballbot using LEGO Mindstorms NXT in 2009. He created a detailed demo to build, model and create controllers using
1980:
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to localize itself in a 2D map of the environment. It also uses the laser range finder for detecting obstacles and avoiding them. Conversely the Kugle robot uses two SICK TiM571 2D
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Prof. Masaaki
Kumagai, who developed BallIP introduced another ball drive mechanism that uses partially sliding rollers. The objective of this design was to develop 3-
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present ballbots developed around the world. Some of them have been developed using LEGO Mindstorms NXT. Other custom designs use omni-wheels to actuate the ball.
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1436:( 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.)
157:(Russia) introduced an algorithm and constructed a ballbot based on LegoNXT robotics kit which performed stability with only two actuators used. Videos on
1346:
1345:
Simon
Doessegger; Peter Fankhauser; Corsin Gwerder; Jonathan Huessy; Jerome Kaeser; Thomas Kammermann; Lukas Limacher; Michael Neunert (June 2010).
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1866:"Development of a ball drive unit using partially sliding rollers — an alternative mechanism for semi-omnidirectional motion —"
126:
Since the introduction of CMU Ballbot in 2005, several other groups around the world have developed ballbots. Prof. Masaaki Kumagai developed
1997:
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desired ball motions by commanding body angles to the balancing controller. The Kugle robot is tested with both linear feedback controllers (
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321:(CMU Ballbot, BallIP, Rezero, Kugle) are usually used. Measuring the body orientation is more complicated and is often done by the use of
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In order to actively control the position and body orientation of a ballbot by a sensor-computer-actuator framework, beside a suitable
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enables improved navigability in narrow, crowded and dynamic environments. The ballbot works on the same principle as that of an
138:, Switzerland developed Rezero in 2010. Rezero re-emphasized the fast and graceful motions that can be achieved using ballbots.
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111:(DOF) arms was added to the CMU Ballbot in 2011, making it the first and currently, the only ballbot in the world with arms.
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793:"State Transition, Balancing, Station Keeping and Yaw Control for a Dynamically Stable Single Spherical Wheel Mobile Robot"
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1280:
M Kumagai; T Ochiai (May 2009). "Development of a Robot Balanced on a Ball: Application of passive motion to transport".
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1052:"Integrated Planning and Control for Graceful Navigation of Shape-Accelerated Underactuated Balancing Mobile Robots"
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The ball is the core element of a ballbot, it has to transmit and bear all arising forces and withstand mechanical
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934:"Dynamic Constraint-based Optimal Shape Trajectory Planner for Shape-Accelerated Underactuated Balancing Systems"
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S, Borgul Alexander; S, Gromov Vladislav; A, Zimenko Konstantin; Maklashevich, Sergey (28 September 2011).
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1424:"NXTBallbot balancing robot Simulation with Microsoft Excel: NXT Ballbot Simulation with Microsoft Excel"
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The mathematical MIMO-model which is needed in order to simulate a ballbot and to design a sufficient
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The first successful ballbot was developed in 2005 by Prof. Ralph Hollis of the Robotics Institute at
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153:(Australia) developed both a LEGO ballbot and a full-scale ballbot in 2009. A group of students from
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1124:"Planning in High-dimensional Shape Space for a Single-wheeled Balancing Mobile Robot with Arms"
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The CMU Ballbot, the first successful ballbot, built by Prof. Ralph Hollis (not in picture) at
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The CMU Ballbot is the first and currently, the only ballbot to have arms. It has a pair of 2-
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828:"Trajectory Planning and Control of a Dynamically Stable Single Spherical Wheel Mobile Robot"
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1211:
Tatsuro Endo; Yoshihiko Nakamura (July 2005). "An Omnidirectional Vehicle on a Basketball".
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wide base for a large polygon of support, and a lot of dead weight in the base to lower the
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In 2005, around the same time when CMU Ballbot was introduced, a group of researchers at
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225:(DOF) than there are independent control inputs. The ball is directly controlled using
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1991:
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1011:"Hybrid Control for Navigation of Shape-Accelerated Underactuated Balancing Systems"
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Journal Scientific and Technical of Information Technologies, Mechanics and Optics
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M Kumagai; T Ochiai (October 2008). "Development of a Robot Balancing on a Ball".
614:"A Dynamically Stable Single-Wheeled Mobile Robot with Inverse Mouse-Ball Drive"
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to localize itself, perform obstacle avoidance and detect people for guidance.
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1559:"Ballbot - A dynamically stable inverted pendulum balancing on a bowling ball"
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Umashankar Nagarajan; Anish Mampetta; George Kantor; Ralph Hollis (May 2009).
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229:, whereas the body has no direct control. The body is kept upright about its
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arms (2011). It is the first – and currently the only – ballbot with arms.
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123:. The robot did not reliably balance and no further work was presented.
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2010 IEEE/RSJ International Conference on Intelligent Robots and Systems
877:"Human-Robot Physical Interaction with Dynamically Stable Mobile Robots"
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BionicMobileAssistant: Mobile Robot System with Pneumatic Gripper Hand
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1405:"NXT BallBot: Balancing Robot Omnidirectional Trajectory correction"
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Umashankar Nagarajan; George Kantor; Ralph Hollis (December 2010).
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The Kugle ballbot developed at Aalborg University, Denmark in 2019
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László Havasi (June 2005). "ERROSphere: an Equilibrator Robot".
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Umashankar Nagarajan; George Kantor; Ralph Hollis (March 2009).
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featured "M-O" (Microbe Obliterator), a ballbot cleaning robot.
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whose measurements are fused into the body orientation through
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Umashankar Nagarajan; George Kantor; Ralph Hollis (May 2012).
826:
Umashankar Nagarajan; George Kantor; Ralph Hollis (May 2009).
1756:"Self-balancing Arduino Ballbot - SPSU senior design project"
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Umashankar Nagarajan; Byungjun Kim; Ralph Hollis (May 2012).
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to show the benefit of its coupled dynamic quaternion model.
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point by controlling the ball, much like the control of an
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Autonomous Systems Lab, ETH Zurich Institute of Technology
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Ballbots have also appeared in the science fiction world.
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Tom Lauwers; George Kantor; Ralph Hollis (October 2005).
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Hands-free wheelchair prototype achieves major milestone
884:
IEEE International Conference on Robotics and Automation
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IEEE International Conference on Robotics and Automation
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IEEE International Conference on Robotics and Automation
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IEEE International Conference on Robotics and Automation
329:(CMU Ballbot, BallIP, Rezero, Kugle) which includes an
389:-based 3D model which couples the motion of all axes.
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Tom Lauwers; George Kantor; Ralph Hollis (May 2006).
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from the original on 2021-12-19 – via YouTube.
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from the original on 2021-12-19 – via YouTube.
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from the original on 2021-12-19 – via YouTube.
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from the original on 2021-12-19 – via YouTube.
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from the original on 2021-12-19 – via YouTube.
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from the original on 2021-12-19 – via YouTube.
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from the original on 2021-12-19 – via YouTube.
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International Conference on Robotics and Automation
381:which stabilizes the system, is very similar to an
1970:Bossa Nova Robotics Launches Mobi Research Ballbot
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1228:International Conference on Control and Automation
1213:12th International Conference on Advanced Robotics
304:actuation on the ball using a low cost mechanism.
35:The BallIP, developed by Prof. Masaaki Kumagai at
1799:Kugle - Modelling and Control of a Ball-balancing
715:"CMU Ballbot on Discovery Channel's Daily Planet"
599:12th International Symposium on Robotics Research
579:Kugle - Modelling and Control of a Ball-balancing
557:"Project Rezero: Ball Balancing Robot With Style"
241:, which results in elegant and graceful motions.
83:designed to balance on a single spherical wheel (
1266:. Seoul, Korea: Automation and Systems: 433–438.
244:Unlike two-wheeled balancing mobile robots like
149:. A group of mechanical engineering students at
1183:"CMU Ballbot: Motions with Constraints on Arms"
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898:"CMU Ballbot: Human-Robot Physical Interaction"
1925:"Ball Actuation using Partial Sliding Rollers"
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1082:"CMU Ballbot: Autonomous Graceful Navigation"
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196:featured "Serge", a ballbot butler robot.
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1796:Jespersen, Thomas Kølbæk (April 2019).
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1131:IEEE Conference on Decision and Control
1059:IEEE Conference on Decision and Control
1018:IEEE Conference on Decision and Control
979:"CMU Ballbot: Fast, Graceful Maneuvers"
501:
473:University of Illinois Urbana-Champaign
348:The CMU Ballbot uses a Hokuyo URG-04LX
75:A ball balancing robot also known as a
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325:(NXT Ballbots) or, more generally, an
1873:. Taipei,Taiwan. pp. 3353–3357.
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886:. San Diego, USA. pp. 3743–3748.
373:System modeling, planning and control
7:
1459:"NXT Ballbot Model-Based Design.pdf"
1511:"Ballbot at University of Adelaide"
1264:International Conference on Control
1020:. Atlanta, USA. pp. 3566–3571.
1403:Tomás Arribas (30 December 2010).
1230:(PDF). Budapest, Hungary: 971–976.
932:Umashankar Nagarajan (June 2010).
837:. Kobe, Japan. pp. 3743–3748.
483:mObi by Bossa Nova Robotics (2012)
14:
1754:Jeroen Waning (2 December 2011).
1557:Samuel Jackson (13 August 2011).
1536:"Ballbot stabilization algorithm"
1422:Arribas, Tomás (5 January 2011).
802:. Kobe, Japan. pp. 998–1003.
765:"CMU Ballbot on UK's Gadget Show"
439:The Ballbot Research Platform at
169:. Equipped with three motors and
67:The CMU Ballbot with a pair of 2-
1937:from the original on 2021-12-19.
1863:Masaaki Kumagai (October 2010).
1523:from the original on 2021-12-19.
1488:from the original on 2021-12-19.
1457:Yorihisa Yamamoto (April 2009).
1195:from the original on 2021-12-19.
1164:from the original on 2021-12-19.
1094:from the original on 2021-12-19.
991:from the original on 2021-12-19.
967:from the original on 2021-12-19.
910:from the original on 2021-12-19.
864:from the original on 2021-12-19.
750:from the original on 2021-12-19.
694:"Dynamic balancing mobile robot"
1669:antonio88m (11 February 2011).
1578:"2-Dimension Inverted Pendulum"
1152:"CMU Ballbot: Motion with Arms"
1702:StAstRobotics (1 March 2011).
1347:"Rezero, Focus Project Report"
252:in order to change direction.
200:Motivation and characteristics
1:
1721:aoki2001 (14 November 2010).
1390:Tomás Arribas (August 2008).
941:Robotics: Science and Systems
673:Ralph Hollis (October 2006).
1998:One-wheeled balancing robots
692:Ralph Hollis (Dec 7, 2010).
1576:double051 (14 March 2011).
955:"CMU Ballbot: Fast Motions"
555:Markus Waibel (June 2010).
383:inverted pendulum on a cart
2014:
1818:"Kugle ballbot repository"
1816:Jespersen, Thomas Kølbæk.
1671:"Ballbot - prima versione"
441:Carnegie Mellon University
105:Carnegie Mellon University
25:Carnegie Mellon University
1879:10.1109/IROS.2010.5651007
1839:"Serge - Battlestar Wiki"
1299:"BallIP on IEEE Spectrum"
1284:. Kobe, Japan: 4106–4111.
738:"CMU Ballbot on ROBORAMA"
486:BionicMobileAssistant by
327:Inertial Measurement Unit
987:(VIDEO). December 2010.
906:(VIDEO). December 2008.
860:(VIDEO). December 2008.
448:Tohoku Gakuin University
431:Notable Ballbot projects
399:sliding mode controllers
132:Tohoku Gakuin University
79:is a dynamically-stable
47:The Rezero developed at
37:Tohoku Gakuin University
1519:(VIDEO). October 2009.
1484:(VIDEO). January 2009.
1191:(VIDEO). October 2011.
852:"CMU Ballbot: Overview"
261:Major design parameters
773:(VIDEO). January 2010.
746:(VIDEO). August 2006.
151:University of Adelaide
72:
60:
52:
40:
28:
1805:. Master Thesis, AAU.
1378:"Rezero on TED Talks"
1356:(PDF). Archived from
1160:(VIDEO). April 2011.
623:. pp. 2884–2889.
541:Prof. Masaaki Kumagai
480:Industrial projects:
422:Possible applications
66:
58:
51:, Switzerland in 2010
46:
34:
22:
963:(VIDEO). June 2010.
231:unstable equilibrium
1380:(VIDEO). July 2011.
723:(VIDEO). June 2007.
679:Scientific American
436:Academic projects:
116:University of Tokyo
16:Mobile robot design
1704:"AST Ballbot - G1"
1476:"LEGO NXT Ballbot"
1090:. September 2011.
943:. Zaragoza, Spain.
698:US Patent #7847504
525:Prof. Ralph Hollis
462:Aalborg University
350:Laser Range Finder
275:Ball and actuation
256:System description
239:centripetal forces
223:degrees of freedom
190:'s 2010 TV series
167:Aalborg University
109:degrees of freedom
73:
61:
53:
41:
29:
1888:978-1-4244-6674-0
681:. pp. 72–78.
397:) and non-linear
284:layer of rubber.
235:inverted pendulum
221:, there are more
207:center of gravity
93:inverted pendulum
89:dynamic stability
2005:
1983:
1978:
1972:
1967:
1961:
1956:
1950:
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1933:. October 2010.
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1841:. Archived from
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1363:on 30 July 2013.
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1133:. St. Paul, USA.
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1061:. St. Paul, USA.
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689:
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592:"One is Enough!"
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413:Safety features
375:
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319:rotary encoders
310:
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155:ITMO University
101:
39:, Japan in 2008
17:
12:
11:
5:
2011:
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314:microprocessor
309:
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180:'s 2008 movie
100:
97:
15:
13:
10:
9:
6:
4:
3:
2:
2010:
1999:
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1845:on 2010-04-02
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1464:. p. 47.
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1301:. April 2010.
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471:prototype at
470:
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359:
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346:
344:
340:
337:and possibly
336:
332:
331:accelerometer
328:
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320:
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215:underactuated
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98:
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26:
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1858:
1847:. Retrieved
1843:the original
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1653:
1644:
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1358:the original
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520:
464:(AAU) (2018)
443:(CMU) (2005)
425:
416:
407:
403:
391:
376:
363:
347:
345:algorithms.
339:magnetometer
311:
299:
290:
286:
278:
264:
243:
218:
211:
203:
191:
181:
175:
163:
144:
140:
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125:
120:
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102:
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81:mobile robot
76:
74:
1723:"玉乗りロボット1号"
514:CMU Ballbot
130:in 2008 at
1849:2010-05-04
675:"Ballbots"
497:References
469:wheelchair
455:ETH Zurich
453:Rezero at
446:BallIP at
387:quaternion
379:controller
323:gyroscopes
294:suspension
171:omniwheels
136:ETH Zurich
121:ERROSphere
49:ETH Zurich
1905:cite book
1650:"YouTube"
1630:"YouTube"
1610:"YouTube"
460:Kugle at
335:gyroscope
227:actuators
1992:Category
1935:Archived
1897:15901355
1760:Archived
1735:cite web
1727:Archived
1708:Archived
1683:cite web
1675:Archived
1590:cite web
1582:Archived
1563:Archived
1546:(5): 58.
1521:Archived
1486:Archived
1409:Archived
1193:Archived
1162:Archived
1092:Archived
989:Archived
965:Archived
908:Archived
862:Archived
748:Archived
268:friction
217:system,
1930:YouTube
1655:YouTube
1635:YouTube
1615:YouTube
1516:YouTube
1481:YouTube
1188:YouTube
1157:YouTube
1087:YouTube
984:YouTube
960:YouTube
903:YouTube
857:YouTube
770:YouTube
743:YouTube
720:YouTube
308:Sensors
193:Caprica
159:YouTube
119:called
99:History
77:ballbot
1948:WALL-E
1895:
1885:
1822:GitHub
490:(2015)
475:(2023)
457:(2010)
450:(2007)
246:Segway
183:Wall-E
147:MATLAB
128:BallIP
1893:S2CID
1803:(PDF)
1462:(PDF)
1361:(PDF)
1350:(PDF)
1127:(PDF)
1055:(PDF)
1014:(PDF)
937:(PDF)
880:(PDF)
831:(PDF)
796:(PDF)
617:(PDF)
595:(PDF)
488:Festo
354:LiDAR
178:Pixar
1911:link
1883:ISBN
1741:link
1689:link
1596:link
562:IEEE
360:Arms
343:AHRS
281:wear
219:i.e.
188:Syfy
85:i.e.
1875:doi
395:LQR
366:DOF
302:DOF
250:yaw
69:DOF
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565:.
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