Ballbot
Encyclopedia
A Ballbot is a mobile robot
designed to balance itself on a single spherical wheel (i.e. a ball), both while in motion or staying in place. 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.
Modern control theory
provides dynamic stability which enables robust robot designs with narrower bases for improved navigability in narrow, crowded and dynamic environments.
. This severely limits their usefulness in normal human environments where human-machine interfaces must be placed at a reasonable height, as the pathways are typically too narrow and often have many obstacles (like humans) that will impair the robot's movement.
In addition, these systems have limitations that make them poorly suited to a constantly changing human environment. They cannot immediately roll in any direction, nor can they turn in place.
A Ballbot addresses these problems by using a single spherical wheel and actuators
to roll it. Said actuators are also used to keep the inherently unstable system upright which results in limited but perpetual position displacements of the Ballbot. This unsteady but stable system state, referred to as dynamic stability
, is much more robust with respect to external disturbances like pushes than static stability. This becomes more true the higher the inertia
of the robot is chosen (i. e. the higher its center of gravity is located).
The dynamic stability of a Ballbot, in combination with its spherical wheel and therefore the reduction of ground contact to one single point, results in a number of unique properties in the field of ground vehicles. A Ballbot is omnidirectional, it can roll in any direction at any given time, limited only by its dynamics but not by mechanical bindings as for example they exist for wheels (no motion in lateral direction possible). Therefore, it has no minimal turning radius and does not have to yaw in order to change direction. Further, a Ballbot has to lean into curves in order to compensate for centripetal forces
which results in very smooth and elegant motions, comparable to ice skating
. Therefore, standing at one spot and exploring the dynamical performance of a Ballbot are equally challenging tasks.
Another particularity is the non-minimum phase behavior a Ballbot. In order to move in any direction, a Ballbot has to pitch forward accordingly to achieve the necessary acceleration. Hence, to specify the desired direction of motion, for a short amount of time, the ball has to be actuated in reverse direction. Having reached a specified speed, the Ballbot moves upright again. Paradoxically, for braking again, its has to build up additional speed in order to overtake its center of gravity by its ball and to reduce speed afterwards in a backwards leaning posture.
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 inertia ratio of the robot body and its ball in order to prevent undesired ball spin, especially while yawing.
, usually three of them in order to control movements in a 2 dimensional plane and the body yaw angle. The motors normally require an energy supply or mobile energy storage device, power electronics
in order to provide the necessary motor currents and, in most cases, a gearbox.
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 encoders
(Ballbot CMU, BallIP, Rezero) are usually used. Measuring the body orientation is more complicated and is often done by the use of gyroscopes
(BallIP, NXT Ballbots) or, more generally, an Inertial Measurement Unit
(Ballbot CMU, BallIP, Rezero).
(Ballbot CMU, BallIP, Rezero), whereas some projects chose special chains (Ballbot CMU), special wheels (B. B. Rider), normal wheels (NXT Ballbots) or drive shafts (Ballbot CMU) in order to transmit the actuation forces onto the ball. Some wheel arrangements allow directly to control the yaw angle by introducing the tangential actuation forces on the sphere in a circular shaped configuration (BallIP, Rezero) instead of a cross-based configuration (Ballbot CMU and Adelaide, B. B. Rider, NXT Ballbots) which, in exchange, allows a higher speed. The solutions also differentiate with respect to the number of force transmission points used, Ballbot models with two (Ballbot, NXT Ballbots), three (BallIP, Rezero) and four (Ballbot Adelaide) of such points exist, all with individual effects on system performance.
Because also 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 gaps between the individual smaller wheels which would result in unsteady rolling motion. Therefore, the BallIP project has introduced a more complex omni wheel with a continuous circumferential contact line. which has been improved by equipping it with roller bearings and a high-friction coating by the team behind Rezero.
caused by rough contact surfaces.
A high friction coefficient of its surface and a low inertia are essential. In practice, in most cases a, massive core (BallIP, Ballbot Adelaide) or hollow ball (Ballbot CMU, NXT Ballbot, Rezero) in combination with an elastic and high friction coating is used. First generation Ballbot models sometimes used basket balls (B.B Rider) or bowling balls (BallIP, Ballbot Adelaide) because the manufacturing of a suitable coated ball is not straightforward and expensive. The Ballbot Rezero was the first model additionally fitted with a mechanical ball arrester which presses the ball against the actuators in order to further increase friction forces and a suspension to dampen vibrations.
. Most Ballbot models consider the actuation wheels in the model (NXT Ballbot, Ballbot Adelaide, Rezero), some neglect them and depend only on the robot body and the ball (CMU Ballbot). For the sake of simplicity, slip and friction are mostly neglected and the system is reduced to two identical 2D models which describe the system in two perpendicular planes. In addition, also simplified versions of the robot's odometry
, describing the dependence of the ball position on the wheel velocities and the body motion, have been introduced (BallIP). In fact, Rezero is so far the only Ballbot which is described completely in three dimensions.
Most Ballbots so far use state feed back control in combination with linear quadratic design methods for controller design (Ballbot CMU, NXT Ballbot, Ballbot Adelaide, Rezero). However, other approaches exist, for example the controller of the BallIP model is designed in a heuristic way while some projects use a fuzzy approach. State feedback controllers result in very robust performance for Ballbots because there is no necessity for observers, all states can be measured directly. However, the frequently chosen approach to control motor torques or currents respectively, leads to an unstable system and thus system failure as soon the Ballbot experiences a lift-off.
In general a Ballbot is granted most potential in public information, daily aid, service robot or for an application in the entertainment industry, for example as a toy. However, so far all Ballbots are still matter of research and serve very narrowly defined purposes.
and shown in 1994. This design had two wheels and used an inverted pendulum for control. The research team later introduced another machine that used a single prolate ellipsoid (somewhat like a rugby
ball) on an axle combined with a hinge to provide stability both forward and backward, through wheel torque, and side-to-side by leaning on the hinge. Since then the Segway Human Transporter has been released along with a number of robots based on its self-balancing concepts.
In 2006, Prof. Ralph Hollis and his team from Carnegie Mellon University
presented their "Ballbot", the first and so far largest Ballbot on a spherical wheel. During the following years, many other Ballbots were developed in Japan, Australia, the United States and Switzerland. During this period, the linguistic usage of the term "Ballbot" changed from entitling Hollis' prototype to denote the class of robots using a single ball for locomotion. In 2010, the BallIP project from Tohoku Gakuin University
and Rezero developed at ETH Zurich
experienced strong public interest because of their next generation performance.
Mobile robot
A mobile robot is an automatic machine that is capable of movement in a given environment.-Overview:Mobile robots have the capability to move around in their environment and are not fixed to one physical location...
designed to balance itself on a single spherical wheel (i.e. a ball), both while in motion or staying in place. 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.
Modern control theory
Control theory
Control theory is an interdisciplinary branch of engineering and mathematics that deals with the behavior of dynamical systems. The desired output of a system is called the reference...
provides dynamic stability which enables robust robot designs with narrower bases for improved navigability in narrow, crowded and dynamic environments.
Background and system properties
Historically, mobile robots have been made to be statically stable which results in the robot not needing to expend energy to remain still. This is typically achieved through the use of three or more wheels combined on a base. Robots built on this model are frequently unstable when moving unless equipped with a very wide base and low center of gravityCenter of gravity
In physics, a center of gravity of a material body is a point that may be used for a summary description of gravitational interactions. In a uniform gravitational field, the center of mass serves as the center of gravity...
. This severely limits their usefulness in normal human environments where human-machine interfaces must be placed at a reasonable height, as the pathways are typically too narrow and often have many obstacles (like humans) that will impair the robot's movement.
In addition, these systems have limitations that make them poorly suited to a constantly changing human environment. They cannot immediately roll in any direction, nor can they turn in place.
A Ballbot addresses these problems by using a single spherical wheel and actuators
Actuator
An actuator is a type of motor for moving or controlling a mechanism or system. It is operated by a source of energy, usually in the form of an electric current, hydraulic fluid pressure or pneumatic pressure, and converts that energy into some kind of motion. An actuator is the mechanism by which...
to roll it. Said actuators are also used to keep the inherently unstable system upright which results in limited but perpetual position displacements of the Ballbot. This unsteady but stable system state, referred to as dynamic stability
Stability theory
In mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions...
, is much more robust with respect to external disturbances like pushes than static stability. This becomes more true the higher the inertia
Inertia
Inertia is the resistance of any physical object to a change in its state of motion or rest, or the tendency of an object to resist any change in its motion. It is proportional to an object's mass. The principle of inertia is one of the fundamental principles of classical physics which are used to...
of the robot is chosen (i. e. the higher its center of gravity is located).
The dynamic stability of a Ballbot, in combination with its spherical wheel and therefore the reduction of ground contact to one single point, results in a number of unique properties in the field of ground vehicles. A Ballbot is omnidirectional, it can roll in any direction at any given time, limited only by its dynamics but not by mechanical bindings as for example they exist for wheels (no motion in lateral direction possible). Therefore, it has no minimal turning radius and does not have to yaw in order to change direction. Further, a Ballbot has to lean into curves in order to compensate for centripetal forces
Centripetal force
Centripetal force is a force that makes a body follow a curved path: it is always directed orthogonal to the velocity of the body, toward the instantaneous center of curvature of the path. The mathematical description was derived in 1659 by Dutch physicist Christiaan Huygens...
which results in very smooth and elegant motions, comparable to ice skating
Ice skating
Ice skating is moving on ice by using ice skates. It can be done for a variety of reasons, including leisure, traveling, and various sports. Ice skating occurs both on specially prepared indoor and outdoor tracks, as well as on naturally occurring bodies of frozen water, such as lakes and...
. Therefore, standing at one spot and exploring the dynamical performance of a Ballbot are equally challenging tasks.
Another particularity is the non-minimum phase behavior a Ballbot. In order to move in any direction, a Ballbot has to pitch forward accordingly to achieve the necessary acceleration. Hence, to specify the desired direction of motion, for a short amount of time, the ball has to be actuated in reverse direction. Having reached a specified speed, the Ballbot moves upright again. Paradoxically, for braking again, its has to build up additional speed in order to overtake its center of gravity by its ball and to reduce speed afterwards in a backwards leaning posture.
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 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. Beside 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 frictionFriction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and/or material elements sliding against each other. There are several types of 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 inertia ratio of the robot body and its ball in order to prevent undesired ball spin, especially while yawing.
Electric components
All Ballbots so far are equipped with electric motorsElectric motor
An electric motor converts electrical energy into mechanical energy.Most electric motors operate through the interaction of magnetic fields and current-carrying conductors to generate force...
, usually three of them in order to control movements in a 2 dimensional plane and the body yaw angle. The motors normally require an energy supply or mobile energy storage device, power electronics
Power electronics
Power electronics is the application of solid-state electronics for the control and conversion of electric power.-Introduction:Power electronic converters can be found wherever there is a need to modify a form of electrical energy...
in order to provide the necessary motor currents and, in most cases, a gearbox.
In order to actively control the position and body orientation of a Ballbot by a sensor-computer-actuator framework, beside a suitable microprocessor
Microprocessor
A microprocessor incorporates the functions of a computer's central processing unit on a single integrated circuit, or at most a few integrated circuits. It is a multipurpose, programmable device that accepts digital data as input, processes it according to instructions stored in its memory, and...
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 encoders
Rotary encoder
A rotary encoder, also called a shaft encoder, is an electro-mechanical device that converts the angular position or motion of a shaft or axle to an analog or digital code. The output of incremental encoders provides information about the motion of the shaft which is typically further processed...
(Ballbot CMU, BallIP, Rezero) are usually used. Measuring the body orientation is more complicated and is often done by the use of gyroscopes
Gyroscope
A gyroscope is a device for measuring or maintaining orientation, based on the principles of angular momentum. In essence, a mechanical gyroscope is a spinning wheel or disk whose axle is free to take any orientation...
(BallIP, NXT Ballbots) or, more generally, an Inertial Measurement Unit
Inertial measurement unit
An inertial measurement unit, or IMU, is an electronic device that measures and reports on a craft's velocity, orientation, and gravitational forces, using a combination of accelerometers and gyroscopes. IMUs are typically used to maneuver aircraft, including UAVs, among many others, and...
(Ballbot CMU, BallIP, Rezero).
Actuation concepts
In order to solve the rather complex problem of actuating a sphere without generating undesired friction, a variety of different attempts has been introduced. Most Ballbots make use of omni wheelsOmni wheel
Omni wheels or poly wheels, similar to Mecanum wheels, are wheels with small discs around the circumference which are perpendicular to the rolling direction. The effect is that the wheel will roll with full force, but will also slide laterally with great ease...
(Ballbot CMU, BallIP, Rezero), whereas some projects chose special chains (Ballbot CMU), special wheels (B. B. Rider), normal wheels (NXT Ballbots) or drive shafts (Ballbot CMU) in order to transmit the actuation forces onto the ball. Some wheel arrangements allow directly to control the yaw angle by introducing the tangential actuation forces on the sphere in a circular shaped configuration (BallIP, Rezero) instead of a cross-based configuration (Ballbot CMU and Adelaide, B. B. Rider, NXT Ballbots) which, in exchange, allows a higher speed. The solutions also differentiate with respect to the number of force transmission points used, Ballbot models with two (Ballbot, NXT Ballbots), three (BallIP, Rezero) and four (Ballbot Adelaide) of such points exist, all with individual effects on system performance.
Because also 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 gaps between the individual smaller wheels which would result in unsteady rolling motion. Therefore, the BallIP project has introduced a more complex omni wheel with a continuous circumferential contact line. which has been improved by equipping it with roller bearings and a high-friction coating by the team behind Rezero.
Ball
The ball is the core element of a Ballbot, it has to transmit and bear all arising forces and withstand mechanical wearWear
In materials science, wear is erosion or sideways displacement of material from its "derivative" and original position on a solid surface performed by the action of another surface....
caused by rough contact surfaces.
A high friction coefficient of its surface and a low inertia are essential. In practice, in most cases a, massive core (BallIP, Ballbot Adelaide) or hollow ball (Ballbot CMU, NXT Ballbot, Rezero) in combination with an elastic and high friction coating is used. First generation Ballbot models sometimes used basket balls (B.B Rider) or bowling balls (BallIP, Ballbot Adelaide) because the manufacturing of a suitable coated ball is not straightforward and expensive. The Ballbot Rezero was the first model additionally fitted with a mechanical ball arrester which presses the ball against the actuators in order to further increase friction forces and a suspension to dampen vibrations.
System modeling and control
The mathematical MIMO-model which is needed in order to simulate a Ballbot and to design a sufficient controller which stabilizes the system, is very similar to an inverted pendulum on a cartInverted pendulum
An inverted pendulum is a pendulum which has its mass above its pivot point. It is often implemented with the pivot point mounted on a cart that can move horizontally and may be called a cart and pole...
. Most Ballbot models consider the actuation wheels in the model (NXT Ballbot, Ballbot Adelaide, Rezero), some neglect them and depend only on the robot body and the ball (CMU Ballbot). For the sake of simplicity, slip and friction are mostly neglected and the system is reduced to two identical 2D models which describe the system in two perpendicular planes. In addition, also simplified versions of the robot's odometry
Odometry
Odometry is the use of data from moving sensors to estimate change in position over time. Odometry is used by some robots, whether they be legged or wheeled, to estimate their position relative to a starting location. This method is sensitive to errors due to the integration of velocity...
, describing the dependence of the ball position on the wheel velocities and the body motion, have been introduced (BallIP). In fact, Rezero is so far the only Ballbot which is described completely in three dimensions.
Most Ballbots so far use state feed back control in combination with linear quadratic design methods for controller design (Ballbot CMU, NXT Ballbot, Ballbot Adelaide, Rezero). However, other approaches exist, for example the controller of the BallIP model is designed in a heuristic way while some projects use a fuzzy approach. State feedback controllers result in very robust performance for Ballbots because there is no necessity for observers, all states can be measured directly. However, the frequently chosen approach to control motor torques or currents respectively, leads to an unstable system and thus system failure as soon the Ballbot experiences a lift-off.
Safety features
Due to the unique properties of a Ballbot, some models feature additional stability and safety functions, especially designed for Ballbots. For example the CMU Ballbot introduced three retractable landing legs which allow the robot to remain standing after being powered down. Rezero featured a roll-over safety mechanism in order to prevent serious damage in case of a system failure.Possible applications
Each of the three unique main characteristics of a Ballbot opens a range of practical applications. Dynamic stability allows a Ballbot to be used in dynamic environments with push-like disturbances like ships, trains and crowded areas, its omnidirectionality makes it suitable for quick navigation in grid-based environments and the Ballbot's favor for a high center of gravity allows unique perspectives in for example human interaction.In general a Ballbot is granted most potential in public information, daily aid, service robot or for an application in the entertainment industry, for example as a toy. However, so far all Ballbots are still matter of research and serve very narrowly defined purposes.
History
The first dynamically stable robot demonstrated for the public was built in JapanJapan
Japan is an island nation in East Asia. Located in the Pacific Ocean, it lies to the east of the Sea of Japan, China, North Korea, South Korea and Russia, stretching from the Sea of Okhotsk in the north to the East China Sea and Taiwan in the south...
and shown in 1994. This design had two wheels and used an inverted pendulum for control. The research team later introduced another machine that used a single prolate ellipsoid (somewhat like a rugby
Rugby football
Rugby football is a style of football named after Rugby School in the United Kingdom. It is seen most prominently in two current sports, rugby league and rugby union.-History:...
ball) on an axle combined with a hinge to provide stability both forward and backward, through wheel torque, and side-to-side by leaning on the hinge. Since then the Segway Human Transporter has been released along with a number of robots based on its self-balancing concepts.
In 2006, Prof. Ralph Hollis and his team from Carnegie Mellon University
Carnegie Mellon University
Carnegie Mellon University is a private research university in Pittsburgh, Pennsylvania, United States....
presented their "Ballbot", the first and so far largest Ballbot on a spherical wheel. During the following years, many other Ballbots were developed in Japan, Australia, the United States and Switzerland. During this period, the linguistic usage of the term "Ballbot" changed from entitling Hollis' prototype to denote the class of robots using a single ball for locomotion. In 2010, the BallIP project from Tohoku Gakuin University
Tohoku Gakuin University
is a private university in Sendai, Japan. It was founded under a Christian background is a private university in Sendai, Japan. It was founded under a Christian background is a private university in Sendai, Japan. It was founded under a Christian background (specifically the German Reformed...
and Rezero developed at ETH Zurich
ETH Zurich
The Swiss Federal Institute of Technology Zurich or ETH Zürich is an engineering, science, technology, mathematics and management university in the City of Zurich, Switzerland....
experienced strong public interest because of their next generation performance.
Ballbot projects
- The Ballbot Research Platform, a project conducted at Carnegie Mellon University (CMU)Carnegie Mellon UniversityCarnegie Mellon University is a private research university in Pittsburgh, Pennsylvania, United States....
: Research focus on Ballbots interacting with humans in human environments. - BallIP, a project conducted at Tohoku Gakuin UniversityTohoku Gakuin Universityis a private university in Sendai, Japan. It was founded under a Christian background is a private university in Sendai, Japan. It was founded under a Christian background is a private university in Sendai, Japan. It was founded under a Christian background (specifically the German Reformed...
: Research focus on transporting loads and cooperative behavior. - Rezero, a project conducted at ETH ZurichETH ZurichThe Swiss Federal Institute of Technology Zurich or ETH Zürich is an engineering, science, technology, mathematics and management university in the City of Zurich, Switzerland....
: Research focus on high agility, acceleration and speed. - Ballbot, a project conducted at the University of AdelaideUniversity of AdelaideThe University of Adelaide is a public university located in Adelaide, South Australia. Established in 1874, it is the third oldest university in Australia...
: Students have developed a NXT- and full scale version. - B. B. Rider, a project conducted at the University of TokyoUniversity of Tokyo, abbreviated as , is a major research university located in Tokyo, Japan. The University has 10 faculties with a total of around 30,000 students, 2,100 of whom are foreign. Its five campuses are in Hongō, Komaba, Kashiwa, Shirokane and Nakano. It is considered to be the most prestigious university...
: Focus on passenger transportation.
See also
- Autonomous robotAutonomous robotAutonomous robots are robots that can perform desired tasks in unstructured environments without continuous human guidance. Many kinds of robots have some degree of autonomy. Different robots can be autonomous in different ways...
- BigDogBigDogBigDog is a dynamically stable quadruped robot created in 2005 by Boston Dynamics with Foster-Miller, the NASA Jet Propulsion Laboratory, and the Harvard University Concord Field Station. BigDog is long, stands tall, and weighs , about the size of a small mule. It is capable of traversing...
(dynamically stable quadruped robot) - Electronic Stability ControlElectronic Stability ControlElectronic stability control is a computerized technology that may potentially improve the safety of a vehicle's stability by detecting and minimizing skids. When ESC detects loss of steering control, it automatically applies the brakes to help "steer" the vehicle where the driver intends to go...
- Humanoid robotHumanoid robotA humanoid robot or an anthropomorphic robot is a robot with its overall appearance, based on that of the human body, allowing interaction with made-for-human tools or environments. In general humanoid robots have a torso with a head, two arms and two legs, although some forms of humanoid robots...
(balance is required to stand and walk)- ASIMOASIMOis a humanoid robot created by Honda. Introduced in 2000, ASIMO, which is an acronym for "Advanced Step in Innovative MObility", was created to be a helper to people. With aspirations of helping people who lack full mobility, ASIMO is used to encourage young people to study science and mathematics...
(can traverse stairs and run)
- ASIMO
- Inverted pendulumInverted pendulumAn inverted pendulum is a pendulum which has its mass above its pivot point. It is often implemented with the pivot point mounted on a cart that can move horizontally and may be called a cart and pole...
- Robot locomotionRobot locomotionRobot locomotion is the collective name for the various methods that robots use to transport themselves from place to place. Although wheeled robots are typically quite energy efficient and simple to control, other forms of locomotion may be more appropriate for a number of reasons...
- Robotic unicycleRobotic unicycleThe problem of creating a self-balancing unicycle, a self-powered unicycle that balances itself in three dimensions, is an interesting problem in robotics and control theory....