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.
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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 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.[1]
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).[2]
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.[3] 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.[3]
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 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.[3]
All Ballbots so far are equipped with electric motors, 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[4]) or, more generally, an Inertial Measurement Unit (Ballbot CMU, BallIP, Rezero).
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 wheels (Ballbot CMU, BallIP, Rezero), whereas some projects chose special chains (Ballbot CMU), special wheels (B. B. Rider[5]), normal wheels (NXT Ballbots[4]) 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[3]. 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.[6]
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.[7] which has been improved by equipping it with roller bearings and a high-friction coating by the team behind Rezero.[3]
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. 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[7], 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.[3]
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 cart. 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.[3] 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[7] while some projects use a fuzzy approach[8]. 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.[3]
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.[1] Rezero featured a roll-over safety mechanism in order to prevent serious damage in case of a system failure.[3]
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.
The first dynamically stable robot demonstrated for the public was built in Japan 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.[1]
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.