A motor rotates the axle on which the pendulum weight is suspended. When the pendulum swings forward, the system's center of mass moves ahead of the vertical axis through the sphere's ground-contact point. Gravity acting on the offset mass creates a torque about the contact point, rolling the shell toward the swing direction. Holding a constant offset yields continuous motion, while reversing the offset side reverses travel. In single-axis systems the pendulum moves only in the driving plane (fore/aft). In two-axis systems a second axle shifts the mass sideways: the sphere tilts and changes its rolling path, enabling steering. Attainable speed and acceleration depend on the pendulum's mass and arm length, which set the maximum available torque. The system is nonholonomic and underactuated, so precise control requires sensor feedback (e.g. an IMU).
How to propel and steer a fully sealed spherical robot without protruding wheels, legs, or exposed drive parts, while keeping the shell tight and resistant to dust, water, and impacts.
A movable mass suspended inside the shell whose deflection shifts the system's center of gravity.
Motor that rotates the pendulum axle and holds its deflection; the source of torque controlling the mass position.
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Element linking the motor to the pendulum; defines the plane in which the mass moves (one axle for fore/aft travel, a second for steering).
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The outer, usually sealed sphere that rolls on the ground and protects the robot internals.
Controllers, sensors (e.g. IMU), and a battery enclosed inside, providing the feedback needed for the underactuated dynamics.
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Driving torque is bounded by the pendulum mass times arm length, so the robot struggles on steep slopes and high-rolling-resistance ground.
In single-axis systems the same mass handles both driving and heading changes, complicating independent control and increasing controller complexity.
Underactuated dynamics cause residual pendulum swing and shell wobble when stopping or changing speed.
Halme, Schönberg, and Wang publish early work on motion control of a spherical robot based on center-of-mass shifting.
Commercial spherical platforms (e.g. Sphero BB-8) popularized locomotion based on internal mass shifting.
Greater mass increases available driving torque (and climbable slopes) but raises energy use and inertia.
A longer arm increases torque for the same deflection but is bounded by the shell's inner diameter.
One axis enables fore/aft travel; a second axis adds direct steering via sideways mass shifting.
The upper range of pendulum deflection bounds the maximum torque and attainable acceleration.
