cs.ROOct 16, 2026

Rollbot 2: Agile Locomotion by a Single-Actuator Spherical Robot

Authors: Jingxian Wang*, Chen Yu*, Sam Kriegman, Michael Rubenstein

Organizations: Northwestern University, Evanston, IL 60208 USA.

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Abstract

Reducing actuator count simplifies robot hardware but also removes independent inputs for maneuvering. The original Rollbot steered by modulating a quasi-stable helical orbit, but moved slowly and relied on external motion capture. Rollbot 2 preserves the single-actuator design while its redesigned mass distribution enables near-straight rolling and more direct travel toward commanded paths and beacon targets. Onboard inertial and ultra-wideband sensing support learned steering, beacon seeking, and waypoint following through one motor-velocity command. Rollbot 2 autonomously approaches UWB beacons without motion capture and completes a 468m manually commanded indoor route at 0.87m/s. On the shared 4.8m ``N'' waypoint benchmark, all 16 trials complete the path with a mean traversal time of 10.8s and mean time-averaged deviation of 7cm. Its fastest traversal takes 8.0s, over 70 times faster than the original Rollbot's 564~s run despite minor protocol differences. These results show how mechanical redesign, onboard sensing, and learning-based control improve the agility and autonomy of a single-actuator spherical robot.

Figures & tables

Fig. 1: Interior and exterior of Rollbot 2. The robot has an outer diameter of 20 cm and weighs 0.90 kg.
Fig. 2: Exploded view of Rollbot 2. As in the original Rollbot, the sole actuator is a central geared BLDC motor that drives the pendulum around the purple axis.
Fig. 3: Illustration of the Rollbot 2 mass distribution. The shell CoM (blue triangle) and pendulum CoM (red circle) are both offset from the shell center, while the shell center lies approximately in the overall CoM trajectory plane. Not drawn to scale. The ground frame is denoted by SS , and the local body frame denoted by S′S^{\prime} has its origin at the sphere center with Z′Z^{\prime} axis aligned with the motor rotation axis.
QuantityValueExplanation
RR0.10 0.10\, mOuter radius of shell
MM0.445 0.445\, kgMass of shell
mm0.455 0.455\, kgPendulum mass
dsd_{s}0.0273 0.0273\, mShell CoM offset from shell center
dpzd_{pz}0.0280 0.0280\, mPendulum CoM offset from shell center in the Z′Z^{\prime} direction
rpr_{p}0.0702 0.0702\, mPendulum CoM offset from motor rotation axis
TABLE I: Physical and actuator parameters of Rollbot 2.
Fig. 4: Waypoint coordinate systems for a 60∘60^{\circ} turn. (a) Contours of progress xcx^{c} (orange) and cross-track error ycy^{c} (green). (b) Active path tangent x′′x^{\prime\prime} (orange) and left-normal direction y′′y^{\prime\prime} (green), with y^′′=−x^′′×z^′′\hat{y}^{\prime\prime}=-\hat{x}^{\prime\prime}\times\hat{z}^{\prime\prime} .
Fig. 5: Rolling-with-steering results. Left: planar trajectories for different steering commands. Right: measured speed and heading θ\theta over time for the same trials.
Fig. 6: Beacon-seeking results. Left: planar trajectories for repeated trials toward the target region. Black arrows indicate the initial z′z^{\prime} direction, and trajectory color indicates elapsed time (green: start; red: over 10 s). Right: target-distance histories for the same trials; the horizontal time axis is compressed after 10 s.
Fig. 7: N-shape waypoint-following results for Rollbot 2. (a) Trajectories from 16 trials following the 4.8 m “N” trajectory. (b) Fastest trial, which completes the path in 8.0 s. (c) A representative trial. Rollbot 2 consistently traverses the full path, although it sometimes moves back and forth near turns to adjust its heading before traversing the next line segment.
Fig. 8: Comparison between the original Rollbot and Rollbot 2 on the 4.8 m “N” trajectory. The gray line shows the desired trajectory, while the blue and orange curves show the trajectories of Rollbot 1 and Rollbot 2, respectively.
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