Rollbot: a Spherical Robot Driven by a Single Actuator

TL;DR

Rollbot demonstrates that a spherical robot can attain controllable 2D locomotion with a single actuator by employing a pendulum-driven barycentric mechanism and a non-holonomic rolling constraint. The work develops a unified dynamics model for internal masses, analyzes the quasi-static regime and perturbation-based stability, and presents a hardware design plus a center-of-curvature control strategy that are validated through open-loop, circular, and waypoint experiments. Key contributions include the explicit equation of motion, the $R_0$–$\omega_0$ relationship, and a practical PID-based controller enabling 2D navigation with minimal actuation. This minimalist robot serves as a versatile testbed for underactuated robotics, with future enhancements including onboard sensing and more advanced path planning on varied surfaces.

Abstract

Here we present Rollbot, the first spherical robot capable of controllably maneuvering on 2D plane with a single actuator. Rollbot rolls on the ground in circular pattern and controls its motion by changing the curvature of the trajectory through accelerating and decelerating its single motor and attached mass. We present the theoretical analysis, design, and control of Rollbot, and demonstrate its ability to move in a controllable circular pattern and follow waypoints.

Figures (12)

• Figure 1: Photo of inside and outside of Rollbot. Rollbot has a outer diameter of $24\,$cm and weighs $1.2\,$kg.
• Figure 2: An exploded view of Rollbot. The only actuator is the BLDC motor at the center which can rotate around the purple axis.
• Figure 3: Illustration of relevant quantities. O-XYZ is the ground reference frame $G$, O'-X'Y'Z' is the shell's body reference frame $B$. $\vec{s}$ is the position of the center of the shell in $G$, $\vec{\omega}$ is the angular velocity of the shell in $G$, and $\vec{r}\,'$ is the position of the mass in $B$. $R,M,I$ are the radius, mass, and the moment of inertia of the shell respectively, and $m$ is the mass of the point mass. $\vec{f},\vec{\tau}$ are the externally applied force and torque on the shell with respect to $O'$, $\vec{N}$ is the sum of normal and friction force ground applies on the shell, and $\vec{F}$ is the force shell applies on the point mass.
• Figure 4: Illustration of quasi-static state at $t=0$. O-XYZ is the non-moving ground reference frame $G$ with origin at the intersection of revolving axis $l$ and ground plane, and X axis pointing towards the contact point. O'-X'Y'Z' is the shell's body reference frame $B$ with Y' axis parallel to $Y'$ axis and Z' aligned with the rotation axis of the motor and on X-Z plane, and the angle between Z and Z' is $\xi$. The shell is revolving around $l$ at angular velocity $\Omega \hat{z}$, plus the shell itself is also spinning at angular velocity $\vec{\omega}_s = - \omega_0 \hat{z}'$ in quasi-static state. The shell's revolving radius is $R_0$.
• Figure 5: Plots of key parameters of quasi-static state versus driving speed $\omega_0$. (a) to (d) show the trends of revolving radius $R_0$, revolving angular velocity $\Omega$, tilting angle of rotating axis of the motor $\xi$ and rotating angle of pendulum mass $\theta_0$ respectively.