Design and Analysis of a Four-Pendulum Omnidirectional Spherical Robot

This paper presents the design, analysis, and comparison of a novel four-pendulum spherical robot. The proposed mechanism rolls omnidirectionally via four tetrahedrally-located pendulums that shift the robot's center of mass to create rolling torque. The nine dynamic equations of motion are derived via the Lagrangian and nonholonomic constraint equations, and then simulated numerically; results show successful propulsion with expected behaviors. The mechanism is then compared to existing center-of-mass designs in terms of directionality, drive torque arm, and inertia eccentricity. In these regards, the four-pendulum design is a balance of existing designs: it is omnidirectional with eccentricity and torque capability that are in the middle of the range exhibited by existing designs. In addition, the new four-pendulum mechanism has been built and tested as a successful proof-of-concept prototype.