Relaxation Dynamics in Oblate Spherical Rolling Robots
Micah Oevermann, Robert Ambrose
AI summary
Problem
Prior spherical robot models have ignored or simplified the non-uniform inertial profiles of outer shells, leaving the cause of high-speed wobbling and end-over-end flipping unexplained.
Approach
The authors adapt satellite relaxation dynamics theory to constrained rolling systems by deriving new governing equations that incorporate translational constraints, then validate the model with slope and flat-ground experiments.
Key results
- Derived dynamics showing rolling constraints act as a pseudo-dissipative load
- Proved oblate shells naturally relax toward major-axis rotation, causing hubcap-to-hubcap flipping
- Experimentally verified relaxation instability and found shell pressure has negligible effect on relaxation rates
- Bridged satellite dynamics theory with ground robotics to explain high-speed rolling instability
Why it matters
Informs the design and control of high-speed spherical robots by revealing how inertial profiles and rolling constraints dictate dynamic stability.
Abstract
Spherical robots rolling on flat ground often ex- hibit a wobbling motion that, at higher speeds, can escalate into end-over-end flipping. This paper proposes a fundamental dynamic cause of this instability: a relaxation effect analogous to the Intermediate Axis Theorem. Rotating bodies with oblate inertial profiles under dissipative loads tend to reorient toward spinning about their major moment of inertia, leading to the observed wobbling in spherical robots. While relaxation dynamics are well-studied in satellites and asteroids, this effect has not been previously applied to rolling systems. We extend these methods to constrained spherical robots, derive the governing dynamics, and conduct experiments with an empty shell on a slope and a reduced pendulum on flat ground and in water to aid in the discussion. Results suggest that translational rolling constraints act as a pseudo-dissipative load to drive the relaxation effect. This work bridges the fields of satellite dynamics theory and ground robotics, providing new insights into the stability of high-speed rolling robots to influence future hardware and control design choices.