Reproduce “Galilean Symmetry in Robotics” on OpenResearch
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About this paper
Robert Mahony, Jonathan Kelly, Stephan Weiss
The paper develops a robotics-oriented account of Galilean symmetry, bringing spatial transformations, time offsets, and inertial velocity into one mathematical framework. Analytic examples show how it relates to rotating-frame navigation, manipulator kinematics, and sensor fusion with timestamp uncertainty; the work is primarily a tutorial and set of derivations, not an empirical comparison.
Key insights
- A Galilean transformation makes time and inertial velocity part of the same geometric representation as spatial pose; a time offset can therefore contribute to spatial uncertainty under a velocity boost.
- Inertial velocity and coordinate velocity are not interchangeable in non-inertial frames: rotation and acceleration of the reference frame introduce additional terms into coordinate motion.
- The two velocity conventions suit different settings: Galilean frames clarify vehicle navigation, while extended poses make joint-driven manipulator motion easier to compose.
Summary by alphaXiv.
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