Zenn tutorial breaks down the quaternion product: 5 use cases from IMU attitude updates to SLERP
4310sy · x · 2026-11-07
A Zenn article, Calculation Quaternion, explains where and why the quaternion product (Hamilton product) shows up in robotics and sensing, praised by a resharing reader for its concrete examples around self-localization and sensor fusion.
The article walks through five scenarios:
- Attitude update: build a micro-rotation Δq from IMU angular velocity and update pose via q(t+Δt) = q(t) ⊗ Δq.
- Frame conversion: rotate body-frame acceleration into the world frame with q ⊗ abody ⊗ q, clarifying what gravity readings really mean.
- Composing rotations: combine terrain, body, and joint rotations for robots/drones, stressing non-commutativity — wrong order, wrong pose.
- Interpolation: SLERP in 3DCG/animation relies on the product (and its inverse) to compute pose differences.
- Sensor fusion correction: Δq = qobs ⊗ q̂⁻¹ captures the gap between predicted attitude and camera/GPS observations in Kalman filtering.
Full expansion formulas for the multiplication are included, making it a solid primer for self-localization, SLAM, or kinematics work.
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