Rigid-Body Motion & Transforms
Rotations, quaternions, SE(3) — where things are in space.
Why it matters in robotics
Almost every robotics interview touches spatial reasoning: expressing a point or pose in different frames, composing transforms, and converting between rotation representations. Interviewers probe whether you understand why quaternions avoid gimbal lock, what makes a matrix a valid rotation (SO(3) orthonormality), and how SE(3) bundles rotation and translation — because getting frames wrong silently breaks perception, planning, and control. Fluency here signals you can debug the coordinate-frame bugs that dominate real robot systems.
Application focus
The same topic, tailored to the robot you're building. Your choice is remembered across the roadmap and every topic.
At a glance
How rigid-body pose is represented: orientation lives in SO(3) (equivalently a unit quaternion), and combining it with position gives a full pose in SE(3).
What to study
- ✓Rotation representations and their tradeoffs: rotation matrices (SO(3)), Euler angles and gimbal lock, axis-angle, and unit quaternions
- ✓Homogeneous transformation matrices and the SE(3) group: composing rotation + translation, frame conventions, and inverting a transform
- ✓Quaternion algebra: unit-quaternion rotation, multiplication/composition, conjugate as inverse, and quaternion-to-matrix conversion
- ✓Exponential coordinates and twists: so(3)/se(3), the matrix exponential and log map, and screw-axis interpretation of rigid-body motion
Study by time budget
Pick the path that fits the time you have before your interview.