Kinematics (FK / IK)
Forward & inverse kinematics, Jacobians.
Why it matters in robotics
Kinematics is the bread-and-butter screening topic for any manipulation, arm, or humanoid role: interviewers expect you to map joint angles to end-effector pose (FK) and back (IK), and to reason about the Jacobian on the spot. Expect to derive or sketch a Jacobian, explain singularities and redundancy, and contrast analytical vs. numerical IK (Newton / damped least squares), including why IK can have no solution or infinitely many. Fluency with frames, the product-of-exponentials formula, and Jacobian-based velocity control signals genuine hands-on robotics maturity.
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
FK maps joint angles to end-effector pose; IK inverts it; the Jacobian links joint and end-effector velocities.
What to study
- āForward kinematics: DH parameters and the product-of-exponentials (PoE) formula in space and body frames
- āVelocity kinematics: the space/body Jacobian, singularities, manipulability, and statics duality (force = J^T wrench)
- āInverse kinematics: closed-form/analytical solutions vs. numerical Newton-Raphson and damped least squares (pseudoinverse)
- āRedundancy and null-space control: handling >6-DOF arms and using the Jacobian for resolved-rate motion control
Study by time budget
Pick the path that fits the time you have before your interview.