Physical AI Lab // Episode 1.1 // One-pager

Coordinate frames and kinematics

Getting a robot arm to reach the cup on the table

Three key points

  1. Coordinate frames: to say "where", first fix an origin and directions; the robot constantly converts camera coordinates into the base's coordinate frame.
  2. Forward kinematics: given each joint's angle, the hand's position is unique and repeatable, worked out in one step (our arm has 3 joints; one research arm has 7 degrees of freedom, O).
  3. Inverse kinematics: working back from "where the hand should go" to joint angles may give many solutions (elbow up / elbow down; at most 16 for 6 joints or fewer, R), or none (out of reach = outside the workspace).

Evidence: O official · R research · M media

O7degrees of freedom (joints) in the arm of Franka Research 3, a force-controlled robot arm, which has 7; the arm in our lab has only 3
R16solutions at most; the inverse kinematics of an arm with six joints or fewer has at most 16 sets (the paper reports)

Further reading