Math & Kinematics

Twist (Spatial Velocity)

A twist is the six-dimensional velocity of a rigid body, combining a three-dimensional angular velocity with a three-dimensional linear velocity into a single element of se(3), the Lie algebra of the group of rigid-body motions. Twists unify the description of screw motion: every rigid displacement is the exponential of a twist, a fact exploited by the product-of-exponentials kinematics formulation. The robot Jacobian maps joint velocities to the end-effector twist, and ROS messages carry commanded twists to mobile bases.

Why it matters for physical AI

Learned policies commonly output end-effector or base twists as their action representation, and fluency with twists and their frame transformations is essential for correctly wiring policies to real controllers across embodiments.