Robot control
Twist
Definition
A twist is a six-component representation of a rigid body's instantaneous motion, combining angular and linear velocity. Its numerical values depend on the reference frame and the point used for the linear component.
Also known as: Rigid-body twist
Updated
Angular and linear motion together
A rotating and translating robot hand needs more than a three-component linear velocity to describe its motion. A twist combines three angular components with three linear components. Modern Robotics orders the angular components first and relates the result to a screw axis multiplied by a motion rate.
The components do not have identical units: angular speed and linear speed describe different physical quantities.
State the frame and reference point
The same rigid motion can have a body-frame or space-frame representation. Moving the reference origin changes the linear component when angular velocity is present. The linear part of a spatial twist is therefore not automatically the ordinary velocity of the body's origin.
The twist transformation lesson uses a 6-by-6 adjoint matrix to change representation. Simply multiplying a six-vector by a 4-by-4 pose transform is not valid.
Twists are useful control quantities
A robot Jacobian maps joint velocities to a compatible end-effector twist. MIT's manipulation notes use spatial velocity commands for differential inverse kinematics.
Angular velocity is not generally the componentwise derivative of Euler angles. A twist also differs from a wrench, which contains force and moment rather than motion.
Sources
Related terms
Screw theory
Screw theory is a geometric framework for describing rigid-body motion and forces using axes, rotation, translation, and pitch. In robotics it provides the basis for twist and wrench representations and screw-axis formulations of kinematics.
Wrench
A wrench is a six-component representation of force and moment acting on a rigid body. It combines three force components with three moment components about a specified reference point.
Robot Jacobian
A robot Jacobian is a configuration-dependent matrix that maps joint velocities to a chosen task velocity, often an end-effector twist. It describes the local relationship between joint motion and task motion.