Frames (Robotics)
A frame consists of an origin
To represent the position and orientation of a rigid body in space, we first first a body frame
- Origin of the body frame
- Directions of the coordinate axes of the body frame
Where both of the above are expressed in the space frame coordinates.
The position and orientation of an object's coordinate frame is referred to as its pose.
The relative pose of a frame
In practical applications, one would have a frame for various entities for e.g. a frame for each joint of a robot, a frame for the camera of the robot and so on. This can be visualized as a collection of coordinate axes, with the world coordinate frame
Below are the key aspects we need to represent with respect to frames:
- Orientations, represented via SO(n).
- Angular velocities, represented via so(3) or exponential coordinates.
- Rigid body transformations, represented via SE(n).
- Rigid body velocities, represented via twists.