Spatial vectors

In RobCoGen, 6D coordinate vectors representing spatial-vectors (twists and wrenches) always follow this convention:

• the first three coordinates represent the angular part of the quantity (either angular velocity or torque)
• the last three coordinates represent the linear part (linear velocity or force)

As far as C++ is concerned, the iit::rbd namespace has some elements to abstract the underlying convention, like a 6-value enum to index symbolically the vectors.

Reference frames

The coordinate frames of links and joints are not mentioned explicitly in robot-model files.

In RobCoGen, the ID (name) of a reference frame defaults to the name of the link or the joint it is attached to.

This policy is implemented in a dedicated module of the Robot Model Tools package.

Coordinate transformation matrices

Coordinate transforms, in the generated code but also in documentation, follow a naming convention in the form:

A_X_B

where A and B refer to some reference frame. This notation immediately conveys the effect of the transform: when right-multiplied by a column vector of coordinates of B, it gives the coordinates of A, as in

v_A = A_X_B * v_B

For example, the transform that maps coordinates in the frame of a link called wrist to coordinates of link trunk, will typically appear in the source code with the identifier trunk_X_wrist.

Left and right frames

In the notation A_X_B, the frames A and B are sometimes referred to as the left and right frame, respectively, because of their relative position with respect to X. The figure below illustrates the notation.

In the first equation A is the left frame while B is the right frame. In the second equation it is the other way round.

Given a certain context, a pair right/left frame uniquely identifies the semantics of a coordinate transform.

Polarity

The two complementary transforms A_X_B and B_X_A are said to have opposite polarity.