Drake

Consider the definition of a contact with interpenetrating collision elements A
and B
.
The single, computed contact point serves as the origin of a contact frame C
, so is designated Co
; we'll shorten that to just C
when it is clear we mean the point rather than the frame. We define the normal as pointing outward from the deformed surface of B
towards the deformed interior of A
. The C
frame's zaxis is aligned along this normal (with arbitrary x and yaxes). We are also interested in the points of bodies A
and B
that are coincident with Co
, which we call Ac
and Bc
, respectively. Because the two forces are equal and opposite, we limit our discussion to the force f
acting on A
at Ac
(such that f
acts on B
at Bc
).
The computation of the contact force is most naturally discussed in the contact frame C
(shown in Figure 1).
The contact force, f
, can be decomposed into two components: normal, fₙ
, and tangential, fₜ
such that f=fₙ+fₜ
. The normal force lies in the direction of the contact frame's zaxis. The tangential component lies parallel to the contact frame's xy plane. In Drake's compliant contact model, the tangential force is a function of the normal force.
The detailed discussion of the contact force computation is decomposed into two parts: a highlevel engineering discussion addressed to end users who care most about working with the model and a further detailed discussion of the mathematical underpinnings of the implemented model. The practical guide should be sufficient for most users.
Next topic: Working with Contacts in Drake