Question

Hw 14 question #2, I'm having trouble understanding the adjoint formula given in class

Answer 1

In the notes Dr. Vela expanded the formula\[F _{C}=Ad ^{T}_{g _{C}^{B}}*F _{B}\] as being \[\left(\begin{matrix}fc \\ \tau _{c}\end{matrix}\right)=\left[\begin{matrix}R _{BC}^{T} & 0 \\ -R _{BC}^{T}*dhat _{BC} & R _{BC}^{T}\end{matrix}\right]*\left(\begin{matrix}f _{B} \\ \tau _{B}\end{matrix}\right)\] but when I calculated this I got a 4x3 matrix. I think the part confusing me is the dhat. I multiplid J*d to get this. is that not right?

Answer 2

The Adjoint matrix for SE2 is a 3x3. You can look at it in the formulas from last week's homework. What you wrote there is the SE3 adjoint matrix. That should clear things up. You should be multiplying a 3x3 by a 3x1.

Answer 3

Oh okay I didn't even think about that. Thanks!

Answer 4

Ish a lil pickle *-*

Answer 5

hurray i found a mod nobody knows about while exploring a dead subject xD