Robotic Systems · Lecture 7

Recursive inverse dynamics and the mass matrix

Simeon Nedelchev

RNEA

A forward pass propagates motion.

A backward pass accumulates wrenches.

Joint projection gives required generalized force.

\operatorname{ID}(q,v,a)=M(q)a+c(q,v)

This ideal form assumes a declared force convention.

M_{:j}=\operatorname{ID}(e_j)-\operatorname{ID}(0)

All calls use the same state.

$M=\begin{bmatrix}5&2\\2&1\end{bmatrix}$ , $c=(3,4)$

$\operatorname{ID}(e_1)=(8,6)$

Difference: $(5,2)$

Composite subtree inertias support mass-matrix assembly.

One mass matrix answers many acceleration queries.

Compare APIs by the quantity they return.