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a/electives/amr/parts/01_kinematics/01_forward.tex +++ b/electives/amr/parts/01_kinematics/01_forward.tex @@ -8,5 +8,8 @@ $ \begin{bmatrix} L_1 \sin(\theta_1) + L_2 \sin(\theta_1 + \theta_2) \end{bmatrix}$\\ } -With workspace (pos) $W$ for $\theta_1, \theta_2 \in [-\pi, \pi]$ -% TODO: Example? (w02s42 possibly) +Similar for $n$R sys (more angles). Wspc $W$ $\theta_1, \theta_2 \in [-\pi, \pi]$. +Last dim may be sum of angles. Jacobian: see \ref{sec:ms-lin} + +\shortdefinition[Singularity] Loss of deg of Freed. $\det(\mat{J}(\vec{\theta})) = 0$ +% TODO: Determinant computation diff --git a/electives/amr/parts/03_multi-sensor-estimation/00_linearization.tex b/electives/amr/parts/03_multi-sensor-estimation/00_linearization.tex index 8cfc94e..b3c8e4a 100644 --- a/electives/amr/parts/03_multi-sensor-estimation/00_linearization.tex +++ b/electives/amr/parts/03_multi-sensor-estimation/00_linearization.tex @@ -1,4 +1,5 @@ \subsection{Linearization} +\label{sec:ms-lin} $\vec{f}(\vec{x}) \approx \vec{f}(\vec{\overline{x}}) + \mat{J}_{\vec{f}} \big|_{x = \overline{x}}(\vec{x} - \vec{\overline{x}})$, $f'$, no vec in 1D; $\vec{\overline{x}}$ lin. p. \shortdefinition[Jac.] $\mat{J}_{\vec{f}}$ rows for eq of $\vec{f}$ cols for vars of each eq.