diff --git a/electives/others/amr/autonomous-mobile-robots-cheatsheet.pdf b/electives/others/amr/autonomous-mobile-robots-cheatsheet.pdf index 6b25456..1547d8e 100644 Binary files a/electives/others/amr/autonomous-mobile-robots-cheatsheet.pdf and b/electives/others/amr/autonomous-mobile-robots-cheatsheet.pdf differ diff --git a/electives/others/amr/parts/01_kinematics/03_temporal-models.tex b/electives/others/amr/parts/01_kinematics/03_temporal-models.tex index 8b0dd31..754bbb3 100644 --- a/electives/others/amr/parts/01_kinematics/03_temporal-models.tex +++ b/electives/others/amr/parts/01_kinematics/03_temporal-models.tex @@ -1,3 +1,6 @@ \subsection{Temporal Models} -Often use cont. time n.-lin. system of ODE $\dot{\vec{x}} = \vec{f}_C(\vec{x}(t), \vec{u}(t))$, with measurements $\vec{z}(t) = \vec{h}(\vec{x}(t))$. -Need linearised (around $\vec{f}_C(\vec{\overline{x}}, \vec{\overline{y}}) = 0$, at \bi{equilibrium}) +Often use cont. time n.-lin. system of ODE $\dot{\vec{x}} = \vec{f}_C(\vec{x}(t), \vec{u}(t))$, with measurements $\vec{z}(t) = \vec{h}(\vec{x}(t)) + \vec{v}(t)$. +Need linearised (around $\vec{f}_C(\vec{\overline{x}}, \vec{\overline{y}}) = 0$, at \bi{equilibrium}):\\ +$\delta \vec{\dot{x}}(t) = \vec{f}_C(\vec{\overline{x}}, \vec{\overline{u}}) + \mat{F}_C \delta \vec{x}(t) + \mat{G}_C \delta \vec{u}(t) + \mat{L}_C \vec{w}(t)$\\ +$\delta \vec{z}(t) = \mat{H} \delta \vec{x}(t) + \vec{v}(t)$. +Herein, $\mat{H}$ is measurements, $\mat{F}_C$ system, $\mat{G}$ input gain, $\vec{w}$ process noise, $\vec{v}$ measurement noise