[AMR] Finished update

electives/amr/parts/05_planning-control/00_feedback-control/01_pid.tex

@@ -1,4 +1,5 @@
 \subsection{Proportional-Integral-Differential (PID)}
-$u(t) = k_p e(t) + k_i \int_{t_0}^{t} e(\tau) \dx \tau + k_d \frac{\dx e(t)}{\dx t}$, where params $k_p$ (curr), $k_i$ (long-term), $k_d$ (trend) reduce corresp. errors
+$u(t) = K_p e(t) + K_i \int_{t_0}^{t} e(\tau) \dx \tau + K_d \frac{\dx e(t)}{\dx t}$, where params $K_p$ (curr), $K_i$ (long-term), $K_d$ (trend) reduce corresp. errors,
+with $e = r - y$
 
 \bi{Drone Control} ${_B}\vec{F}$ and ${_B}\vec{M}$ as in sect. \ref{sec:rigid-body-dynamics}, use $\vec{u}' = {_B}\vec{M}$.

electives/amr/parts/05_planning-control/01_motion-planning-exploration/00_intro.tex

@@ -3,9 +3,14 @@
 
 \bi{Free C-Space}: $\cC_{\text{free}}$, \bi{C-Space Obstacles} $\cC_\text{obst}$ (occupied)
 
-\bi{Collision checker}: $c(\vec{x}) : \cC \rightarrow \{ 0, 1 \}$ 
+\bi{Collision checker}: $c(\vec{x}) : \cC \rightarrow \{ 0, 1 \}$
 
 \bi{Visibility graph}: Connect corners, goal outside obstacles
 
 \bi{Voronoi Diagram}: Edges at max. dist. from obst. (benefit: safer paths).
 Also tends to be faster than Dijkstra.
+
+\bi{Discrete} {\scriptsize via graph/grid}: {\color{ForestGreen} complete solution}, {\color{red} Curse of dimensions}
+
+\bi{Continuous} {\scriptsize probabilistic}: {\color{ForestGreen} High-D okay, differential constraints ok},
+{\color{red} Probabilistic, depending on setup may not find correct sol. or run forever}

electives/amr/parts/05_planning-control/01_motion-planning-exploration/03_rrt.tex

@@ -1,3 +1,4 @@
+\newpage
 \subsubsection{Rapidly-Exploring Random Tree (RRT)}
 \begin{algorithm}
     \small
@@ -45,3 +46,4 @@ Extension to RRT* to make path better:
 \end{algorithm}
 
 \bi{Informed RRT*} extension: Once conn. betw. start and goal found, restrict sampling to (hyper)ellipsoid.
+$b = 0.5 \sqr{d^2 - ||x_s - x_g||^2}$.

electives/amr/parts/05_planning-control/01_motion-planning-exploration/04_collision-avoidance.tex

@@ -2,7 +2,7 @@
 \bi{Dynamic Window Approach} Assume: Robot moves inst. on circ. arcs $(v, \omega)$.
 Compute arcs with coll. {\color{ForestGreen} Accounts for Kino-Dyn}, {\color{red} Cost func prone to loc. min, assumes static obj}
 
-\bi{Vel. Obst.} Assume: Robot in str. line $(v_x, v_y)$. Comp pos with coll.
+\bi{Velocity Obstacles} Assume: Robot in str. line $(v_x, v_y)$. Comp pos with coll.
     {\color{ForestGreen} Vel. of obj}, {\color{red} prone to local optima, no kino-dyn.}
 
 \bi{Potential Field Methods} Define {\color{gray} \textit{repulsive}} and {\color{purple} attractive} potential $c = {\color{purple} c_{\text{att}}} + {\color{gray} c_{\text{rep}}}$.
@@ -10,5 +10,4 @@ With e.g. ${\color{purple} c_\text{att}} = \frac{1}{2} k_\text{att} ||\vec{x} -
         \frac{1}{2} k_\text{rep} \left( \frac{1}{\rho(\vec{x})} + \frac{1}{\rho_{\lim}} \right) & \rho \leq \rho_{\lim} \\
         0                                                                                       & \text{else}
     \end{cases}$
-
 {\color{ForestGreen} Simple control laws}, {\color{red} may trap in loc. min., no diff. const, no guar. to avoid coll}

electives/amr/parts/05_planning-control/02_learning-to-act/01_mdp.tex

@@ -16,16 +16,16 @@ Repeat until conv. to $V^*$ ($\tco{|\cU||\cX|^2}$ per iter). Optimal policy:
     \vec{\pi}^*(\vec{x}) = \text{argmax}_{\vec{u}} Q(\vec{x}, \vec{u})
 \]
 
-Using policy iter:
+Using \bi{policy iter}:
 \begin{algorithm}
     \begin{algorithmic}[1]
         \State Choose $\vec{\pi}_0(\vec{x})$
         \While{\textit{policy} has not converged}
-        \Repeat $V_{i + 1}^{\vec{\pi}_j}(\vec{x}) = Q(\vec{x}, \vec{\pi}(\vec{x}))$ $\forall \vec{x}$ and \textit{fixed} pol. $\vec{\pi}_j$
+            \Repeat $V_{i + 1}^{\vec{\pi}_j}(\vec{x}) = Q(\vec{x}, \vec{\pi}(\vec{x}))$ $\forall \vec{x}$ and \textit{fixed} pol. $\vec{\pi}_j$
             \Until{values converge}
         \EndWhile
         \State One step: $\vec{\pi}_{j + 1}(\vec{x}) = \text{argmax}_{\vec{u}} Q(\vec{x}. \vec{u})$ with $V_i = V_{i + 1}^{\pi_j}$
     \end{algorithmic}
 \end{algorithm}
 
-Model-based learning uses empirical models of $\cT$ and $\cR$
+\bi{Model-based} learning uses empirical models of $\cT$ and $\cR$