[AMR] Finished update

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}