1 files changed, 57 insertions, 8 deletions
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+++ b/doc/results.tex
@@ -3,18 +3,67 @@
 
 \section{Reflexes in Simple Leg Model}
 
-\TODO{Describe results}
+The simulation of the \emph{Simple Leg Model} led to the expected stretch reflex behavior. Given an initial 
+activation of the \emph{Rectus Femoris}, the \emph{Biceps Femoris} was caused to shorten proportional to the 
+speed of the shortening of the \emph{Rectus Femoris}. Since this will again cause \emph{Rectus Femoris} to be 
+shortened, the reflex is triggered in the other direction. For initial tests, the knee joint in the model was 
+fixed in all but one degree of freedom (pin joint) in order to permit flexion and tension. Unfortunately this 
+didn't lead to a realistic behavior with respect to the movement of the lower leg, as the knee joint remained 
+fixed during the entire simulation (see figure \ref{fig:simpleleg_sequence} for a sequence of two stretch 
+cycles). However since this simulation served as a test of the principal methods and the results were 
+satisfying enough, this problem was not further investigated.
 
-\section{Random Data}
+\begin{figure}[htb!]
+\centering
+\includegraphics[width=\textwidth]{images/simple_leg_sequence.png}
+\caption{Sequence of the \emph{SimpleLeg} model during simulation of two cycles of the stretch reflex.}
+\label{fig:simpleleg_sequence}
+\end{figure}
 
-In order to validate the principal working of the two-legged musculoskeletal model (see section \ref{subsec:two_legged_model}) and the corresponding controller (see section \ref{subsec:locomotor_primitives_controller}), random data resembling muscle activation patterns was generated for all the 53 muscles of the model.
+\section{Random Data in Two-Legged Model}
 
-\TODO{Add example plot}
+In order to validate the principal working of the two-legged musculoskeletal model (see section 
+\ref{subsec:two_legged_model}) and to test the corresponding controller (see section 
+\ref{subsec:locomotor_primitives_controller}), random data resembling muscle activation patterns was generated 
+for all the 32 muscles of the model. In the initial version, the data contained discontinuities and the 
+activation values were generally too high. As a consequence, the simulation of the model took very long or in 
+some situations didn't complete at all.
 
-Problems with random data: discontinuities, not fitted to muscle model and musculoskeletal model. Simulation time thus very high (or even unable to simulate). Smoothing of data needed, smaller activations. Works, but leads to unrealistic behavior.
+Thus the script used to generate the data was adjusted in order to smoothen the data and provide smaller 
+activation values. With this second set of data, the simulation succeeded, but of course showed unrealistic 
+behavior. Since the simulation now completed with any type of generated pattern, the model and controller were 
+considered ready for usage with the real data.
 
-\section{Locomotor Primitives Study Data}
+\section{Locomotor Primitive Patterns in Two-Legged Model}
 
-\TODO{Add example plot}
+Only results for an adult subject was obtained using the locomotor primitive patterns (rightmost two columns in figure \ref{fig:dominici_patterns_graphs}). The simulation was run for $1.5$, $2.0$, $2.5$ and $3.0$ seconds respectively. The locomotor patterns were scaled to the according timespan. The visualization of a part of the simulation run is shown in figure \ref{fig:locomotor_primitives_sequence}.
 
-\TODO{Add example image sequence of simulation}
-\ No newline at end of file
+It can be seen from the sequence that the muscle activations lead to an unrealistic movement of the legs (knees 
+bending backwards, twisting of the feet). Part of the effect can be attributed to the improper scaling of the 
+muscle activations. Thus different scalings factors were tried ($0.25$, $0.33$, $0.5$, $0.66$ and $0.75$) but 
+with all of them the basic improper movement pattern remained.
+
+\begin{figure}[htb!]
+\centering
+\includegraphics[width=\textwidth]{images/locomotor_primitives_sequence.png}
+\caption{Sequence of the two-legged \emph{LocomotorPrimitives} model. Only the first $1.2$ seconds are 
+         visualized. Total duration of simulation: $3.0$ seconds.}
+\label{fig:locomotor_primitives_sequence}
+\end{figure}
+
+When looking at the exerted muscle forces for a simulation run with the muscle activations scaled by $0.25$  
+(figure \ref{fig:locomotor_primitives_reported_forces}), the activations are only partially reflected. For the 
+\emph{Biceps Femoris-Long Head} and the \emph{Semimembranosus} (which are both part of the hamstring muscle 
+group, see section \ref{subsec:two_legged_model}) the reported forces match the muscle activation patterns (see 
+figure \ref{fig:dominici_patterns_graphs}) quite closely, while in the case of the \emph{Soleus} and the 
+\emph{Rectus Femoris}, the patterns don't directly reflect the activations. Overall the exerted forces don't 
+show unrealistically high values.
+
+\begin{figure}[htb!]
+\centering
+\includegraphics[width=\textwidth]{images/locomotor_primitives_reported_forces.png}
+\caption{Muscle forces exerted on the model during simulation for the muscles \emph{Soleus (soleus)}, 
+         \emph{Rectus Femoris (rect\_fem)}, \emph{Semimembranosus (semimem)} and \emph{Biceps Femoris-Long Head 
+         (bifemlh)} in both legs. X-axis is time from $0.0$--$3.0$ seconds, Y-axis is force in $N$.}
+\label{fig:locomotor_primitives_reported_forces}
+\end{figure}
+\ No newline at end of file