# Space Robot Sensor Noise Amelioration Using Trajectory Shaping
## 5 Conclusions  
The whiplash trajectory generation scheme shows a 133.3% improvement when only rate sensor noise is included. The step function method has the least mean error in rotation angle when only the state sensor noise is enabled, as well as when both rate and state sensor noises are enabled.  
Without noise included, the sinusoid trajectory shows the most improved performance. However, in the presence of state and rate sensor noises, the step function has the smallest mean error values for the rotation angle. When noise is included, the step function has a 13.64% improvement in mean error when compared to the sinusoid trajectory.  
Future research should be conducted to investigate more optimal, continuous trajectory schemes. This could also include investigating the most appropriate solver in MATLAB(r). Depending on the solver and step size chosen in MATLAB(r)'s SIMULINK(r), the resulting trajectories could produce different results. Investigating which solver and step size is the most appropriate for this application would render additional confidence in the results. Additionally, more trajectory generation schemes could be evaluated and compared to the sinusoid and whiplash methods. Evaluating additional methods could lead to a more optimal solution with less error.  
**Author Contributions:** Formal analysis, E.K.; investigation, E.K.; conceptualization, T.S.; methodology, T.S.; software, T.S.; validation, T.S.; resources, T.S.; data curation, E.K.; writing--original draft preparation, E.K. and T.S.; writing--review and editing, E.K. and T.S.; visualization, E.K.; supervision, T.S.; project administration, T.S.; funding acquisition, T.S. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research received no external funding.  
**Data Availability Statement:** To access the data, please contact the corresponding author.  
**Conflicts of Interest:** The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & \begin{tabular}{c} **Rotation Angle** \\ **\# Error** \\ **Standard** \\ **Deviation** \\ \end{tabular} & \
\begin{tabular}{c} **Rotation Angle \# Error Mean** \\ **Deviation** \\ \end{tabular} &
\begin{tabular}{c} **Rotation Angle \# Error Standard** \\ **Deviation** \\ \end{tabular} \\ \hline Step & — & — \\ Sinusoid & –97.39\% & 0.0141 \\ Whiplash & 42.16\% & 0.2097 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Percent errors for reaction wheel angle.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \begin{tabular}{c} **Rotation Angle** \\ **\# Error Mean** \\ **Deviation** \\ \end{tabular} & \begin{tabular}{c} **Rotation Angle** \\ **\# Error Mean** \\ **Deviation** \\ \end{tabular} & \begin{tabular}{c} **Rotation Angle** \# Error Mean** \\ **Deviation** \\ \end{tabular} & \begin{tabular}{c} **Rotation Angle** \# Error \\ **Deviation** \\ \end{tabular} & \begin{tabular}{c} **Rotation Angle**, \\ **\# Error** \\ **Deviation** \\ \end{tabular} \\ \hline \hline \multirow{4}{*}{**Method**} & \begin{tabular}{c} **With Rotation Angle** \\ **Sensor Noise** \\ \end{tabular} & \
\begin{tabular}{c} **With Rotation Angle** \\ **Rate Sensor Noise** \\ \end{tabular} &
\begin{tabular}{c} **With Rotation Angle Sensor** \\ **and Rate Sensor Noise** \\ \end{tabular} \\ \hline Step & — & — & — & — & — \\ Sinusoid & 220.0\% & –90.75\% & \(900\times 10^{6}\%\) & –381 \(\times\) 10\% & 13.64\% & –51.28\% \\ Whiplash & 40.00\% & –181.0\% & –133.3\% & –79.88\% & 168.2\% & 38.46\% \\ \hline \hline \end{tabular}
\end{table}
Table 7: Monte Carlo analysis of random perturbations (percent performance improvement).