conclude.tex

\chapter{Conclusions}
\label{chap:conc}
\section{A Pro-Epilogue}
In the light of all the arguments presented so far, we believe that we have clarified the underlying discrepancy between the actual 
bilateral teleoperation problem and how academic literature handles it. Moreover, we have provided a competitive alternative method that 
led to a high degree of realism experimentally. Therefore, we can safely claim that many technical problems reported in the literature 
are methodological and can be solved efficiently via careful modeling and robust control design phases without invoking questionable 
assumptions a priori. However, this claim does not reach out to the real solution of the bilateral teleoperation problem. Put better, we 
only claim that we have provided the solution for the simplified version of the problem. The actual question of \emph{What makes this 
device good?} or even the harder \emph{How can we improve the device?} are completely open. Unfortunately, we believe that clarifying 
this fact is a contribution.

Nevertheless, an important property of the method proposed here is that it provides consistent performance over different motion profiles 
and does not suffer from the artifacts of the method we have utilized. Moreover, we do not alter the hardware specifications by introducing 
virtual dissipation elements hence the results can be used to create devices that can be used in the investigations of the aforementioned 
open questions.  

Another important problem that we have not touched upon is the delayed bilateral teleoperation synthesis problem that somewhat dominated the
literature as if the undelayed case is completely studied. To justify our deliberate choice we distinguish two cases; there is a strong 
possibility backed by various studies that there exists an upper bound on the delay duration a human operator can cognitively compensate for 
during a bilateral teleoperation task. Beyond this delay value the human cannot associate the remote motion with the local device motion. 
Therefore let us denote this upper bound by $T$ whatever it might be other than being very likely to be around \SI{1}{\second}, then we 
have the following obvious dichotomy,

\begin{itemize}
	\item The actual transmission delay is greater than $T$,
    \item The actual transmission delay is less than or equal to $T$.
\end{itemize}

In the first case, we believe that there is no need to even consider the problem yet since it is even harder to find the relevant 
performance objectives of how a human operator can be made to immerse into the task with an excessive time delay. In the second case, 
if there is significant time delay, one can use the multipliers given \Cref{chap:analysis} for delay uncertainties and utilize it in the 
synthesis method given in \Cref{chap:synth} directly, with guaranteed improvements over the existing techniques. Additionally, if the 
communication delay is of the time-varying nature, one can always buffer the input/output to regularize the delay and use the known upper 
bound of the buffer period. The reason why this would always give a better performance is because the existing time-varying delay robustness 
analysis and synthesis tools are simply too conservative. Utilizing them surely would lead to stable interconnections but at the cost of 
unacceptable low performance levels which undermines the motivation the problem. Dealing with a known constant time-delay is, in turn, 
much easier and sharper results can be obtained. Note that practically every packet-switched network video/audio stream protocol use such 
buffering schemes unlike the vast majority of the time-delay teleoperation literature. In fact, this is not even a control-theoretical 
issue and should be left to digital communication experts for the optimal methods which go well-beyond control design knowledge. Moreover, 
the problem is far more sophisticated than the choice between TCP or UDP protocols. 

\section{Final Remarks}
Following this line of reasoning, we have the following conclusions elaborated in this thesis;
\begin{enumerate}
    \item The bilateral teleoperation is fundamentally an interdisciplinary problem. Current literature underestimates the broadness of 
the scope of this technology and claims to solve a stability problem that is not inline with the actual bilateral teleoperation. The 
majority of the proposed problem formulations are of \emph{What if we had sampling, two users, time-varying delay?} nature. Though, these 
scenarios are certainly worth considering, the proposed solutions only handle the stability issues. Our first conclusion emphasizes this;
    
    {\bfseries The bilateral teleoperation problem is not a typical control problem in which stabilization is the crucial point and 
    achievable performance is an extra bonus. Without the required performance levels, a stable bilateral teleoperation system is useless.It 
    might even decrease the human task performance.}
    
    \item As we have shown in \Cref{chap:application}, the 2-port network modeling framework is not general enough to capture the problem in
    its entirety. Over the last two decades, certain derivations are established as facts for the perfect transparent device however one 
    can still obtain better designs with alternative methods that do not obey the predicted performance conditions which are stated in 
    numerous sources. If the following definition of transparency is adopted
    \begin{displayquote}[\cite{hirchebookchap}][.]
    Transparency is defined, meaning that the human operator should ideally feel as if directly acting in the remote environment
    (is not able to feel the technical systems/communication network at all).
    \end{displayquote}
    which seems to be the case in the literature, then there is a discrepancy between what is being sought after and the corresponding 
    formulation. 
    
    {\bfseries Transparency objective that relates the performance to the operator feel and comfort with the definiton above does not 
    necessarily imply that an ideal teleoperation system should have a hybrid system representation
    $\begin{psmallmatrix}0&I\\I&0\end{psmallmatrix}$. 
    This formulation completely ignores the human perception and moreover it is impossible to achieve. Additionally, as a control objective 
    it relies on naive control concepts such as exact dynamics cancellation and plant inversion. In a time-varying system these arguments 
    are invalid.
    }
    \item A vast majority of the network-theory based stability conditions can be rederived by the IQC framework in a lossless fashion. 
    Due to this equivalence there is no added value of using scattering transformations or wave variables over the proposed framework. 
    
    {\bfseries Insisting on the network theoretical treatment of the subject is a matter of preference. IQC framework already covers the 
    classical methods and offers significantly larger set of possibilities to be utilized in stability analysis and controller synthesis. 
    Here the emphasis is on the anachronistic focus of the literature. 
    }
    \item As we have shown via a simple implementation, high-performance controllers can be designed using a sufficiently accurate model of
    the system and careful simplifications by the robust control design methodology. 
    
    {\bfseries The $D$-$K$ iteration with dynamic multipliers leads to significantly less conservative results compared to static multiplier 
    based designs which includes wave-variable- and passivity-based methods. The disadvantage of model based design is obtaining the 
    accurate models and the weight selection. The latter is a significant obstacle in judging the true optimality of the design. Even in the 
    cases where the problem solution is guaranteed to be optimal, the design itself due to the performance weights selection can be 
    non-optimal. However, this difficulty is not in par with the conservative methods. In other words, this difficulty can be overcome with 
    educated guesses in a trial-and-error phase which permits at least some systematic procedure up to an extent. A conservative method does 
    not permit such by-pass steps.
    }
    \item It is shown that depending on the uncertainty modeling complexity, the control design problem can be made robust to different 
    uncertain operators of different kind including delays, parameters, particular nonlinearities etc. However, as reassuring and positive 
    it might seem, more robust solutions lead necessarily to lower performance levels. Therefore, it is the highest priority to get a 
    model with reduced uncertainty as much as possible. Even if there does not exist a suitable method to handle the resulting obstacles, 
    this will nevertheless make the problem visible and unambiguous. 
    
    {\bfseries Due to the absence of a rigorous objective, we might pursue for the improvements over the method presented here. The 
    immediate improvement that can be relevant is the application of Linear Parameter Varying controller synthesis via scheduling over the 
    forces sensed in remote and local environments. The synthesis framework is already established however once again, the performance 
    objective is missing therefore we hit the same bottleneck. 
    }
    \item The teleoperation literature (and partially the general control theory literature) has the tendency to motivate engineering 
    problems inside a seemingly rigorous mathematical framework. Often, however, there is an implicit transition from the actual problem to 
    the watered down, oversimplified version of the same problem that disconnects the solution from the physical motivation. Alternatively, 
    unrealistic reasons are used to justify certain assumptions. Take the claim that force sensors are expensive to implement and hence 
    force-sensorless possibilities are explored. That statement is only true relatively if the remote and/or local device cost is 
    significantly low. If we can succeed providing the operator a realistic touch sensation, the sensors would compensate the investment 
    costs in a very short amount time--A surgical robotic system price is in the order of M\EUR{} with very high maintenance 
    costs. The typical force sensor cost is not even high enough to be considered as negligible. We certainly refrain from declaring what 
    is worth of focus or not however motivating a mathematical problem with questionable engineering scenarios is false and unfortunately 
    very common. Same problems can be investigated for the sake of the problem alone without any naive engineering motivation.
    
    {\bfseries There are more important open problems than, say, the rather specialized delayed teleoperation problem or force-sensorless 
    teleoperation. The delay robustness problem is studied in the last two decades extensively outside the teleoperation context. As a 
    result of this effort we already have a variety of methods IQCs, Lyapunov-Krasovskii functionals etc. The importance of the delay 
    instability is due to the unrealistic ambitious objective of physics equalization. Similarly force-sensorless teleoperation, multi-user 
    teleoperation etc. are problems with invalid motivation from a technological point of view since the bilateral teleoperation system is 
    a human oriented technology not a network controlled system. The problem is finding the right tool for designing the controller but 
    not modifying the problem for the existing control design tool.
    }
    
\end{enumerate}