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% Estado da Arte
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%\section{}\label{sec:art}

This chapter of the dissertation discusses relevant background information for the project. FALAR AQUI DO EQUILIBRIO DE ROBOTS!!!!!!
It presents a brief introduction to human balance to give a better perspective on stimuli types. It also presents related works about balance assessment machines to learn what has been done and how it was done. And finally it presents a very brief introduction to force control with servos motors just to give a small idea on how to control servos based on force readings.

\section{Bipedal robot balance}

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% Breve introdução ao balanço humano
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\section{Brief Introduction to Human Balance}\label{sec:balanceintro}
Human balance consists of maintaining the line of gravity (vertical line from centre of mass) of one's body within the base support and doing so with minimal postural sway \cite{Shumway-Cook1988}. Both Humans and humanoid robots only have two legs, this makes their upright posture mechanically unstable. The ability to maintain an upright posture is achieved with the assistance of three sensing systems. Perturbations applied to vestibular\cite{Day1997}, visual\cite{Dijkstra1994} and proprioceptive\cite{KavounoudiasAGilhodesJCRollR1999} systems have provoked body sway, thus proving that these are the three input systems that contribute to postural control.

 The vestibular system, located in the inner ear, is responsible for determining the orientation of the body with respect to gravity, self generated movements and external perturbations. It can produce many involuntary reactions to make compensatory movements or postural adjustments\cite{Gray}. Some of these reactions control head and eye movement.
 
 Vision also gives important information for stabilization. When we move, the images of objects in the environment move over our retina. Since the vestibular system measures accelerations it can't detect slow movements or movements at constant velocity. So our brain assumes that the visual environment is static. Consequently, when the visual world
moves over our retina we have the perception that we move ourselves. This problem is solved by analysing all the sensory information; one sensor can be easily deceived, but to deceive all of them is much harder\cite{Dijkstra1994}.

The proprioceptive system gives information about the relative position of the body parts and the effort being made to maintain posture. Some muscles, tendons and joint capsules are responsible for sensing all that data. This information is critical to employ the optimal strategy to maintain balance\cite{Riemann2002}.


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% Breve introdução ao balanço ROBOT
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\section{Bipedal robot balance}




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% Sistemas de teste de balanço
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\section{Balance Testing Systems}\label{sec:baltest}
There are different systems to test the equilibrium of a human, and they can be split in two categories: static and dynamic.
A static test measures some quantities, such as weight distribution and Center of Pressure (CoP) with a non moving subject. The dynamic analysis applies a balance disrupting stimulus, most commonly below the feet, such as a translation or rotation, or those two combined. The measured quantities are CoP, weight distribution, accelerations and muscle electrical signals. The dynamic approach is more complete, giving more data to be analysed by experts in biomechanics and equilibrium.

An example of a static and dynamic balance evaluating machine is IsiMove, seen in figure \ref{figure:isimove}. \begin{quote}{\cite{Kharboutly2015}}
 ``It allows the evaluation of the static and dynamic balance of a human placed on a force plate. IsiMove is a robotic platform open kinematic with four degrees of freedom: anteroposterior tilt, mediolateral tilt, vertical rotation, and horizontal translation. It is capable of measuring the displacement of the center of pressure over time, with a resolution of 0.1 mm for each foot and support a human of about 120 kg. IsiMove can generate various types of balance perturbations based on parameters such as direction, amplitude, frequency and shape.'' \end{quote}

	\begin{figure}[!hb]
	\centering
	\includegraphics{Imagens/isimove.png}
	\caption{IsiMove platform and its axis of motion\cite{Kharboutly2015}.}
	\label{figure:isimove}
	\end{figure}

Another example of a similar system is IsiSkate, depicted in figure \ref{figure:isikate}. 
\begin{quote}{\cite{Kharboutly2014}}
	``It is specially designed to reproduce the perturbation of a public transportation in a laboratory environment. It is equipped with force and inertial sensors intended for the evaluation of human posture for static and dynamic equilibrium analysis of a human subject standing on it. This platform is able to disturb the balance of a human weighing 120 kg with an acceleration of 3 m/s$^2$ , which is above the safe limit 1.9 m/s$^2$ in public transportation. The platform is capable of measuring in real time the displacement of the center of pressure independently for the left and right foot. With its integrated inertial sensor, the platform is also capable of estimating the displacement of center of mass of the human subject as well as the motion of the ankle, knee, and hip joint.''
\end{quote}


	\begin{figure}[!hb]
	\centering
	\includegraphics{Imagens/isiskate.png}
	\caption{IsiSkate platform for balance analysis, user standing
on omnidirectional mobile robot with three inertial sensors attached to his body\cite{Kharboutly2014}.}
	\label{figure:isikate}
	\end{figure}

Another type of balance recovery assessment, is the stress test, introduced by Wolfson et al.\cite{Wolfson1986}. This test consists of postural perturbations that solicit balance recovery reactions measured during a normal upright position, using a simple pulley weight system that displaces the centre of gravity behind the base of support. More precisely, subjects have to withstand a series of posterior perturbations impulses that are applied at the level of the subject's waist using three different perturbation intensities (i.e., 1.5\%, 3\% and 4\% of the body mass)\cite{Granacher2012}. To administer this test, subjects must be placed 2 m from the pulley structure, with their upper limbs parallel to the body and the feet 10 to 15 cm apart. There are two points where the perturbation can be applied, on the shoulder and on the waist (at the level of the iliac crests)\cite{Producao2007}, as shown in figure \ref{figure:shoulder} and \ref{figure:iliac}, respectively.

	\begin{figure}[!hb]
	\centering
	\includegraphics{Imagens/shoulder.png}
	\caption{Balance disruption applied in the posterior direction at shoulder level\cite{Producao2007}.}
	\label{figure:shoulder}
	\end{figure}

	\begin{figure}[!hb]
	\centering
	\includegraphics{Imagens/iliac.png}
	\caption{Balance disruption applied in the posterior direction at iliac crest level\cite{Producao2007}.}
	\label{figure:iliac}
	\end{figure}

The last method presented is the most similar to the one that is being designed \cite{Mergner2003}. This study uses a contact force as an external perturbation. The stimulus is created by applying a force controlled pull on the subject's body around the ankle joints in the anteroposterior direction. It measures 
centre of mass (CoM) and centre of pressure (CoP) excursions to sinusoidal pull stimuli at different frequencies and with various force magnitudes.
The setup allows the application of a pull on the subject's body in the sagittal plane and thereby exert a defined torque about their ankle joints. The stimuli is applied via a body harness by means of two force controlled rope winches (servo motors) under computer control, as shown schematically in figure \ref{figure:stuart_hexapod}. Sinusoidal stimulus profiles are applied at five different frequencies (0.05, 0.1, 0.2, 0.4 and 0.8 Hz) and three different amplitudes of torque about the ankle joint ($\pm$1, $\pm$4 and $\pm$16 \si{N.m}). During these stimuli, subjects are standing upright, heels 5 cm apart, on a motion platform. The platform rests on six 'legs', each incorporating a motor capable of producing a change in the length of the leg (hexapod with Stuart principle). The motors are controlled by a computer to generate platform tilts in the sagittal plane with the axis through subjects' ankle joint during some of the stimuli.

	\begin{figure}[!hb]
	\centering
	\includegraphics{Imagens/stuart_hexapod.png}
	\caption{Schematic presentation of stimulus conditions. Sinusoidal pull stimuli were applied by means of two force-controlled cable winches via a padded body harness to exert defined torques about the subject's ankle joint in the a-p direction. The subject stood on a motion platform which was either stationary or was tilted in fixed register with spontaneous and stimulus-evoked body excursions\cite{Mergner2003}.}
	\label{figure:stuart_hexapod}
	\end{figure}
	
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% Controlo de força
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\section{Force control with servo motors}\label{sec:force_control_servos}	
	
%Not much relevant information was found to assist this project. 
Force control is applied mainly in industrial manipulators to perform tasks that require force control along a nominal path or velocity. 
\begin{quote}{\cite{Whitney1987}}
 ``Robot force control involves integration of task goals, trajectory generation, force and position feedback, and modification of the trajectories. It requires understanding contact tasks so that effective strategies and trajectories can be planned and feedback data can be understood. It also requires control so that the robot's responses will be stable. Finally, it requires filtering and estimation to remove unwanted signals, such as noise and robot motion errors, so that usable feedback information can be obtained. These issues - task analysis, strategy generation, control stabilization, and filtering - must be dealt with together if effective force control systems are to be created.''
\end{quote}
A general example of robot force feedback architecture can be seen in figure \ref{figure:force_feedback}.


	\begin{figure}[!hb]
	\centering
	\includegraphics{Imagens/force_feedback.png}
	\caption{Architecture of robot force feedback\cite{Whitney1987}.}
	\label{figure:force_feedback}
	\end{figure}
