text:
\section{Introduction}
\label{section1}

Although a joint friction compensation is one of the most fundamental problems in robotics control, it is still an open problem; see e.g., \cite{verbert2016adaptive}. There are several branches in the friction observer studies. \cite{olsson1996observer, johanastrom2008revisiting,maged2019dynamic} proposed friction observers using the LuGre model that can describe most of physical phenomena of the friction. Model-based approaches will undoubtedly provide the best friction compensation performance, but at the cost of increased complexity. \cite{kaneko1990motion, ruderman2015observer} proposed model-free observers for motion control applications, but these may eliminate the interaction capability which is important in modern robotics.

To achieve friction compensation while preserving interaction capability, equipping the robot joints with a joint torque sensor (JTS) would be helpful because it allows to employ the flexible joint robot (FJR) model. In the FJR model, the overall robot dynamics are divided into the motor-side and link-side dynamics. Conceptually speaking, by applying a friction observer only to the motor-side dynamics, the link-side is still open to the interaction. Under the Spong's assumption \cite{spong1990modeling} which is valid when, for instance, the gear reduction ratio is high enough, the FJRs can be mathematically modeled as follows.
\begin{align}
\label{eq:link_dyn}
M(q)\ddot{q} + C(q,\dot{q})\dot{q} + g(q) &= \tau_j + \tau_{ext}, \\
\label{eq:motor_dyn}
B \ddot{\theta} + \tau_j &= \tau_m + \tau_f, \\
\label{eq:torque}
\tau_j &= K_j (\theta - q),
\end{align}
where $M, C, g$ represent link-side inertia, Coriolis/centrifugal, gravity matrix/vector and $B$ represents motor-side inertia matrix. $q$, $\theta$ respectively denote the link-side and motor-side variables, and $K_j$, $\tau_j$ respectively denote the joint stiffness and joint torque which is measurable using JTS. $\tau_{ext}$ is the external torque resulting from interation, $\tau_m$ is the motor command, and $\tau_f$ is the joint friction to be compensated for.

An important remark here is that most of the significant friction can be included in the motor-side dynamics (\ref{eq:motor_dyn}) because the JTS is typically installed after the gear reduction. Therefore, it is reasonable to apply the friction observer to the motor-side dynamics which are governed by a 2nd order linear ordinary differential equation (w.r.t. $\theta$). Namely, we can apply linear control techniques to compensate for the friction. In this paper, friction observers are designed based on this observation.

\subsection{Related Work}
\label{sec:related_work}

The idea of applying friction compensation on the motor-side was realized in \cite{kaneko1990motion, zhang1997control,park2007disturbance} using disturbance observer (DOB) technique. In a very early study \cite{kaneko1990motion}, however, the joint torque information was not taken into account, meaning that the interaction on the link-side was treated as a disturbance. However, in robotics applications, it can be beneficial to close the loop around the motor-side dynamics using $\tau_j$  because then the link-side dynamics can interact with the environment through $\tau_{ext}$. \cite{zhang1997control} considered the joint torque information in the observer design, but the analysis was limited to a single-link robot. \cite{park2007disturbance} proposed an observer for multi-link robots, but the friction model was assumed to be linear and known.

To the best of the authors' knowledge, the approach proposed in \cite{le2008friction} was the first model-free friction observer for multi-link robotic systems (see Fig. \ref{fig:friction_observers}b). In this approach, the resulting observed value corresponds to the real friction smoothed by a 1st order low-pass filter (LPF). Despite successful experimental validation, however, theoretical analysis was not complete. The main challenge is the fact that the observer dynamics may break stability/passivity of the controller. Later, \cite{kim2014robust} and \cite{kim2015disturbance} proposed Fig. \ref{fig:friction_observers}c to establish a theoretically sound friction observer that guarantees stability of the whole system consisting of the friction observer dynamics and the FJR dynamics (\ref{eq:link_dyn})-(\ref{eq:torque}).\footnote{
To be precise, the scope of \cite{kim2014robust,kim2015disturbance} was about DOB-based control structures. The DOB becomes the friction observer when the motor inertia is known.
}

\begin{figure}[]
	\centering
	\subfigure[FJR control with the proposed friction observer]
	{\includegraphics[scale=0.28]{Fig1a.pdf}} \\
	\subfigure[Friction observer in \cite{le2008friction}]
	{\includegraphics[scale=0.24]{Fig1b.pdf}}
	\subfigure[Friction observer in \cite{kim2015disturbance}]
	{\includegraphics[scale=0.24]{Fig1c.pdf}}
	\caption{ The dashed red boxes represent the friction observers, where $P(s)=1/Bs^2$ is the motor-side dynamics and $C(s)$ is the friction compensator. (a) The FJR control with the proposed friction observer.  (b) Friction observer proposed in \cite{le2008friction} where no stability proof is provided. (c) Friction observer proposed in \cite{kim2015disturbance}. Nominal motor signal ($\theta_n$) feedback makes the closed-loop system stable together with an auxiliary control input $\tau_k$. The limitation is that $\tau_k$ cannot be implemented around the equilibrium point. In (b) and (c), differences with the proposed observer (a) are highlighted with blue color.}
	\label{fig:friction_observers}
\end{figure}

The main feature of this structure is that the nominal motor signal $\theta_n$ (instead of the measured signal $\theta$) is fed back into the controller. In Fig. \ref{fig:friction_observers}, $\theta_n$  can be thought of as the nominal motor signal because it is the outcome of the friction-free motor dynamics $P(s)$. Although asymptotic stability can be shown theoretically, the approach in Fig. \ref{fig:friction_observers}c still has a limitation that it contains an intractable input $\tau_k$ which cannot be implemented around the equilibrium point. Therefore, it was neglected in the experimental validation under the naive expectation that the influence is negligible \cite{kim2014robust}. Interestingly, the experiments were successful, and asymptotically stable behavior was shown. Nevertheless, it is questionable if $\tau_k$ can be neglected in general. This paper, therefore, shows that asymptotic stability can be guaranteed without $\tau_k$. Moreover, if the controller is designed to satisfy passivity of an input-output pair $(\tau_{ext},\dot{q})$, the friction observer preserves this property.

At this point, it is worth mentioning that the aforementioned approaches share a common keyword DOB. By virtue of the DOB-based structures, the outcomes of the observers are the low-pass filtered value of the real friction. However, the LPF property does not provide enough understanding for the observer's behavior, especially when the robot is stuck in the stiction. Stiction compensation needs a special treatment as it has a very complicated characteristics which is hard to be captured in the model-free approaches.

Indeed, one thing commonly missed in the model-free friction observer studies is the stiction compensation. This paper also neglects the dynamic behavior of the stiction in the beginning.  By doing so, it can be shown that the controlled system converges into the stiction region. However, the friction observers tend to generate energy during the stiction compensation, which may result in an oscillatory robot motion around the desired point. The proposed observer provides a better understanding on this phenomenon, and allows us to avoid the energy generation using passivity theory.

\begin{figure}
	\centering
	{\includegraphics[scale=0.45]{Fig2.pdf}}
	\caption{A gravity-free single-link FJR with the motor-side PD controller. Friction observer is applied to compensate for the friction $\tau_f$ acting on the motor-side.}
	\label{fig:stiction_example}
\end{figure}

\subsection{Scope and contribution of the paper}
\label{sec:scope_contribution}

This paper focuses mainly on the regulation scenario in which the robot eventually is stationary. Nevertheless, the tracking scenario is also discussed for the sake of completeness. We focus on the regulation case because the convergence can be argued only when the robot is supposed to be static. Convergence is hard to be concluded for the tracking case because the friction is observed by the relation of a LPF which always has a phase lag. Instead, we can claim practical stability which might be sufficient for tracking scenarios in practical point of view.

Within the regulation scenario, this paper proposes friction observers that can be applied to controllers designed to be asymptotically stable for friction-free FJRs. Three main contributions are summarized as follows. First, it will be shown that asymptotic stability of the controller is preserved. Second, if, in addition, the controller is designed to satisfy passivity of $(\tau_{ext}, \dot{q})$, this is preserved as well. Third, a solution to prevent energy generation during the stiction compensation is presented. We would like to underline that, in the third contribution, the stiction region around the desired point is of interest in this paper.

\subsection{Organization of the paper}

The proposed friction observer is introduced in Section \ref{sec:friction_obs_design} with a theoretical justification in Section \ref{sec:theory}. Section \ref{sec:discussion} presents several features of the proposed friction observer as well as interpretations for the required technical conditions of the theory. The proposed features are validated in Section \ref{sec:validation} through simulations and experiments. Finally, Section \ref{sec:conclusion} concludes the paper.

\section{Model-Free Friction Observers for FJR}
\label{sec:friction_obs_design}

\subsection{Overview of the proposed friction observers}
\label{sec:proposed_fo}

This section introduces the proposed friction observers shown in Fig. \ref{fig:friction_observers}a without rigorous mathematical treatments which will be introduced in the subsequent sections.  Given a controller $\tau_c$ which is designed to be asymptotically stable for the nominal friction-free FJRs, the friction observer generates $-\widehat{\tau}_f$ to compensate for the friction $\tau_f$ in the motor-side dynamics (\ref{eq:motor_dyn}). Namely, the resulting motor command is
\begin{align}
\tau_m = \tau_c - \widehat{\tau}_f.
\label{eq:motor_command}
\end{align}

The following well-known motor-side PD controller \cite{tomei1991simple} is used as an example throughout the paper.
\begin{align}
	\tau_c(\theta, \dot{\theta}) = -K_p (\theta - \theta_d) - K_d \dot{\theta} + g(q_d),
	\label{eq:pd_controller}
\end{align}
where $K_p$, $K_d$ are PD gains,  and $\theta_d = q_d + K_j^{-1}g(q_d)$ with the desired value $q_d$.  This controller is known to satisfy asymptotic stability and passivity of $(\tau_{ext},\dot{q})$ for sufficiently large $K_p$. When the friction observer is applied, as shown in Fig. \ref{fig:friction_observers}a, the controller should be defined using nominal signals:
\begin{align}
	\tau_c(\theta_n, \dot{\theta}_n) = -K_p (\theta_n - \theta_d) - K_d \dot{\theta}_n + g(q_d).
	\label{eq:pd_controller_with_nominal}
\end{align}
In Fig. \ref{fig:friction_observers}a, $C(s)$ represents the friction observer. The following two observers are introduced in this paper.
\begin{align}
\label{eq:PID-type}
\text{PID-type:}& \;\; C(s) = - BL \left( s + L_p + \frac{L_i}{s} \right) \; \text{with} \; L_p^2> 2L_i, \\
\label{eq:PD-type}
\text{PD-type:}& \;\; C(s) = - BL \left( s + L_p \right),
\end{align}
where $L,L_p,L_i>0$ are observer gains.

It is important to note that, due to the additional observer dynamics, stability of the overall system may not be guaranteed even if the controller is designed to be stable for the nominal systems. This paper shows that the observer preserves asymptotic stability and/or passivity of the controller if the observer gain $L$ is sufficiently large for the regulation case; see Theorem \ref{thm:asymp_stable} in Section \ref{sec:stability} for the required technical conditions. When the tracking is of interest, friction-free behavior is achieved as the observer gain $L$ increases, but the convergence cannot be claimed for finite $L$; see Section \ref{sec:discuss_conditions} and Appendix.

One limitation of Theorem \ref{thm:asymp_stable} is the fact that dynamics of the stiction friction are neglected. Roughly speaking, the value of stiction friction has the same amount as net applied force/torque with the opposite sign. The following example motivates an additional analysis for the stiction compensation.

\underline{\it Motivating example:} Consider the gravity-free mass shown in Fig. \ref{fig:stiction_example} with the initial condition $\theta(0)=\dot{\theta}(0)=0$ and $q(0)=\dot{q}(0)=0$ (so that $\tau_j(0)=0$). The PD controller (\ref{eq:pd_controller}) or (\ref{eq:pd_controller_with_nominal}) is applied with $K_p=50$, $K_d=5$, and $\theta_d=0.01$. Let us assume that the maximum stiction value is $1.5 \mathrm{N}$.
Because the PD control input (which is $50 \times 0.01 = 0.5 \mathrm{N}$ at the beginning) is not strong enough to break the stiction $1.5 \mathrm{N}$, the mass does not move due to the friction $-0.5 \mathrm{N}$. When the friction observer is applied, it produces $0.5 \mathrm{N}$ (i.e., $\widehat{\tau}_f=-0.5 \mathrm{N}$) to compensate for the friction. However, at the same time, the resulting friction increases to $-1 \mathrm{N}$ which is the net applied force. As a consequence, the friction compensation action will also increase to $1 \mathrm{N}$ which results in the net force $1.5 \mathrm{N}$ that can break the stiction. However, if the control error remains due to, for instance, stick-slip effect, the above mentioned procedure may be repeated. \QEDA

This example demonstrates that the friction observers tend to generate energy during the stiction compensation, and may result in an oscillatory motion. We would like to underline again that the stiction region around the desired regulating point is of main interest in this paper. An analysis for the stiction region that the robot enters instantly due to the change of velocity sign during the motion is out of scope.

According to Theorem \ref{thm:passivity} in Section \ref{sec:behavior_in_stiction}, it is guaranteed that the PD-type observer does not generate the energy in the stiction region, whereas the PID-type may generate; see also Fig. \ref{fig:stiction_comp_stiction}a. However, we do not conclude which one is better in general. Section \ref{sec:validation} shows that PD- and PID-type observers have different characteristics with respective pros and cons. In practice, therefore, one should carefully design a friction observer depending on the application and hardware used.

\subsection{State-space representation of the overall dynamics}

To express the dynamics in state-space form, the most straightforward choice for the states would be $\theta_n$, $\dot{\theta}_n$, $\theta$, $\dot{\theta}$, $q$, and $\dot{q}$. In this paper, however, $e_{nr}=\theta_n - \theta$ and $\dot{e}_{nr}$  will be used instead of $\theta$ and $\dot{\theta}$, and will be collectively represented as $x_{nr}$.  The definition of $x_{nr}$ will depend on the friction observer $C(s)$ design. For example, when (\ref{eq:PID-type}) is used, one simple choice is $x_{nr}= [\int e_{nr}^T, \; e_{nr}^T, \; \dot{e}_{nr}^T]^T$. Similarly,  the state related to $\theta_n$ and $q$ will be collectively represented as $x_{n,q}$ of which the definition depends on the controller $\tau_c$. With the motor-side PD controller (\ref{eq:pd_controller_with_nominal}),  $x_{n,q}= [(\theta_n - \theta_d)^T, \; \dot{\theta}_n^T, \; (q - q_d)^T, \; \dot{q}^T]^T$ is a typical choice.

The overall dynamics can be expressed as
\begin{align}
\label{eq:deriv_link}
M(q) \ddot{q} + C(q,\dot{q})\dot{q} + g(q) &= K_j(\theta-q) + \tau_{ext}, \\
\label{eq:deriv_nom_motor}
B\ddot{\theta}_n + K_j(\theta-q)& = \tau_c(x_{n,q}), \\
\label{eq:deriv_diff_dyn}
B\ddot{e}_{nr} &= \widehat{\tau}_f(x_{nr}) - \tau_f.
\end{align}
(\ref{eq:deriv_diff_dyn}) is called difference dynamics and can be obtained by subtracting (\ref{eq:motor_dyn}) from (\ref{eq:deriv_nom_motor}); recall also $\tau_m=\tau_c-\widehat{\tau}_f$ in (\ref{eq:motor_command}). Since $\theta$ is not a state, let us rewrite (\ref{eq:deriv_link})-(\ref{eq:deriv_nom_motor}) as
\begin{align}
\label{eq:nom_link_re}
M(q) \ddot{q} + C(q,\dot{q})\dot{q} + g(q) &= K_j(\theta_n-q) - K_j e_{nr} + \tau_{ext}, \\
\label{eq:nom_motor_re}
B\ddot{\theta}_n + K_j(\theta_n-q)& = \tau_c(x_{n,q}) + K_j e_{nr}.
\end{align}

In the state-space form, (\ref{eq:nom_link_re})-(\ref{eq:nom_motor_re}) can be represented as
\begin{align}
\label{eq:nq_dyn_ss}
\dot{x}_{n,q} = f_{n,q}(x_{n,q})+g_{n,q}(x_{nr}) + h_{n,q}(x_{nr})\tau_{ext}
\end{align}
with properly defined $f_{n,q}$, $g_{n,q}$, and $h_{n,q}$. Here, $g_{n,q}$ represents the perturbation caused by $K_je_{nr}$.  The state-space representation of (\ref{eq:deriv_diff_dyn}) is
\begin{align}
\dot{x}_{nr} = A_{nr} x_{nr} + B_{nr} \widehat{\tau}_f + B_{nr} w,
\label{eq:diff_ss}
\end{align}
with properly defined constant matrices $A_{nr}$ and $B_{nr}$.  $w$ represents the perturbation which may contain state dependent terms in addition to the friction $\tau_f$. By allowing $w$ to have state-dependent terms, the design procedure of the friction observer may become easier as we have more freedom.
\begin{lem}
	\label{lem:w_bound}
	Assume that $w$ is bounded by
	\begin{align}
	||w|| \leq b_1 ||x_{nr}|| + b_2 ||\dot{\theta}|| + b_3 ||\dot{\theta}_n|| +  b_4,
	\label{eq:w_bound_condition}
	\end{align}
	for some $b_i \geq 0$. Then, $||w||^2$ can be bounded by
	\begin{align}
	||w||^2 \leq c_1 ||x_{nr}||^2 + c_2 ||x_{nr}|| +c_3 ||\dot{\theta}_n||^2 + c_4,
	\label{eq:w_sq_bound_condition}
	\end{align}
	for some $c_i \geq 0$.
\end{lem}
\begin{proof}
	First, use $\dot{\theta}=\dot{\theta}_n - \dot{e}_{nr}$ to get rid of $\dot{\theta}$ which is not a state of the closed-loop dynamics. Then, (\ref{eq:w_sq_bound_condition}) is obtained by algebraic calculation. When squaring $||w||$, a mixed term $||a||\cdot ||b||$ can be split using Young's inequality $ab \leq a^2/2 +b^2/2$.
\end{proof}

In the observer design, the following properties of the friction are required. LuGre model, for example, satisfies these \cite{johanastrom2008revisiting} .
\begin{property}
	\label{ass:friction}
	The friction $\tau_f(v)$ can be bounded by
	\begin{align}
	||\tau_f|| \leq a_1 ||v|| + a_2,
	\label{eq:friction_bound}
	\end{align}
	for some $a_i>0$.
\end{property}
\begin{property}
	\label{prop:fric_passivity}
	The friction $\tau_f(v)$ defines a passive input-output pair $(v,-\tau_f(v))$.
\end{property}

\subsection{Friction observer designs}
\label{sec:stability}

This section presents the stability analysis for a class of controllers that satisfy the following assumption.
\begin{ass}
	\label{ass:V_nq}
	Let us consider the ideal friction-free system
	\begin{align}
	\label{eq:ideal_friction_free}
	\dot{x}_{n,q} = f_{n,q}(x_{n,q}) + h_{n,q}(x_{n,q}) \tau_{ext}.
	\end{align}
	When $\tau_{ext}=0$, there exists $V_{n,q}(x_{n,q}) \geq 0$ such that
	\begin{align}
	\label{eq:V_nq_partial}
	\left|\left| \frac{\partial V_{n,q}}{\partial x_{n,q}} \right|\right| \leq& \beta_{nq1}\phi_{nq}(||x_{n,q}||) + \beta_{nq2}, \\
	\label{eq:V_nq_dot}
	\dot{V}_{n,q} \leq& -\alpha_{nq} ||\dot{\theta}_n||^2,
	\end{align}
	where $\phi_{nq}(\cdot)$ is a positive definite function, and $\alpha_{nq}$, $\beta_{nq1}$, $\beta_{nq2}>0$ are some constants. Moreover, if $\tau_c$ is designed to satisfy the passivity of $(\tau_{ext},\dot{q})$, then there exists a storage function $V_{n,q} \geq 0$ that satisfies (\ref{eq:V_nq_partial}) and
	\begin{align}
	\label{eq:V_nq_dot_passive}
	\dot{V}_{n,q} \leq -\alpha_{nq} ||\dot{\theta}_n||^2 + \tau_{ext}^T\dot{q} .
	\end{align}
\end{ass}
Note that $V_{n,q}$ does not necessarily have to be a Lyapunov function since positive definiteness is not required. This assumption is not restrictive as it can be satisfied for most of practical robot controllers, because $\phi_{nq}(\cdot)$ can be an arbitrary positive definite function and  $-\alpha_{nq} ||\dot{\theta}_n||^2$ comes from the D-control action which always exists to satisfy stability.\footnote{
For example, consider a typical choice of Lyapunov function defined by quadratic term plus gravity potential. Then (\ref{eq:V_nq_partial}) is trivial.} The controller (\ref{eq:pd_controller_with_nominal}) satisfies this assumption using (27) in \cite{tomei1991simple} as $V_{n,q}$ of which time derivative is given by
\begin{align}
\label{eq:V_dot_nq_pd_controller}
\dot{V}_{n,q}=-\dot{\theta}_n^T K_d \dot{\theta}_n + \tau_{ext}^T \dot{q}.
\end{align}

\begin{thm}
	\label{thm:asymp_stable}
	In addition to Assumption \ref{ass:V_nq}, assume that  (i) $\dot{\theta}_d=0$, (ii) the friction value is constant in stiction, and (iii) the controller $\tau_c$ is designed to be asymptotically stable for friction-free system (\ref{eq:ideal_friction_free}), and satisfies $\alpha_{nq} - \beta_{nr}c_3>0$. If the friction observer is designed to satisfy that
	\begin{enumerate}
		\item the difference dynamics (\ref{eq:diff_ss}) are exponentially stable when $w=0$, so that there exists $V_{nr}(x_{nr})>0$  (by Lyapunov converse Theorem \cite{khalil2002nonlinear}) satisfying
		\begin{align}
		\left|\left| \frac{\partial V_{nr}}{\partial x_{nr} } \right|\right| \leq& \bar{\beta}_{nr} ||x_{nr}||, \\
		\dot{V}_{nr} \leq& - \bar{\alpha}_{nr} ||x_{nr}||^2 ,
		\end{align}
		for some $\bar{\alpha}_{nr}, \bar{\beta}_{nr}>0$.  Therefore, when $w \neq 0$,
		\begin{align}
		\nonumber \dot{V}_{nr} \leq&  - \bar{\alpha}_{nr} ||x_{nr}||^2  + \bar{\beta}_{nr}||B_{nr}|| \cdot ||x_{nr}|| \cdot ||w|| \\
		\leq& - \alpha_{nr} ||x_{nr}||^2  + \beta_{nr}\cdot ||w||^2,
		\label{eq:V_nr_dot}
		\end{align}
		for some $\alpha_{nr},\beta_{nr}>0$,\footnote{$||x_{nr}|| \cdot ||w|| \leq \frac{1}{2}||x_{nr}||^2+\frac{1}{2}||w||^2$ using Young's inequality.}
		\item $w$ can be bounded by (\ref{eq:w_bound_condition}), and therefore (\ref{eq:w_sq_bound_condition}) is satisfied,
		\item $\alpha_{nr}$ is positive and increases with a certain observer gain, whereas $\beta_{nr}>0$ does not,
		\item there exists a unique equilibrium point of $x_{nq}$ and $x_{nr}$,
	\end{enumerate}
	then the overall closed-loop dynamics (\ref{eq:deriv_nom_motor})-(\ref{eq:deriv_diff_dyn}) are asymptotically stable when the observer gain associated with $\alpha_{nr}$ is chosen sufficiently large with $\tau_{ext}=0$ .

	Moreover, when $\tau_{ext} \neq 0$, if $V_{n,q}$ in Assumption \ref{ass:V_nq} is a storage function that satisfies (\ref{eq:V_nq_dot_passive}),  the passivity of $(\tau_{ext},\dot{q})$ is preserved for $||\tau_{ext}|| \leq b_{ext}<\infty$ for some $b_{ext}>0$.
\end{thm}
\begin{proof}
	See Section \ref{sec:proof_as}.
\end{proof}
Interpretations for the seven requirements in this theorem are addressed in Section \ref{sec:discuss_conditions}. Theorem \ref{thm:asymp_stable} concludes asymptotic stability of $x_{n,q}$ and $x_{nr}$, which is not the original goal of the controller. Asymptotic stability for $\theta$ can be concluded using $\theta=-e_{nr}+\theta_n$. The following corollaries propose a couple of friction observers.
\begin{cor}[PID-type $C(s)$]
	\label{cor:pid}
Consider $C(s)$ defined by (\ref{eq:PID-type}). If the observer gain $L$ is chosen sufficiently large, then the closed-loop dynamics of Theorem \ref{thm:asymp_stable} are asymptotically stable to  the equilibrium point $x_{n,q}=0$, $\dot{e}_{nr}=0$, $e_{nr}=0$, and $\int e_{nr}= L_i^{-1}L^{-1}B^{-1}\bar{\tau}_f$, where $\bar{\tau}_f$ is the friction at steady-state.
\end{cor}
\begin{proof}
	See Section \ref{sec:proof_cor_pid}
\end{proof}

\begin{cor}[PD-type $C(s)$]
	\label{cor:pd}
Consider $C(s)$ defined by (\ref{eq:PD-type}). If the observer gain $L$ is chosen sufficiently large, then the closed-loop dynamics of Theorem \ref{thm:asymp_stable} are asymptotically stable to $\dot{e}_{nr}=0$, $e_{nr}=L_p^{-1}L^{-1}B^{-1}\bar{\tau}_f$, but the equilibrium point of $x_{n,q}$ may be perturbed due to nonzero $e_{nr}$.
\end{cor}
\begin{proof}
	See Section \ref{sec:proof_cor_pd}
\end{proof}

It might be informative to mention that, for the proposed PID-/PD-type observers, $\alpha_{nr}$ increases and $\beta_{nr}$ decreases as the observer gain $L$ increases.

\subsection{Behavior of the friction observers in the stiction region}
\label{sec:behavior_in_stiction}

Theorem \ref{thm:asymp_stable} states asymptotic stability while neglecting dynamic behavior of the stiction. Therefore, it only implies that the robot trajectory converges to the stiction region around the desired point.  However, as illustrated in the motivating example in Section \ref{sec:proposed_fo},  dynamic behavior of the stiction may result in an oscillatory motion due to the energy generation during the stiction compensation (see Fig. \ref{fig:stiction_comp_stiction}a). To perform a further analysis, let us begin with the following assumption which is valid when the closed-loop dynamics have converged to the stiction region according to Theorem \ref{thm:asymp_stable}; hence $\tau_j=K_j(\theta-q)$ is constant because $\dot{\theta}=\dot{q} =0$.
\begin{ass}
	\label{ass:fric_passive}
	 Assume that, as a consequence of Theorem \ref{thm:asymp_stable}, the JTS measurement $\tau_j$ is constant. Then, the nominal motor-side dynamics (\ref{eq:deriv_nom_motor}) are not excited, and $\dot{\theta}_n=0$ can be further assumed. As a result, the friction can be written as $\tau_f(\dot{\theta}) = \tau_f(\dot{\theta}_n-\dot{e}_{nr}) = \tau_f(-\dot{e}_{nr})$.
\end{ass}

\begin{figure}
	\centering
	\begin{subfigure}[]
		{\includegraphics[height=2.61cm]{Fig3a.pdf}}
	\end{subfigure}
	\centering
	\begin{subfigure}[]
		{\includegraphics[height=2.74cm]{Fig3b.pdf}}
	\end{subfigure}
	\caption{(a) Conceptual roles of the main results. Although asymptotic stability (for regulation) is guaranteed by Theorem 1 while neglecting the dynamics of stiction, an oscillatory motion may occur due to the energy generation during stiction compensation. (b) Passivity-based analysis to prevent the energy generation. The resulting equilibrium point, however, may differ from the desired one.}
	\label{fig:stiction_comp_stiction}
\end{figure}

It is now sufficient to investigate if the energy is generated in the closed-loop difference dynamics because the other sub-dynamics are not excited.
\begin{align}
\label{eq:deriv_diff_dyn_stiction}
B\ddot{e}_{nr} = \widehat{\tau}_f(x_{nr}) - \tau_f(-\dot{e}_{nr}).
\end{align}
Noting that the input-output pair $(-\dot{e}_{nr},-\tau_f(-\dot{e}_{nr}))$ of the friction dynamics is passive according to the Property \ref{prop:fric_passivity}, the following theorem is straightforward.
\begin{thm}
	\label{thm:passivity}
	Under Assumption \ref{ass:fric_passive}, if $\widehat{\tau}_f$ is designed to satisfy passivity of the input-output pair $(-\dot{e}_{nr}, \widehat{\tau}_f)$, then (\ref{eq:deriv_diff_dyn_stiction}) can be represented as feedback interconnections of passive subsystems.
\end{thm}
\begin{proof}
	Passivity of ``Closed-loop dynamics in stiction'' block is trivial because its dynamics are $1/Bs$, and that of ``Friction'' block is satisfied from the Property \ref{prop:fric_passivity}. If the ``friction observer'' block is also passive, the entire structure is represented by feedback interconnections of passive subsystems; see Fig. \ref{fig:stiction_comp_stiction}b.
\end{proof}
This theorem indicates that the energy is not generated during the stiction compensation if the friction observer is designed to be passive. Therefore, the PD-type observer (\ref{eq:PD-type}) guarantees that the closed-loop dynamics do not escape the stiction region, whereas the PID-type (\ref{eq:PID-type}) does not.

\section{Theoretical Derivation}
\label{sec:theory}

\subsection{Proof of Theorem \ref{thm:asymp_stable}}
\label{sec:proof_as}

Because the $\tau_c$ is a stabilizing controller for the nominal system (\ref{eq:ideal_friction_free}), the converse Lyapunov Theorem \cite{khalil2002nonlinear} guarantees the existence of $V_{n,q}^c>0$ (where the superscript $c$ stands for converse) such that
\begin{align}
\label{eq:V_qn_dot}
\dot{V}^c_{n,q} \leq -\alpha_{c} \phi_{1}(||x_{n,q}||) \;\; \text{and} \;\;
\left|\left|\frac{\partial V^c_{n,q}}{\partial x_{n,q}}\right|\right| \leq \beta_{c} \phi_{2}(||x_{n,q}||)
\end{align}
for some $\alpha_c>0$, $\beta_c>0$, and for some positive definite functions $\phi_{1}(\cdot)$ and $\phi_{2}(\cdot)$. Therefore, for the original system (\ref{eq:nq_dyn_ss}),  $\dot{V}_{n,q}+\dot{V}^c_{n,q}$ can be upper bounded as follows since $||g_{n,q}|| \leq \beta_g ||x_{nr}||$ for some $\beta_g>0$.
\begin{align}
	\dot{V}&_{n,q}+\dot{V}^c_{n,q} \leq - \alpha_{nq} ||\dot{\theta}_n||^2 -\alpha_{c} \phi_1(||x_{n,q}||) + \phi_3(||x_{n,q}||) ||x_{nr}||,
\label{eq:V_c_nq_dot}
\end{align}
where $\phi_3(\cdot) = \beta_g \left( \beta_c\phi_2(\cdot) + \beta_{nq1}\phi_{nq}(\cdot) + \beta_{nq2} \phi_{nq2} \right)$.

Let us define a Lyapunov-like function $V(x_{n,q}, x_{nr})=V_{n,q}(x_{n,q})+V^c_{n,q}(x_{n,q})+V_{nr}(x_{nr})>0$. Using (\ref{eq:V_nr_dot}) and(\ref{eq:V_c_nq_dot}),
\begin{align}
\nonumber \dot{V} \leq &  - \alpha_{nq} ||\dot{\theta}_n||^2 -\alpha_{c} \phi_1(||x_{n,q}||) + \phi_3(||x_{n,q}||) ||x_{nr}||  \\
& - \alpha_{nr} ||x_{nr}||^2 + \beta_{nr} ||w||^2.
\end{align}
 Using Lemma \ref{lem:w_bound},
\begin{align}
\label{eq:Vdot_first}
 \dot{V} \leq & -d_1 ||x_{nr}||^2  + d_2 ||x_{nr}|| + d_3 \\
\label{eq:Vdot_second}
&- \alpha_c \phi_1(||x_{n,q}||) - (\alpha_{nq} - \beta_{nr}c_3)||\dot{\theta}_n||^2 ,
\end{align}
where $d_1 = \alpha_{nr} -\beta_{nr}c_1$, $d_2 = \beta_{nr}c_2+ \phi_3(||x_{n,q}||)$, and $d_3 = \beta_{nr}c_4$.
To save space, we borrow the result of Appendix from which the boundedness of the solution can be guaranteed. Based on this, convergence of $||x_{nr}||$, $||x_{n,q}||$, and $||\dot{\theta}_n||$ to certain values can be claimed because $d_2$ is bounded. We conclude the proof by showing that the states can only converge to the unique equilibrium point. First, $\dot{\theta}_n$ should converge to zero because otherwise $||x_{n,q}||$ cannot converge to a constant (hence contradiction). With $\dot{\theta}_n=0$, the difference dynamics become $B\ddot{e}_{nr} = \widehat{\tau}_f(x_{nr}) - \tau_f(-\dot{e}_{nr})$ because $\dot{\theta} = -\dot{e}_{nr} + \dot{\theta}_n=-\dot{e}_{nr} $. Hence $x_{nr}$ converges to the unique equilibrium, and this indicates the convergence of $x_{n,q}$ to its equilibrium as well.

Passivity  can be shown by simple extension. Nonzero $\tau_{ext}$ appears in time derivatives of $V_{n,q}$ and $V_{n,q}^c$. In $\dot{V}_{n,q}^c$, using (\ref{eq:V_qn_dot}), $\tau_{ext}$ appears as $\dot{V}_{n,q}^c \leq \beta_{c} \phi_{2}(||x_{n,q}||) ||\tau_{ext}||\leq b_{ext}\beta_{c} \phi_{2}(||x_{n,q}||)$ which eventually can be absorbed into  $d_3$ and plays no role by the same reasoning with the previous. Finally,  $\tau_{ext}^T\dot{q}$ included in $\dot{V}_{n,q}$ will result in  $\dot{V} \leq \tau_{ext}^T\dot{q}$, which indicates that the passivity is preserved.

\subsection{Proof of Corollary \ref{cor:pid}}
\label{sec:proof_cor_pid}

Let us express the closed-loop difference dynamics as
\begin{align}
\nonumber B (\ddot{e}_{nr} + L_p \dot{e}_{nr} + L_i e_{nr}) + \underbrace{R (\dot{e}_{nr} + L_p e_{nr} + L_i \int e_{nr})}_{=-\widehat{\tau}_f} \\
= \underbrace{-\tau_f + BL_p \dot{e}_{nr} + BL_i e_{nr}}_{=w},
\end{align}
where $R=BL$ is used for simplicity. Therefore, it is obvious that the first requirement of Theorem \ref{thm:asymp_stable} is true. The closed-loop difference dynamics can be expressed in the state-space with
\begin{align}
A_{nr}
=
\left[
\begin{array}{ccc}
0 & I & 0 \\
0 & 0 & I \\
0 &  -L_i & - L_p
\end{array}
\right], \;
B_{nr}
=
\left[
\begin{array}{c}
0 \\
0 \\
B^{-1}
\end{array}
\right].
\end{align}
Define $P$ and $Q$ as
\begin{align}
\label{eq:P_define}
P=
\left[
\begin{array}{ccc}
BL_i^2 + L_i L_p R & BL_p L_i + L_i R& BL_i \\
BL_p L_i  + L_i R   & BL_p^2 + L_p R & BL_p \\
BL_i   & BL_p & B
\end{array}
\right]
\end{align}
and $Q= diag\{ L_i^2 R, \;  (L_p^2-2L_i)R, \; R\}$. Then, $A_{nr}$, $B_{nr}$, $P$, and $Q$ satisfy the following:\footnote{
	Noting that (\ref{eq:riccati}) is the  Riccati equation associated with the $\mathcal{H}_\infty$ optimal control problem, the friction compensation input attenuates $w$ in the sense of $\mathcal{H}_\infty$ optimality \cite{kim2015bringing}:
	\begin{align}
\nonumber	\int x_{nr}^T Q x_{nr}^T + \widehat{\tau}_f^T R^{-1} \widehat{\tau}_f \leq \int w^T w,
	\end{align}
}
\begin{align}
A_{nr}^TP + P A_{nr} - P B_{nr} R B_{nr}^T P + Q = 0.
\label{eq:riccati}
\end{align}
Using this relation, we claim the following Lemma.

\begin{lem}
	\label{lem:nr}
	Using $V_{nr}=x_{nr}^T P x_{nr}>0$, we have
	\begin{align}
	\label{eq:bdd_V_nr_dot}
	\dot{V}_{nr} \leq -\lambda_{m}(Q)||x_{nr}||^2 + R^{-1} ||w||^2,
	\end{align}
	where $\lambda_{m}(Q)$ represents the minimum eigenvalue of $Q$.
\end{lem}
\begin{proof}
	$V_{nr}>0$ can be shown as follows:
	\begin{align}
	\nonumber V_{nr} =& (\dot{e}_{nr} + L_p e_{nr} + L_i\int e_{nr})^T B (\dot{e}_{nr} + L_p e_{nr} + L_i \int e_{nr}) \\
	+&
	\left[
	\begin{array}{c}
	\int e_{nr} \\
	e_{nr} \\
	\end{array}
	\right]^T
	\underbrace{
		\left[
		\begin{array}{cc}
		L_i L_p R & L_i R \\
		L_i R & L_p R  \\
		\end{array}
		\right]
	}_{\triangleq P_1}
	\left[
	\begin{array}{c}
	\int e_{nr} \\
	e_{nr} \\
	\end{array}
	\right],
	\end{align}
	where $P_1>0$ can be shown using Schur complement. Here, let us assume $\lambda_{m}(Q)=R$ for simplicity (the other cases can be analyzed similarly). Then,
	\begin{align}
	\nonumber \dot{V}_{nr} =& 2x_{nr}^T P (A_{nr}x_{nr} + B_{nr} \widehat{\tau}_f + B_{nr}w) \\
	\nonumber =& 2x_{nr}^T P (A_{nr}x_{nr} - B_{nr} R B_{nr}^TPx_{nr} + B_{nr}w) \\
			 =& -x_{nr}^T Q x_{nr} - z^T R z + R^{-1} ||w||^2,
	\end{align}
	where $z=P B_{nr}  x_{nr} - R^{-1}w$. Hence (\ref{eq:bdd_V_nr_dot}) follows.
\end{proof}

Therefore, the second requirement of Theorem \ref{thm:asymp_stable} is true. Finally, the following Lemma tells that there is only one possible equilibrium point that the system state can converge to. Therefore, the third requirement in Theorem \ref{thm:asymp_stable} is also true.

\begin{lem}
	The equilibrium point of the overall dynamics (\ref{eq:deriv_nom_motor})-(\ref{eq:deriv_diff_dyn})  is uniquely given by $e_{nr}=\dot{e}_{nr}=0$, $\int e_{nr} = L_i^{-1} L^{-1}B^{-1} \bar{\tau}_f$ and $x_{n,q}=0$.
\end{lem}
\begin{proof}
	To begin with, note that $x_{n,q}=0$ is the equilibrium point of the ideal friction-free model (\ref{eq:ideal_friction_free}). Now, let us consider the steady state of the overall dynamics (\ref{eq:nq_dyn_ss})-(\ref{eq:diff_ss}). For (\ref{eq:diff_ss}), it is clear that the equilibrium point is $e_{nr}=\dot{e}_{nr}=0$ and $\int e_{nr} = L_i^{-1} L^{-1}B^{-1} \bar{\tau}_f$. Using $e_{nr}=0$, the equilibrium of (\ref{eq:nq_dyn_ss}) is that of (\ref{eq:ideal_friction_free}). Hence $x_{n,q}=0$ is the unique equilibrium point.
\end{proof}

\subsection{Proof of Corollary \ref{cor:pd}}
\label{sec:proof_cor_pd}

The following $P$ and $Q$ can be used.
\begin{align}
P=
\left[
\begin{array}{cc}
 BL_p^2 + B L_p R & B L_p \\
 B L_p & B
\end{array}
\right], \; \text{and} \;
Q=
\left[
\begin{array}{ccc}
L_p^2 R & 0 \\
0 &  R
\end{array}
\right].
\end{align}
The same procedure as in Section \ref{sec:proof_cor_pid} can be followed.

\section{Discussions}
\label{sec:discussion}

\subsection{Working principle and generalization}
\label{sec:phyiscal_inter}

Combining (\ref{eq:PID-type}) with (\ref{eq:deriv_diff_dyn}) results in
\begin{align}
\label{eq:fric_obs_lpf_PID}
\widehat{\tau}_f = \frac{L s^2 + L L_p s + L L_i}{s^3 + L s^2 + L L_p s + L L_i}\tau_f,
\end{align}
which is the 3-2 order LPF.\footnote{$a$-$b$ order LPF means that it has $a$-th order denominator and $b$-th order numerator.}$^,$\footnote{Observer gains are treated as scalar in transfer functions. This simplification is possible when they are constant diagonal matrices.} Namely, the resulting $\widehat{\tau}_f$ is the low-pass filtered value of $\tau_f$. Similarly, the PD-type $C(s)$ in (\ref{eq:PD-type})  results in the 2-1 order LPF (use $L_i=0$ in (\ref{eq:fric_obs_lpf_PID})).

In addition to the LPF property, the proposed friction observer can be alternatively interpreted as follows: $C(s)$ is a control action that attenuates the influence of friction $\tau_f$ on $e_{nr}$ (or $x_{nr}$) in the difference dynamics (\ref{eq:deriv_diff_dyn}). The associated LPF can be derived from $C(s)$, and vice versa:
\begin{align}
\label{eq:relation_C_LPF}
LPF(s) = \frac{P(s)C(s)}{P(s)C(s)-1}, \;\; C(s) = \frac{LPF(s)}{P(s)\left\{LPF(s) -1 \right\} }.
\end{align}

\subsection{On the conditions of Theorem \ref{thm:asymp_stable}}
\label{sec:discuss_conditions}

This section presents interpretations for the seven conditions in Theorem \ref{thm:asymp_stable}. The conditions (i)-(iii) are assumptions  on the controller and friction, and conditions 1)-4) are requirements for the friction observer design.

{\it(i) $\dot{\theta}_d=0$:} As discussed in Section \ref{sec:phyiscal_inter}, the observer compensates for the friction by the relation of LPF which always has a phase lag. Namely, a perfect compensation cannot be achieved when the system is in motion, and therefore, we cannot say anything about convergence. This is a fundamental limitation of model-free approaches that cannot provide model-based friction feed-forward. To argue something about convergence, the system should be commanded to be stationary.

Practical stability can be shown for the tracking case, as presented in Appendix. We would like to underline that the tracking case does not require any conditions needed in Theorem \ref{thm:asymp_stable}. As far as the controller is stable (in any sense) and guarantees existence of a unique solution, practical stability can be concluded. It roughly means that the resulting trajectory approaches the unique solution as the observer gain increases.

{\it(ii) The friction value is constant in stiction:} Theorem \ref{thm:asymp_stable} states asymptotic stability while neglecting the dynamic behavior of the stiction friction. Namely, Theorem \ref{thm:asymp_stable} can only claim that the closed-loop dynamics are attracted to the stiction region, but there is no guarantee if the system stays there when the dynamics of stiction start to play a significant role. To answer this question, a passivity-based analysis on the stiction compensation is presented in Section \ref{sec:behavior_in_stiction}.

{\it(iii) The controller $\tau_c$ is nominally designed to be asymptotically stable, and satisfies $\alpha_{nq}-\beta_{nr}c_3>0$:} The link-side and nominal motor-side dynamics (\ref{eq:nom_link_re})-(\ref{eq:nom_motor_re}) are perturbed by $e_{nr}$. Therefore, the controller has to be strong enough to endure some amount of perturbation until the friction observer suppresses $e_{nr}$ sufficiently (recall also Section \ref{sec:phyiscal_inter}). A sufficient condition for this is $\alpha_{nq}-\beta_{nr}c_3>0$. When (\ref{eq:pd_controller_with_nominal}) is used with (\ref{eq:PID-type}), we have $\alpha_{nq}=K_d$ (recall (\ref{eq:V_dot_nq_pd_controller})), $\beta_{nr}=(BL)^{-1}$. $c_3$ is the coefficient for the viscous friction. In our experimental setup, $c_3 \simeq 10$, $B\simeq 1$. Hence the resulting sufficient condition was, roughly, $K_d \geq 10/L$. This was not restrictive in our experiments, because $L$ could be selected greater than 100.

{\it1) the difference dynamics (\ref{eq:diff_ss}) are exponentially stable when $w=0$, so that we have $\dot{V}_{nr} \leq -\alpha_{nr}||x_{nr}||^2 + \beta_{nr}||w||^2$:} Since the difference dynamics (\ref{eq:diff_ss}) are the 2nd order linear system, exponential stability is a reasonable requirement when $w=0$. In the proof, $-\alpha_{nr}||x_{nr}||^2$ is used to dominate $||w||^2$.

{\it2) $w$ can be bounded by (\ref{eq:w_bound_condition}), and therefore (\ref{eq:w_sq_bound_condition}) is satisfied:} The perturbation should be bounded not greater than linearly. Otherwise, the observer may not dominate the perturbation. We also remark that Assumption \ref{ass:V_nq} is introduced to dominate the perturbation $c_3 ||\dot{\theta}_n||^2$ in (\ref{eq:w_sq_bound_condition}), which is the only term that cannot be dominated by $-\alpha_{nr}||x_{nr}||^2$.

{\it3) $\alpha_{nr}$ is positive and increases with a certain observer gain, whereas $\beta_{nr}$ does not:} This requirement lies in the same line with the conditions 1) and 2). If $\alpha_{nr}$ increases with the observer gain while $\beta_{nr}$ does not, then the perturbation can be dominated by increasing the observer gain. Recall that for the proposed observers (\ref{eq:PID-type}) and (\ref{eq:PD-type}), $\alpha_{nr}=BL$ and $\beta_{nr}=(BL)^{-1}$.

{\it4) there exists a unique equilibrium point of $x_{nq}$ and $x_{nr}$:} Equilibrium point must be defined to claim stability.

\begin{figure*}
	\centering
	\begin{subfigure}[PID-type observer with low gains]
		{\includegraphics[width=5.85cm]{Fig4a.eps}}
	\end{subfigure}
	\begin{subfigure}[PD-type observer with low gains]
		{\includegraphics[width=5.85cm]{Fig4b.eps}}
	\end{subfigure}
	\begin{subfigure}[Observer from \cite{le2008friction} with low gains]
		{\includegraphics[width=5.85cm]{Fig4c.eps}}
	\end{subfigure}\\
	\centering
	\begin{subfigure}[PID-type observer with high gains]
		{\includegraphics[width=5.85cm]{Fig4d.eps}}
	\end{subfigure}
	\begin{subfigure}[PD-type observer with high gains]
		{\includegraphics[width=5.85cm]{Fig4e.eps}}
	\end{subfigure}
	\begin{subfigure}[Observer from \cite{le2008friction} with high gains]
		{\includegraphics[width=5.85cm]{Fig4f.eps}}
	\end{subfigure}
	\caption{Simulation results. For each plot, the top row shows the resulting motor-side positions with the magnified views in the second row. $\theta$ and $\theta_n$ are shown together with the ideal behavior $\theta_{\text{ideal}}$ which is simulated using friction-free ideal FJR. The third row shows $\tau_f$ and $\widehat{\tau}_f$.}
	\label{fig:simul}
\end{figure*}

\subsection{Separation-like property}

In linear system theories, an observer is said to have separation property when the control gains and observer gains do not affect each other (hence can be designed separately). For the proposed friction observer, a similar property can be observed. In (\ref{eq:Vdot_second}), the decaying rate of $x_{n,q}$ is determined by  $\alpha_c$ which comes from the control design. Likewise, in (\ref{eq:Vdot_first}), the decaying rate of $||x_{nr}||$ is determined by $d_1$ in which the observer gain plays a dominant role when it is sufficiently large. Therefore the controller and friction observer can be designed separately.

\section{Validation}
\label{sec:validation}

\subsection{Simulations}

Simulations were performed to validate the proposed friction observer with the LuGre friction model:
\begin{align}
\label{eq:lugre_1}
\tau_f(v) = \sigma_0 z + \sigma_1 \dot{z} + \sigma_2 v \;\; {\text{with}} \;\;
 \dot{z} = v - \sigma_0  \frac{|v|}{g(v)}z,
\end{align}
where $g(v) = f_c + (f_s - f_c)e^{-(v/v_s)^2}$. The parameters of the friction model are taken from \cite{de1995new}: $\sigma_0 = 10^5$, $\sigma_1 = \sqrt{10^5}$, $\sigma_2=0.4$, $f_c=1$, $F_s=1.5$, and $v_s=0.001$. The motivating example in Section \ref{sec:proposed_fo} was simulated with system parameters $B=1\mathrm{kg}$, $M=1\mathrm{kg}$, $K_j=3000\mathrm{N/m}$, $g(q)=0\mathrm{N}$. As illustrated in the example, PD gains were $K_p=50\mathrm{N/m}$ and $K_d=5\mathrm{N\cdot s/m}$. The desired position $\theta_d=0.01\mathrm{m}$ was commanded as step with zero initial conditions. Because the purpose of the simulation study is to validate the theoretical findings, we did not include any additional effects such as quantization, sensor noise, and link-side friction. The performance in the presence of these effects will be evaluated by the experiments.

Two sets of observer gains (low and high) were compared for both PID- and PD-type observers. The observer proposed in \cite{le2008friction} (shown in Fig. \ref{fig:friction_observers}b) was also implemented for comparison. $L=50$, $L_p=10$, $L_i=25$ were used for low gains, and $L=100$, $L_p=20$, $L_i=100$ were used for high gains. $L_i=0$ was set for the PD-type observer, and $L_p=L_i=0$ for the observer in \cite{le2008friction}. The simulation results are summarized in Fig. \ref{fig:simul}.

\begin{figure}
	\centering
	{\includegraphics[scale=0.39]{Fig5.jpg}}
	\caption{7DOF surgical robot MIRO used in the experiments}
	\label{fig:miro}
\end{figure}

When the low gains were used, as shown in Fig. \ref{fig:simul}a, the PID-type observer resulted in an oscillation around the desired equilibrium point. In the third row of the figure, $\widehat{\tau}_f$ varied together with $\tau_f$ due to the integrator since $e_{nr}$ was not zero. As illustrated in the motivating example, $\theta$ started to move when $\widehat{\tau}_f$ was large enough to break the stiction (see also the second row). In contrast, as shown in Fig. \ref{fig:simul}b, the oscillation did not occur for the PD-type observer which, however, resulted in constant steady-state error. Due to the absence of integral action, $\widehat{\tau}_f$ could converge to a certain value inside the stiction region, as shown in the third row. The observer in \cite{le2008friction} also showed oscillatory motion around the desired point (Fig. \ref{fig:simul}c)

When the PID-type was used with high gains, as shown in Fig. \ref{fig:simul}d, the oscillatory motion was hardly observed because the integral action did not play a significant role since $e_{nr}$ could be strongly suppressed. We report that, $e_{nr} \rightarrow 0$ (namely, constant $\widehat{\tau}_f$ and $\theta \rightarrow \theta_d$) could be achieved. For the PD-type, as shown in Fig. \ref{fig:simul}e, although the steady-state error was reduced due to the increased gains, it did not converge to zero, as expected from Corollary \ref{cor:pd}. For the observer in \cite{le2008friction}, the oscillatory motion remained although the amplitude was decreased.

From the simulation results, we can conclude that the PD- and the PID-type observers have different characteristics. The PD-type observer guarantees convergence to a certain point regardless of the observer gains, however, at the price of some steady-state error. PID-type observer may result in oscillatory motion, but there is also the possibility that it may outperform the PD-type observers.

\subsection{Experiments}

Two experiments were performed using a 7-link surgical robot MIRO shown in Fig. \ref{fig:miro}. The first experiment is designed to repeat the scenario of simulation studies to validate the theoretic findings. The second experiment shows the tracking scenario using task-space controller. Apart from these, the video attachment shows interaction of the robot with human operator as illustrated in Fig. \ref{fig:miro}.

In the first experiment, the motor-side PD controller was used similar to the simulations with the following scenario: (i) initially, the robot was commanded to keep its initial position; (ii) at $t=3\mathrm{s}$, every joint was commanded to move $-5\mathrm{deg}$; (iii) at $t \approx 13\mathrm{s}$, a human operator applied external force. In addition to the proposed PID- and PD-type observer, the friction observer from \cite{le2008friction} was implemented for comparison. The case without friction observer is shown to provide reference. Similar to the simulation study, two sets of observer gains were used; low and high. Fig. \ref{fig:exp_joint} shows the error plot for the 2nd joint only, since this joint showed the different characteristics most clearly. For this joint, the control gains were $K_p=50\mathrm{Nm/rad}$ and $K_d=2\mathrm{Nm\cdot s/rad}$ with $B \approx 1 \mathrm{kg\cdot m^2}$; therefore, the joint should show under-damped motion if the friction is correctly compensated for. Similar to the simulation, with the PID-type observer, the oscillations occurred when the observer gains were low. When the high observer gains were used, the oscillations were barely observable. On the other hand, the PD-type observers did not show any oscillations for both low and high gains. Another interesting thing to observe is that the steady-state error was different after the human interaction because the joint can be stuck anywhere in the reduced stiction region. For the low gain case, for example, the steady-state error before the interaction was $0.003635\mathrm{rad}$ and after the interaction was $0.001881\mathrm{rad}$. When the friction observer from \cite{le2008friction} was used, asymptotically stable behavior was not achieved for both low and high gains.

In the second experiment, the following task-space impedance controller was implemented:
\begin{align}
\tau_c = J^{T}(\theta_n) \left( - K_p e_x - K_d \dot{e}_x\right)  + g(\bar{q}(\theta_n)),
\end{align}
where $J$ is the Jacobian matrix and $e_x=x(\theta_n) - x_d$. $x$ is a task-space variable which contains position/orientation of the end-effector as well as that of the third joint (in $\mathrm{rad}$). With the gravity compensation $g(\bar{q}(\theta_n))$ computed using quasi-statically estimated link-side position $\bar{q}$, this controller is known to satisfy asymptotic stability and passivity for regulation  \cite{ott2008passivity}. The control gains were selected as $K_p=1000\mathrm{N/m}$ , $K_d=200\mathrm{N \cdot s/m}$ for end-effector positions, $K_p=10\mathrm{Nm/rad}$, $K_d=2 \mathrm{Nm \cdot s/rad}$ for end-effector orientations and elbow. The end-effector was commanded to track a piecewise smooth (up to acceleration) square trajectory while keeping the end-effector orientation and elbow position fixed, in 5 seconds. The length of each line segment was $15\mathrm{cm}$. After $t=5\mathrm{s}$, the desired end-effector position was set to be constant. Compared to the case without friction observer, the friction observers contributed to improve the tracking performance, as shown in Fig. \ref{fig:exp_task}.

The video attachment of this paper shows the second experiment with human interaction. In the video, the control gains $K_p$, $K_d$ of the end-effector position were lowered in order to show the effect of friction observers and to show interaction capability more clearly.

\begin{figure}
	\centering
	{\includegraphics[scale=0.315]{Fig6.eps}}
\caption{Experimental results for the joint space PD regulation control. Step command ($5^\circ$) was commanded to all joints at $t=3\mathrm{s}$, and a human operator applied external force at $t \simeq 13\mathrm{s}$. Top row: low observer gains, bottom row: high observer gains.}
	\label{fig:exp_joint}
\end{figure}

\begin{figure}
	\centering
	{\includegraphics[scale=0.215]{Fig7.eps}}
	\caption{Experimental results for the task space tracking control. }
	\label{fig:exp_task}
\end{figure}

\section{Summary and Conclusion}
\label{sec:conclusion}

This paper proposed model-free friction observers that do not harm stability/passivity of the original controller. The main feature of the proposed approach is the use of nominal motor signals in the control law (Fig. \ref{fig:friction_observers}a). A similar friction observer was proposed in the previous study, but there was an intractable input ($\tau_k$ in Fig. \ref{fig:friction_observers}c) which cannot be implemented around the equilibrium point. For this reason, $\tau_k$ has been neglected under the expectation that it has little influence on stability. This paper theoretically clarifies that $\tau_k$ can be neglected in general. The proposed approach has another advantage that it provides a better understanding on the stiction compensation during which the friction observers tend to generate energy. In particular, it is possible to design a passive friction observer that does not generate  energy. The proposed scheme is validated through simulations and experiments.

redpajama_set_name: RedPajamaArXiv


Ethereum vs Bitcoin Comparison 2018 | Who Will Be the Big Winner?
Shakespeare style question in cryptoworld is "Ethereum or Bitcoin that is the question."
What is each one backed up by?
As an investor, an initial aim is to create success in all potential investments that you would like to undertake. For many years, financial investment companies have always managed to control the progress of financial success of investors especially by managing their portfolios and charging high fees. The revolutionary invention of cryptocurrency managed to break these barriers and surrender investment control to the investors directly.
Bitcoin and Ethereum (ETH) are currently recognized to be the two largest cryptocurrencies in the world as Bitcoin (BTC) takes the lead. Ethereum's performance in the past few years has opinionated the possibility of taking on the lead in the near future. However, bitcoin is observed to maintain a steady and higher performance in spite of the volatile market trends in 2017.
Bitcoin being the "mother" of founding cryptocurrencies has led to the innovative gesture of new digital coinage globally such as Ethereum its current major competitor. No matter how similar they may seem, you would be concerned with analyzing the major differences between Ethereum and Bitcoin. Recognizing these difference would help you in the process of decision making while choosing the best cryptocurrency to invest in.
ETH vs BTC has stirred an instrumental structure of allowing the larger audience to learn more about the differences between both digital assets. Along these guidelines, investors possessing either one of the assets or even both at the same time will be able to enlist the benefits and the limitations of each asset. The comparison of these benefits and limitation forms the foundation of stirring up the debate of Bitcoin versus Ethereum.
As a new investor, you will need to be aware of the market tendencies that ensure solid investment ventures that are often demonstrated by the unpredictable volatile trends of the market prices. Investing in the cryptocurrency industry will require your constant need to enroll an analytical strategy that will be able to enhance your ability to make a safe and pleasant decision.
Bitcoin may seem more attractive than Ethereum due to its leading performance in the cryptocurrency marketplace. However, this does not affirm that it will always have a definitive high performance. The debate of ETH vs. BTC has been ongoing for the past few months. Major differences identified between Ethereum Bitcoin digital assets are addressed below.
It was initially developed and launched on January 3, 2009. This asset was designed to operate as a secure P2P (peer-to-peer) decentralized payment system.
Bitcoin uses the C++ programming language which has less than seventy specified commands to be utilized to provide high-security levels. It also utilizes the proof of work model which increases security and validity of transactions.
It is circulated through a process known as mining which also rewards completion of the transaction at a rate of 12.5 Bitcoin per block. This reward is usually halved upon completing 210,000 blocks. Bitcoins limit the volume created each year thus halving the reward. The time consumed to create Bitcoin blocks is ten minutes which is very long and more energy consuming. At the moment there are only 21 million Bitcoins that can be mined.
Was initially developed and launched on July 30, 2015. It is a decentralized online platform that enables smart contracts to be operated. It has a much wider spectrum by allowing the development and running of an application on its platform by different.
Ethereum can program a variety of smart contracts within the system as it is written in Turing complete programming languages. The Turing language in this system contains seven different programming languages that enhance the flexibility and operational functions to developing different smart contracts.
Complete transactions/ blocks are rewarded at a rate of 5 ether per block. This reward does not change throughout since this asset does not apply a maximum number limitation. It simply caps the volume of ethers released each new year. The time taken to create Ethereum block is fourteen seconds which saves time and is less tiresome.
Bitcoin was designed to serve as a decentralized peer- to- peer payment system whereas Ethereum was designed to serve as a decentralized platform that operates smart contracts.
Bitcoin system utilizes the C++ programming language while Ethereum system uses the Turing complete language system which contains seven different programming languages. Bitcoin programming language is not diversified nor as flexible as the one used in Ethereum systems.
Bitcoin will usually reward a client with 12.5 bitcoins for completing each Bitcoin mining block. This is very different from Ethereum rewarding system which rewards 5 ethers to their clients for every Ethereum mining block completed.
Bitcoins rewards are eventually halved once you create 210,000 blocks and above while Ethereum maintains the reward of 5 ether per block throughout. Ethereum does not alter the 5 ether reward no matter how many Ethereum mining blocks you create. Bitcoin limits the volume of Bitcoins blocks created each year to 21,000,000 while Ethereum does not have a maximum volume of Ether blocks created each year. Instead, Ethereum caps the volume released each year.
Bitcoin system takes a much longer time to complete each block than Ethereum. If you work with Bitcoin system you will use up to ten minutes to create one block. Whereas, when you use Ethereum system you will use only fourteen seconds to create each block in the blockchain. This means that when you use ten minutes to create one Bitcoin mining block your reward will be 12.5 Bitcoins. Whereas, when you use the same ten minutes to create Ethereum mining block you will produce 42 ETH mining blocks. The will, therefore, be 210 Ethers.
Bitcoin system takes more time as it involves solving complex mathematical problems which provide high security and waste both time and energy. Whereas, Ethereum system is flexible as it enables the usage of seven different programming languages which are much easier to use to create each ether block at a shorter period of time.
The models of charging transaction fees are very different when considering BTC vs. ETH.
Bitcoin transaction fees are usually charged according to blocks and timespan. If you would like for your transaction to take the shortest amount time possible such as 5 minutes to 15 minutes you will need to pay the highest possible fee. When you pay lower fees your transaction will take from 10-30 minutes to be confirmed. Bitcoin system also charges a higher transaction fee for 3 blocks than for 6 blocks.
In Ethereum technology, the transaction fee is calculated differently using a two-step process. First of all, you will need to measure ETH gas price which is usually very minute. It can be measured in Szabo's whereby 0.000001 ether is equal to 1 Szabo. The second step is to take the gas price and then multiply it by the total amount of ETH gas units being purchased in each block in ETH blockchain system. The answer will give you the total transaction fees to be charged in an ETH transaction.
You should note that Bitcoin transaction fees are actually higher than Ethereum transaction fees. BTC transaction fees have been reported to charge up to 40% of the transaction block value. Ethereum transaction fee, on the other hand, is much lower such that it may not even reach 10% of your ETH block value.
In the crypto market, BTC price level has been observed to attain 1,500% rise in the price level in 2017. The rise is presented by the price rise that reached well above $15,000 in 2017. However, even with this great rise in price levels, the market share of bitcoin in the cryptocurrency market has gradually depreciated. In the last year alone, Bitcoin market share fell from 90% to 42% in 2017 and is predicted to fall further in 2018 due to higher competition from other altcoins being preferred by clients globally. Even with a decreasing market share, Bitcoin is still expected to increase in market price value to $100,000 per bitcoin in 2018.
The proof of work model has mitigated the security of operations of Bitcoin but also considered to produce several hindrances of time and energy wastage. You may feel a greater sense of assurance to invest in Bitcoin cryptocurrency due to its high level of security. However, the time wasted in using ten minutes to get just one block completed greatly discourages and limits the potential profit growth of clientele accounts.
Since it takes ten minutes to earn 12.5 Bitcoins in the mining process, then the average energy cost of one bitcoin will be equivalent to 20 barrels of oil. However, the current value of Bitcoin to oil is 1bitcoin= 100 barrels of oil. This makes Bitcoin cryptocurrency become one of the most valuable commodities to have globally. As the value of Bitcoin towards oil increases, mining of Bitcoins has become extremely valuable especially if the energy costs of mining are kept low.
On the other hand, Ethereum is looking up to a rising opportunity of increasing both its crypto market share and its crypto market price. The switch from using the proof of work model to proof of stake model using Casper protocol is greatly influencing the structural behavior of clients globally. Ethereum is bound to increase due to the fact that you can manage to create each block at a much lesser amount of time than Bitcoin. The reward remains the same throughout and the programming language is much more flexible to utilize than the one in Bitcoin system.
At this rate of progress and innovative changes to proof of stake, Ethereum is bound to become the leading coin in the crypto market due to its ability to offer higher efficiency to clients. You will be able to earn many ethers since it takes only 14 seconds to create an ether block in the blockchain system. Since it takes a lesser amount of time to create an ether block and earn 5 ethers per block the energy consumption rate is also lower thus reducing the cost of mining. ETH mining in comparison to bitcoin mining is much cheaper since energy consumption is far much lesser than the energy used to mine bitcoins.
Ethereum uses oil and energy costs that are equivalent to the energy consumption in a small country whereas, Bitcoin oil and energy consumption and costs are equivalent to energy consumption in 159 countries. Ethereum saves energy cost by more 99.4% in comparison to Bitcoin energy consumption levels. Eventually, Bitcoin will run out of energy resources to utilize in its mining process especially with utilizing its proof of work model.
On the other hand, Ethereum will save more energy costs even as it shifts to utilizing the new proof of stake model. This is because the new model will eliminate the usage of mining process to create the blocks. It will rather use validators which eases the process of validating and securing legitimate smart contracts operations digitally.
Bitcoin- one of the most important criticisms of bitcoins is that it is not backed by anything, nor is it intrinsically valuable. Bitcoin is considered too volatile in the crypto market and it does have a characteristic of being natively deflationary. This means that Bitcoin has been noted to erratically deplete its market value in the shortest amount of time possible. Its high charges in transaction fees also discourage clients from acquiring more Bitcoins and they rather alter to less expensive cryptocurrencies that are more affordable. You cannot lend your Bitcoins as a means of creating a source of income as an interest charge has zero value on this asset.
Several Bitcoin clients have also complained about the slow transaction, fees, and process while sending Bitcoins to another client. You will experience this mainly because once you send your bitcoins to another person, the transaction will go through different computers in order for Bitcoin protocol to be run globally. This ensures the validity of the transaction and once it is verified, the transaction then waits in the Mempool. Your Bitcoin transaction is basically waiting to be collected by a Bitcoin miner. Bitcoin miner will collect it and place it in the block transaction section of the blockchain system. This delay is one reason for the delay in the transaction process. The other reason is that due to the current price increase of Bitcoins the number of transactions has also increased. Each block in the blockchain can only hold a finite number of a block placed in the blockchain system. As a result, you will need to wait for quite some time for your transaction to be picked by a Bitcoin miner all while realizing that there are many transaction waiting in the mempool.
In spite of all of these delays and discrepancies in Bitcoin system, we should all be thankful to BTC for having provided us with the freedom to make more wealth. As Nelson Mandela once quoted, 'money won't create success, the freedom to make it will.' We should also be thankful to BTC for introducing us to the new and highly developed technology of blockchain system and digital currency. However, innovative improvements on this amazing technology are required in order to enhance the models in which digital currency can be created with an intrinsic value, lending capabilities, and low transactions fees.
Healthcare systems globally will be able to store, share and access their patient's records. This will be a key component towards preventing or controlling viral outbreaks as new vaccines are developed due to having sufficient information. As a patient, you will be able to access health care while visiting a foreign country as your health information can be accessed online by all hospitals globally.
You can use Ethereum for security purposes since Ethereum security system is not centralized therefore hackers will have a very hard time in being able to access your personal information. Your personal information is also safe from third parties as Ethereum blockchain technology makes it impossible for third parties to collect personal data even through search engines as done before.
Ethereum through smart contracts enables you to make an exchange with anything of value. This type of exchange is also completely risk-free since the transaction is computer coded and securely stored.
You will be able to place your political vote on a safe platform no matter which country you live in. Ethereum system will be able to apply high-security measures that report every change in votes and it will be directly and publicly displayed. Transparency, therefore, will be more applicable using this system and democracy in politics will reach its greatest heights.
If you are a great fan of taking on high risks especially in the gambling sector, you will now be able to relax as Ethereum technology will offer a fast, safe and no scamming platform. You will be able to gamble at no extra loss or risk as well receive a big push in exploiting your high-risk investment ambitions.
You will also be able to store data with Ethereum technology as it is encrypted and it enables users to transfer data quickly between millions of servers.
Ethereum will also engage in the Google project of mass producing self- driving cars in mid- 2020. It will make the self- driving cars much safer to use and communicate with at a pace that is a thousand times faster than is humanly possible.
Include your own ideas and wisdom that is also leveraged with the wisdom of the larger populace. You will be able to utilize the ERC20 which in full is known as Ethereum Request for Comments. It is a platform in which you and the larger populace can propose any improvements needed to be conducted on Ethereum technology.
Spreading the funding systems over time thus ensuring availability and accessibility of funds in the long-term period thus making the asset a store of value for you and the larger populace.
Ethereum technology does not fully trust the centralized system in order to operate. Instead, it applies the decentralized system in order to ensure that hackers will not gain access to your profile and personal data.
From the information provided above, you realize that Ethereum is backed up by amazing products and platforms that will ensure its continued usage and growth in the long run.
Ethereum technology has created a platform that facilitates the creation of the products being used by clients. For example, ETH token which is a product is created on the ETH platform by developers. Since the ETH platform uses the Turing language that contains seven different languages making it flexible for many users to be able to develop smart contracts within the shortest amount of time. The flexibility of using seven different languages will influence clientele to develop more smart contracts in each New Year as it is easier apply and understand.
The ETH platform is equipped with other tools such as compilers and IDEs that support the development of ETH products. The platforms and the products developed the platform is developed to abide by the procedures and the conventions as defined in the protocols system.
Smart contracts which are considered to be a large product that contains standalone assets such as Ethereum tokens and ETH cryptocurrency. You will be encouraged to use the smart contract as they do contain an intrinsic value, can be lent and are completely risk-free. They take a much shorter amount of time to create and can be easily used in various aspects of real life as discussed above.
Decentralized applications (DApp) are also another product of Ethereum technology. They provide high-security measures and minimize risk attacks by more than 51%. This assures clients of their privacy and security, as fraud and online theft of their wealth is prevented from the get-go.
From an investor's point of view, you would be well advised to invest in Ethereum than in Bitcoin system as it carries a larger weight of benefits. The proof of stake will offer a more efficient structure of validation than the proof of work model and you can also address any challenges with Ethereum system through the ERC20. The DAICO innovation by Buterin will enhance the overall performance of this asset in the long run while stabilizing its volatility in the marketplace.
Ethereum versus Bitcoin has offered an in-depth analysis of the operational approaches being used by each digital asset well enough to have a clearer picture of Ethereum being the better investment.
Thank you for taking the time to read through this informative piece, we hope you enjoyed. Visit our website for more informative content, see you next time!


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Around the nation: Chicago jail gives naloxone to departing inmates
Illinois: Since last summer, Cook County Jail in Chicago, the largest single-site jail in the United States, has trained roughly 900 inmates on how to use the overdose-reversing drug naloxone and has given 400 at-risk inmates a naloxone nasal spray device upon their release. The goal of the program, officials said, is to curb overdose fatalities among former inmates who have misused drugs and help saturate the community with naloxone (Babwin, AP/Sacramento Bee, 7/29).
New Mexico: Presbyterian Healthcare Services has tapped Roger Larsen to serve as CFO and SVP. In the role, Larsen will supervise the financial management and performance of the health system. Larsen has previously served as CFO for Sutter Health's Bay Area Foundation in Sacramento, as well as East Bay Hospitals in northern California (Haefner, Becker's Hospital Review, 7/28).
Utah: Intermountain Healthcare has announced that it will be the first health care system in the United States to draw blood without needles from patients who already have an IV in place. Instead, the health system will be using a needle-free technology called PIVO, a single-use, disposable device that connects to an exterior IV catheter to extract a blood sample—sparing the patient repeated needle sticks for blood draws and reducing providers' exposure to needles (Al Idrus, FierceBiotech, 7/28; Monegain, Healthcare IT News, 7/28).
Reduce opioid misuse and abuse with our new report
Opioid misuse and abuse is one of the most pressing public health issues in the U.S., and hospitals and health systems are on the front lines. Currently, most health systems focus their opioid management efforts on select medical specialties.
This report outlines three imperatives to guide hospitals and health systems in their efforts to reduce the impact of inappropriate opioid prescribing and misuse.
Inside Amazon's 'secret lab' developing new EHR and telemedicine technologies
Current ArticleAround the nation: Chicago jail gives naloxone to departing inmates
Don't call it 'dead' yet: Why the GOP may still have months—or years—to repeal the ACA
If your money isn't buying happiness, you might be spending it wrong, research suggests
Cleveland Clinic, Boston Children's announce first-of-its-kind partnership for pediatric cardiac care
Scientists edit genes of human embryos for the first time in US
Opioid misuse is a 'national emergency,' White House commission says
Inpatient rehab, skilled nursing facilities will see payment bump in FY 2018, CMS says

redpajama_set_name: RedPajamaCommonCrawl


I started with the first one as from experience I know that if SAP table had K at the end of the name that this must be configuration of header (Kopf).
I've inserted my new delivery type as target delivery type and I've filled data transfer of header data with 301 - which is a special routine for delivery header without reference.
I've run my code again, and I was surprised that I have still the same error message.
But when I double clicked on details I saw that there is now additional info beside delivery type.
I guessed that I have to open the second view now and this was what I did.
This time I've entered item category which was visible in error details and I user routine 302 for data transfer of item data without reference order.
Once saved I rerun the program and finally I received positive result.
Bellow you can find piece of code which I used to create outbound delivery without reference document.
append lines of error_log to bapi_log.
loop at error_log assigning field-symbol(<err>) where type ca 'EAX'.


As we head into spring, it may appear a slightly odd time of year to consider picking up some knitting needles, but Save the Children charity is giving you a very good reason to consider doing so. Partnering up with Guardian pharmacies, Save the Children are again organising their "Guardian Angel Knitting Program", which encourages people of all ages and capabilities to knit garments and blankets to be given to those in need.
The Guardian Angel Knitting Program has been operating for fifteen years and, over that time, more than 2 million garments have been knitted to go to projects supporting the world's poor – many of whom are women and children. Given that approximately 7.6 million deaths of children under the age of 5 are due to pneumonia, the cause is an important one to consider not just during the Australian winter, but throughout the year.
Save the Children's General Manager of Fundraising and Partnerships, Mr Anthony Trainer, is delighted for the charity to be partnered with the Program and says community support has been overwhelming, with approximately 100,000 garments being knitted last year.
Whilst the program runs specifically from June to August, Mr Trainor says that people are encouraged to get involved all year round.
So if you are feeling inspired by Julia Gillard's knitted kangaroo, or the latest knitting projects on Pinterest, why not harness your creative juices into supporting a good cause?
'When people knit something they feel more connected to it and feel like they have done something good. Which they have', says Mr Trainor.
Those who wish to get involved can find more information on the Guardian Angel KnittingProgram here or pick up the guide from Guardian pharmacies.
This entry was posted in Get Involved and tagged get involved, save the children. Bookmark the permalink.


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The Hunted Woman is a 1925 American silent drama film directed by Jack Conway and starring Seena Owen, Earl Schenck, and Victor McLaglen.

Plot
As described in a film magazine review, a young woman goes North to find out whether her husband is dead or alive and also to effect the release of her innocent brother from jail. She meets a youth who has staked out a gold claim and has a romance with him. She does not surrender her love until her husband is found and killed, meeting death in a fight with the youth's partner.

Cast

Preservation
With no prints of The Hunted Woman located in any film archives, it is a lost film.

References

Bibliography
 Munden, Kenneth White. The American Film Institute Catalog of Motion Pictures Produced in the United States, Part 1. University of California Press, 1997.

External links

1925 films
1925 drama films
Silent American drama films
American silent feature films
1920s English-language films
Fox Film films
Films directed by Jack Conway
American black-and-white films
Films based on works by James Oliver Curwood
1920s American films

redpajama_set_name: RedPajamaWikipedia


It is not difficult to remedy cloudy pool water. The challenge is to keep your pool from getting cloudy in the first place. Although the causes of cloudy pool water range from heavy bather use to clogged filters, the biggest culprit is probably going to be incorrect applications of pool chemicals. Starting here, and then troubleshooting filtration systems, quality of water and maintenance techniques will save you unnecessary expenditure.
A clean pool will give you years of service if maintained properly. Once a month schedule a Saturday morning cleaning session. Before the sun gets too high in the sky in the summer (or around noon in the winter) don a pair of old shorts, flip flops and an old tee shirt and tackle the pool filter. Remove the bolts securing the housing for the filter and gently remove the filter. Twist your hose nozzle for a wide spray and clean between the filter elements. Wash out the filter housing, and carefully replace the filter element. Mix diatomaceousearth (DE is used as a filtration aid) with water in a large bucket and slowly run through the filter to insure it coats the filter element.
With a stiff fibre brush (avoid wire brushes as they may be too harsh for your pool) brush the pool, beginning at the top of the sides all the way to the middle of the pool on one side. Work your way carefully around the pool until you come back to where you started. If you have a pool ladder and steps, start here and be sure to scrub all the steps, including inside and under them.
Add water to your pool to bring it up to level. Use your pool chemical kit to run tests for PH, total alkalinity and calcium content. Add a pool shocker to insure you are getting rid of algae buildup. Using the chemical kit again, check to see if you need to add algaecide or acid and add the appropriate chemicals. Override the filter timer and allow the filter to run for approximately 12 hours to circulate the new chemicals you have added and to insure the DE has coated the filter element and it is filtering correctly.
If you use a solar blanket, make sure it is clean and free from debris before using it to cover your pool. Be sure to ask your family and friends to shower before using the pool to remove sweat, body oils and make-up. Check shrubs, trees and lawn areas to insure no plant material enters the pool. Check the pool filter at least every Saturday morning and remove debris no matter how small. Be sure to store all pool cleaning equipment on racks that receive sun and are free from dust, dirt and shrubbery. If you are in doubt about the contents of your pool water, take a sample to your local pool supply for analyzing. They can tell you what chemicals you need and diagnose the water properties of your pool.
Pool Water Testing: How Often?


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« ESPN Suspends Robert Parker, Indefinitely | Main | Update: Virtually Nothing In The Original Reports About the Killer Was Correct »
Killer Killed His Parents First
Parents first.
He then went to Connecticut to kill a woman he was involved with somehow -- whether wife or ex-girlfriend -- and also to kill all the children near her.
I think we were just talking a few weeks ago about a certain form of intensely narcissistic psychopathy that spurs people to kill everyone close to them rather than just taking the gentleman's way out of suicide. (I don't mean to give a nod towards suicide but if the difference is between killing yourself and murdering your whole family for your failures and inadequacies, let's put in a good word for suicide.)
I've said this before but I think the media can help reduce these things from occurring. These nutters see themselves heroically, sort of as bigger-than-life agents of mayhem and evil. Now that may sound like a bad thing to you, but it doesn't sound bad to them: They've embraced it.
And what Evil is usually described as, in popular mythology, which these guys are not, is potent and capable. Yes, Evil is horrible, but these guys are embracing it for the Power of it. Because they are failures and hopelessly inadequate in their own lives, they contrive a fantasy in which they become Dark Heroes -- larger than life and big as death -- by murdering a lot of people.
Obviously we have a debased value system here. But it does seem to me that that one thing they value and cherish is their self-conception of the Big Scary Man, who you should Take Serious Notice Of because he's Scary and Capable of Anything.
And a lot of media coverage tends to play this angle up. And I don't mean to knock the press too badly on this -- evil sells, and these people are evil.
However, I think it would do at least something to dissuade the next potential mass murderer to know, for example, that coverage on him will not focus on the Evil Menace part of him (which is a self-conception he finds flattering), but the Sad, Lonely Pathetic Guy Who Has a Small Dick and Couldn't Keep a Woman or a Job and Just Couldn't Hack It part of him. The part that's actually much more relevant to his crime -- masterful men do not have to kill people to let the world know "I exist" -- and the party that he's actually afraid of other people knowing about.
If I were the media, I'd allow myself to get very personal in publishing accounts of these guys. Personal, and nasty.
And not only is this a bit of a public service, but, as I said, this is much more relevant to the actual reasons for his crime than this puffed-up faux-heroic claimed motivations. The maniac in Colorado did not shoot up a theater because of Batman, and to even say that credits his self-conception as true and puffs up his fantasy connection to Batman.
No, the maniac in Colorado shot up the theater because he was a pathetic weakling unloved by women and incapable of satisfying them and so retreated into a twisted babydick world of power fantasy.
Same thing with this guy.
I'm going to go against my political team, here-- although conservatives often say "Label evil as what it is, Evil, and leave therapy and psychology out of it," I'm going to say No, not in these instances. Because Evil (notice the capital letter E) is powerful in these sad losers' imaginations, and they want to be called the Big Scary Man, the Shadow That Menaces At Midnight.
For an impotent, weak, ineffectual man, that is an attractive fantasy.
What they do not want and could not abide is an accurate assessment of their psychology, their physical stature and shortcomings, their ability to succeed in work or school, their loser history with women, and so on.
To the average people, the idea of being called Evil is bracing and restraining. Not to these fellers. All of these bizarre murders are motivated, at root, by the psychology of utter failure. These are flop-sweat murders, sexual panic murders, too weak to carry on murders. Reporting them as such would not only provide at least as small disincentive to the Power Fantasy losers who commit them, but would actually be much, much closer to the truth than "Heavy Metal poisoned his mind."
No, being the runt who no one loved all his life poisoned his mind. Heavy Metal was just his escape from that. Or Batman, or video games, or Jared Laugher's Conspiracy By Manipulation of Grammar, etc. Promoting the Batman/Heavy Metal angle takes the lunatic's diagnosis of himself as credible.
It's not.
There's a Pink Floyd song that mentions a sentence of being exposed before your peers. Let's strip the Mystery away from these guys. The Mystery angle is both complimentary (in the only way it matters-- as they assess a compliment) and false. The thoughts of a loser gone lunatic are not particularly mysterious, and not very interesting; they're all basically the same, as FBI profilers can tell you.
So less of that.
These guys are Romanticizing murder and conceiving it as some sort of Blaze of Glory heroic Act III. Everything we do and say should refuse that romanticization. Where they seek to seem big, we should make them small (which, again, is actually on the mark as far as accurately). Where they wish to seem Potent -- capable of inflicting their will on the world -- we should strip them down to what they actually are, impotent in virtually all ways. A little finger pulling a gun they didn't build is the one sad skill they've had any success with.
Let them know that murder will not be an escape from that pitiful truth, but rather a life sentence of being confronted with it.
"Theater:" A commenter "beach" cites an expert diagnosing this sort of crime.
A key word is "theater" -- the psychopath chooses this sort of senseless, large-scale murder for the theatrical element. Obviously there is no "motive" as it is usually understood -- murdering a bunch of kids does not advance his cause (the way murdering a man for his car would get you, temporarily, a car).
He wants to be discussed; he's giving a performance; he wants to move the audience.
The audience shouldn't indulge him by considering him in the terms her prefers.


Dinner with Bevy's Bevy Smith gives us her ten commandments.
Fashion Queens host Bevy Smith has such a flair for hosting dinner parties, she does so professionally, counting Pharrell, Charlize Theron, and CNN's Soledad O'Brien as guests on any given night. So who better than Smith to help us tradition-bucking, penny-pinching millennials discover the lost art of having our friends over for supper?
Whether you're nervous about how to actually get people to come, or curious about how to not lose your sh*t when someone hijacks your meticulously-curated playlist, don't worry—Bevy's got you. Here, find her ten commandments for being an all-business hostess with the mostess.
In the age of Facebook, we're receiving all sort of invites, to go all sorts of places. You've got to step up your game and it's *all* about personalization. "Don't go with a mass text," advises Smith. "Instead send a Paperless Post invite and try to include a one-line note, like 'Hey, congrats on the new gig! Hope you can make it!' and then put the information. This is for a dinner party, not a rave."
While it some instances a weekend night makes more sense—like if you plan on going out for a bar crawl afterwards—Smith believes that people just want to chill on the weekend. "I like weekdays specifically because I come directly from work, you could just put on a higher heel, put on a piece of jewelry and you're ready to go," says Smith. Plus, it gives your guest something to look forward to at the end of a long work day.
Don't get us wrong, just because it's Wednesday is a plenty good reason, but it's always nice to celebrate a friend's milestone, whether big or small. "If it's someone's promotion or birthday, you can have people bring photos or write anecdotes on a piece of paper. Put them in a big glass bowl so that the person has a commemorative moment and something they can take away."
The men of the hour, Dean & Dan of @dsquared2 thank you for incredible fashion & a wonderful evening!
Frenemies: "If you're inviting people to your home, it should be people that you trust and that you feel really good about—people who won't make you feel like you're being judged."
Coworkers: "At home, at a party with all of your real friends is just not the time to get to know a coworker. You may not want them to know that you like to dance to trap music, take copious amounts of tequila shots, or how much money you make as told by your fabulous apartment."
The Ex: "It's your home and all of the sudden you're thinking about the way you spent time there when you dated, and before you know it you've made the mistake of getting in bed with them again. You broke up with him for a reason!"
While BYOB is tempting for saving funds, in the end it could come back to bite you by way of drunken guests and having to play bartender. "If you start getting into somebody's regular bottle of tequila, then you've got to bring all of the mixers, and before you know it people are in your kitchen, cutting up lemons and turning on the blender and it's like, 'okay girl,' now the house is a mess." says Smith. "When people bring their own alcohol, all of a sudden one drink is half a glass of alcohol, and then people get drunk and bad things happen to your apartment.
Instead, stock up on red and white wine and create a signature drink for the evening, which will allow you to control just how much liquor goes into it and cut down on cost.
#ItHappenedLastNight thanks to @dsquared2 I had a fashionable night in l.a. Imagine that?
There's no need to be slaving in the kitchen all night. Instead buy pre-made hors d'oeuvres, like mini quiches, egg rolls, or pigs in a blanket at Trader Joe's (Bevy's go-to spot). It's cost and time effective because you can throw them in the oven. For the main course, keep things just as simple. "I love a warm pot dish, like a chili or a stew," says Smith. "You can also do a pizza bar, macaroni and cheese assortment...anything that's a timesaver ,where you pop it in the oven or just let it simmer on the stove and then voilà."
If you're price conscious, making it a potluck is totally okay—you just have to make sure that all bases are covered.
"When you're doing potluck, you cannot leave it to the guest," says Smith. "You must ask them what they're making and if somebody is already making a roast chicken, and you're short on starches or side dishes, ask them to make that instead. Otherwise everyone thinks that it's a good idea to bring hummus and vegetables and that's not a great potluck meal."
"You want people to know this is your event," says Smith. "That doesn't mean that you need to wear a ball gown, but you definitely shouldn't have your dinner party and be wearing sweats." In other words, be confident and comfortable, but kick it up a notch or two.
It's our firm belief that the vibe of a party always hangs in the next song—in other words, make sure you've got a killer playlist. If you think the dinner is going to last two hours, make your playlist last three hours, say Smith.
When it comes time to choose your music, she suggests starting things off with mid-tempo tunes that melt into the background, then slowly ramping it up to the loud, up-tempo stuff that calls for an impromptu party. (If that's what you're going for, of course).
As for what to do when your good ol' pal Billy unplugs your iPod to show you this killer new dubstep track, Smith has some no-nonsense advice for you. "You kind of have to be in a place of authority," she explains. "I would nicely tell that person, 'Oh my god, that is so cool. When you have your dinner party at your place, I so want to hear it!" and just laugh it off. You're totally within your rights to be like, 'um, no.'"
Don't leave it until the end—you'll be very, very sorry. Additionally, you shouldn't be a one person army and the best way to get it is by looking to that friend.
"We all have that one dear friend who is super organized and who loves to help and they should always be invited—and rewarded," she explains. "To that person, you say, 'Come early to have a cocktail,' or 'Stay behind. I'm going to save this special pie that I got from this great bakery. You can just chill and have a slice.' You have to reward them, because you don't want to use the person. It's more like, I gotchu.'"
Creating a custom hastag for your event gets people excited and is a fun, interactive way to look back on the night—just be weary of who might see it. "The only bad thing about creating one is that other people are going to see and ask why they weren't invited," says Smith. "Social media can be a double-edged sword, but at this point there's no way to avoid people posting."


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Dr. Rowena Delos Santos to Chair AST Conflicts of Interest Committee
By Cynthia Ritter • January 9, 2020 January 13, 2020
Dr. Rowena Delos Santos, director of WashU's Transplant Nephrology Fellowship, is the new chair of the American Society of Transplantation Conflicts of Interest Committee.
Rowena Delos Santos, MD, assistant professor of medicine, Division of Nephrology, and current co-chair of the American Society of Transplantation (AST) Conflicts of Interest (COI) Committee, will take over as chair of the committee in June 2020.
"It is a great honor and responsibility to serve on this AST Committee," says Dr. Delos Santos of her new position. "I am lucky to work with such wonderful colleagues in transplant, and have learned a lot since joining the committee." Delos Santos is also director of WashU's Transplant Nephrology Fellowship.
The AST was founded in 1982 for physicians and health professionals interested in transplantation medicine and biology. Its mission is to advance the field of transplantation and improve patient care by promoting research, education, advocacy, organ donation, and service to the community.
The society is the largest transplant organization in North America with more than 4,000 professionals. Recognized as the premier society for transplantation, AST members are sought out as transplant experts and advocates.
Dr. Delos Santos was chair of the AST Trainee and Young Faculty Community of Practice from 2017 – 2018, and past-chair from 2018-2019. In 2018, she was asked to join both the AST Transplant Nephrology Fellowship Training Accreditation Program Review Committee and the COI Committee. She became co-chair of the COI committee in 2019.
The COI committee reviews all disclosures of potential conflicts of interest made by speakers, moderators, and planning committee members and provides conflict resolution as needed.
"We have been a busy committee lately, and I look forward to continuing to serve and work to meet the needs of the AST," she says.
Read more about Dr. Delos Santos and the Transplant Nephrology Fellowship program.
Please enjoy the 2019 ASN TV video highlighting WashU's Transplantation program below.
american society of transplantationASN TV videoConflicts of Interest committeerowena delos santostransplant nephrologyTransplant Nephrology FellowshipTransplant Nephrology Fellowship Training Accreditation Program Review Committee