text:
\section{Introduction}
Multi-robot systems have been applied to different tasks, such as search and rescue~\cite{drew2021multi,liu2013robotic}, delivery~\cite{camisa2021multi,mathew2015optimal}, mechanical weeding~\cite{mcallister2019agbots}, and underwater missions~\cite{das2016cooperative,kulkarni2010task}. Although recent research efforts have made noteworthy progress on developing trustworthy robot autonomy~\cite{kayacan2018embedded,sivakumar2021learned,zhang2020high}, the deployment of low-cost robots in real-world environments has shown that they usually face difficulties in completing the tasks independently~\cite{rosenfeld2017intelligent}. For example, due to the environmental complexity and terrain variability in agricultural environments, compact field robots (Figure~\ref{subfig:terrasentia}) deployed between rows of crops may fail the navigation task and get stuck in error states (Figure~\ref{subfig:robot-failure}), in which physical assistance from a human supervisor is required to continue the robot task~\cite{ji2020multi,ji2022proactive}. To ensure the smooth operation of such multi-robot systems, the supervision and management of robot fleets are necessary in the presence of imperfect autonomy. However, optimally identifying which robot to assist in which order in an uncertain environment is a challenging task for human supervisors. As shown in recent user studies on operating multi-robot teams, a single operator can get overwhelmed by the number of requests and messages, resulting in sub-optimal performance~\cite{chen2011effects,chien2013imperfect,lewis2013human}. Moreover, the increase of the number of robots can cause further performance degradation of the human-robot team~\cite{olsen2004fan}.

As opposed to purely relying on the supervisor to make decisions, algorithmic approaches have been proposed to provide advice on which robot to assist and when~\cite{drew2021multi}. Many previous works modeled the supervision problem of multi-robot systems as a Markov Decision Process (MDP)~\cite{dahiya2021scalable,rosenfeld2017intelligent}. However, calculating the optimal solution to such MDPs is intractable due to the exponential size of the state space, the high uncertainty induced by the environment, and the complexity of multi-robot problems~\cite{korsah2013comprehensive,kumar2012survey}. Instead, myopic/greedy approaches were used under the assumption that the robots can be managed through \textit{teleoperation}. One benefit that \textit{teleoperation} brings is that which robot the supervisor chooses to assist at the current time step will not affect the cost of assisting other robots at the next time step. However, in robotic applications where \textit{physical} assistance is required, approaching and rescuing a robot can change the cost of rescuing other robots as the physical distance between the supervisor and each robot varies with the action of the supervisor. As a result, the local optimum of \textit{a robot}, provided by myopic/greedy approaches, can be significantly different from the global optimum of a \textit{robot fleet}.

An alternative solution is to learn rational human decisions on supervision problem in easy settings with a few robots and then deploy the learned model in hard settings to model the user's choice of which robot to assist~\cite{swamy2020scaled,xu2016towards}. The underlying assumption behind this approach is that the human decision is approximately optimal in the sense of maximizing the performance of the human-robot team. However, such human decision modeling also benefits from the \textit{teleoperation} of robot fleets: the supervisor can easily decide which robot to assist solely based on how useful it would be to assist each robot without the need to consider the cost of assistance, which is made constant for each robot by \textit{teleoperation}. With varying cost in robotic systems where \textit{physical} assistance is required, the supervisor can struggle with making optimal decisions that can benefit the robot fleet as a whole.

\begin{figure}[t]
  \centering
  \begin{subfigure}[b]{0.49\linewidth}
    \includegraphics[width=\linewidth]{Figures/Terrasentia.jpg}
    \caption{TerraSentia robot.}
    \label{subfig:terrasentia}
  \end{subfigure}
  \begin{subfigure}[b]{0.49\linewidth}
    \includegraphics[width=\linewidth]{Figures/robot_failure.jpg}
    \caption{Untraversable obstacle.}
    \label{subfig:robot-failure}
  \end{subfigure}
  \caption{\textbf{(a)} The field robot, TerraSentia~\cite{kayacan2018embedded}, navigates between rows of crops for plant phenotyping. \textbf{(b)} Robot navigation failure may occur due to untraversable obstacles, such as fallen plants and dense weeds.}
  \label{fig:field-robot-example}
  \vspace{-3mm}
\end{figure}

A typical example in which \textit{physical} assistance is required involves robot navigation in uncertain environments (e.g., agricultural fields). \textit{Teleoperation} is inadequate and/or impossible for robot assistance for two main reasons. First, a common failure mode of such field robots is encountering untraversable obstacles blocking the narrow path (Figure~\ref{subfig:robot-failure}), the removal of which is beyond the robot autonomy and requires external assistance~\cite{ji2020multi}. Second, successful teleoperation often requires rich and detailed feedback signals (e.g., videos and images) from the robots, which is not supported in low-cost multi-robot systems or requires the relocation of robots to a given rendezvous point due to the limited bandwidth of the long range communication network in outdoor environments~\cite{waharte2010supporting,lam2017lora}.

In this paper, we formulate the one-to-many supervision problem of a multi-robot system, to our knowledge for the first time, as a dynamic graph traversal problem (GTP). The supervisor is monitoring the fleet to provide \textit{physical} assistance to each robot when necessary. During operation, a robot may fail the navigation task at each location with different probabilities and can only resume the autonomy with assistance from the supervisor. Figure~\ref{fig:system-overview} presents an overview of the problem setup instantiated on an autonomous farm, showing $n$ robots navigating in the field, moving from start to goal locations respectively. To help the supervisor decide which robot to rescue, we construct a static graph with well-defined node rewards and edge costs from the current state of the human-robot team, solve the optimal path based on an objective maximizing the team performance, and execute the optimal actions for the supervisor in a receding horizon manner. Specifically, our contributions can be summarized as:
\begin{enumerate}
\item
We formulate the supervision of a multi-robot system in uncertain environments as a dynamic graph traversal problem, which is necessary in real-world applications where \textit{teleoperation} is disabled and \textit{physical} assistance is required.
\item
We approximate the solution to the intractable \textit{dynamic} problem by solving a \textit{static} graph traversal problem and develop a bound on the approximation error.
\item
A practical implementation of the static GTP is presented based on the profitable tour problem (PTP).
\item
A simulation environment of an autonomous farm is developed and our case study shows that the proposed method outperforms baseline methods in task completion time and human working time during the human-robot collaboration tasks.
\end{enumerate}

\begin{figure}[t]
  \centering
  \includegraphics[width=0.8\linewidth]{Figures/system_overview_final.pdf}
  \caption{\textbf{Overview of the multi-robot assistance problem for field robots navigating on an autonomous farm.} A complete directed graph is constructed from the current state of the human-robot team, and the optimal path is computed and provided to the supervisor as the actions for robot assistance.}
  \label{fig:system-overview}
  \vspace{-3mm}
\end{figure}
\section{Related Work}
The problem of multi-robot assistance bares similarities with the disciplines of human-multi-robot team collaboration and task allocation. In this section, we briefly review the related research and introduce the profitable tour problem.

Multi-robot supervision has been widely explored to enable human operators to assist multiple robots such as a team of navigating robots and a team performing search and rescue operations. \citet{rosenfeld2017intelligent} formulate the one-to-many supervision problem as a Myopic Advice Optimization Problem (MYAO), which models the maximization of the operator's performance by selecting when and which advice on robot assistance provided to the operator in a greedy fasion. \citet{dahiya2021scalable} study the problem where each robot is required to complete a sequence of tasks, each characterized by a different probability of successful completion. An index-based policy is then developed to provide advice on which robot requires attention. \citet{swamy2020scaled} learns the decision-making model of human operator with small robot fleets and tries to replicate the behavior for large robot fleets, optimizing based on the operator's internal utility function. However, the problem formulation of these approaches depends on the availability of teleoperation of robot fleets and does not encompass situations where \textit{physical} assistance is required.

The task allocation problem forms another class of problems similar to the supervision problem, which can alternatively be viewed as allocating the supervisor to a series of robots in order. ~\citet{lee2018resource} considers the problem of allocating multiple robots to multiple tasks (e.g., delivery missions) and proposes a resource-based task allocation algorithm to improve the overall task completion time. ~\citet{liu2018reinforcement} proposes a reinforcement-learning-based resource allocation scheme to efficiently allocate the resources of a cloud computing service platform to different requests. However, our problem setup is different because the cost of allocation/supervision varies over time with the movement of each robot, and our problem presents a collaborative task, where both the robots and the supervisor are working to achieve a common goal.

The closest prior work that involves stochastic and non-stationary rewards and costs in task allocation for multi-robot systems is Gittins-Index-based approach used in mechanical robotic weeding, where a team of autonomous robots are allocated to different rows to weed agricultural fields~\cite{mcallister2019agbots}. The reward of weeding a row varies over time according to weed growth models, and the cost of each allocation is dependent on the distance from the robot to the candidate row. To allocate weeding tasks to each robot, an optimization-based approach over a \textit{one-step} planning horizon using Gittins Index is utilized. In this work, we perform \textit{long-horizon} planning by constructing a graph from the human-robot team and provide advice to the supervisor in a receding horizon manner.

The profitable tour problem is a variant of the well-known traveling salesman problem (TSP), which is also referred to as prize collecting TSP~\cite{balas1989prize}. The objective is to find a tour that visits a subset of vertices such that the sum of rewards associated with vertices in the tour minus the length of the tour is as large as possible. In addition to exact solutions, approximation algorithms have been proposed to solve the PTP under the assumption that the edge costs satisfy the triangle inequality~\cite{archer2011improved,bienstock1993note,goemans1995general,nguyen2010primal}. However, the formulation of the PTP considers time-invariant node rewards and edge costs, and it remains unclear how well the solution on such static graphs generalizes to more practical dynamic graphs.
\section{Problem Formulation}
\label{sec:problem-formulation}
Our goal is to help the supervisor choose which robot to rescue at any given time. To this end, we formulate the one-to-many supervision over a robot fleet as a dynamic graph traversal problem.

We model the human-robot team as a directed graph $G=(V,A)$, where $V = \{0,\dots,n + 1\}$ is the set of vertices and $A$ is the set of arcs. Vertices in $N = V \backslash \{0, n+1\} = \{1,\dots,n\}$ correspond to the robots, vertex $0$ corresponds to the supervisor, and vertex $n+1$ corresponds to the control center, in which the supervisor rests when not assisting any robots. As a result, a path to rescue the robots should start from the supervisor and end with the control center. Formally, we define a \textit{path} $\pi \coloneqq (v_k)_{k=0}^{L}$ in the graph as a sequence of \textit{vertices} $v_k \in V$, where $L$ is the length of the path. Henceforth, we use $v_k^\pi$ and $a_k^\pi \coloneqq (v_k^\pi, v_{k+1}^\pi)$ to denote the $k$-th vertex and the $k$-th arc on the path $\pi$, respectively. In our planning problem, a path $\pi$ is a \textit{valid} path if $v_0^\pi = 0$ and $v_L^\pi = n + 1$.

A \textit{time-varying} nonnegative scalar reward $r_i(t) \in \mathbb{R}$ is associated with each robot $i \in N$, while a reward $r_0(t)=0, \, \forall t \ge 0$ and $r_{n+1}(t)=0, \, \forall t \ge 0$ is associated with the supervisor and the control center, respectively. A \textit{time-varying} nonnegative scalar cost $c_{ij}(t) \in \mathbb{R}$ is associated with each arc $(i,j) \in A$. Here, we define the reward $r_i(t)$ for each robot as the \textit{net} expected distance that the robot can travel with supervisor intervention, i.e. the reward is the expected distance that the robot can travel if visited, minus the distance if ignored by the supervisor. The definition of the reward reflects the ``value" of visiting a robot at a given time. Thus, the reward $r_i(t), i \in N$ is positive only when the robot fails the navigation task and is kept zero during normal operation. We define the cost $c_{ij}(t)$ as the time required to travel between the two nodes $i, j \in V$ in the graph\footnote{Note that the graph $G$ is defined as a directed graph, in which the edge cost can be generalized to be asymmetric, i.e., $c_{ij}(t) \neq c_{ji}(t), \, \forall (i, j) \in A$.}. We note that our problem formulation differs from the classical PTP and TSP in that the rewards and costs are dynamic. For notational brevity, we define $t_k^\pi$ to represent the time at which the supervisor reaches the $k$-th vertex $v_k^\pi$ on the path $\pi$:
\begin{equation}
t_k^\pi = \sum_{i=0}^{k-1} c_{a_i^\pi}(t_i^\pi), \quad t_0^\pi = 0, \quad k = 0, 1, \dots, L.
\end{equation}

To plan a path to rescue the robots with minimum time cost, we define the value of a path $\pi$ by:
\begin{equation}
\label{eq:value-function-tv-complete}
Q^\pi = \sum_{k=0}^{L} e^{-\lambda t_k^\pi} r_{v_k^\pi} (t_k^\pi) - \sum_{k=0}^{L-1} e^{-\lambda t_k^\pi} \mu c_{a_k^\pi} (t_k^\pi),
\end{equation}
where $\mu$ is the weighting factor and $\lambda$ is the discount factor. The first term in the value function~(\ref{eq:value-function-tv-complete}) collects the total discounted reward by visiting the robots on the path, while the second term represents the total discounted traveling cost of the supervisor. The hyperparameter $\mu$ controls the relative weight between the value of rescuing the robot and the human labor cost. A higher unit profit from engaging the robot autonomy and a lower human labor cost can result in a lower $\mu$, and vice versa. For example, if the human labor cost is negligible compared to the profit made by a normal working robot, the edge cost incurred by adding a robot to the path can be ignored and thus the optimal path must contain all the robots that have positive rewards. Henceforth, we use $\hat{r}_i(t)$ and $\hat{c}_{ij}(t)$ to denote $r_i(t)$ and $\mu c_{ij}(t)$, respectively, for the brevity of notation. The value function~(\ref{eq:value-function-tv-complete}) can be rewritten in the form:
\begin{equation}
\label{eq:value-function-tv}
Q^\pi = \sum_{k=0}^{|\pi|} e^{-\lambda t_k^\pi} \hat{r}_{v_k^\pi} (t_k^\pi) - \sum_{k=0}^{|\pi|-1} e^{-\lambda t_k^\pi} \hat{c}_{a_k^\pi} (t_k^\pi),
\end{equation}
where $|\pi|$ denotes the length of the path. We assume that the reward of each robot can be collected at most once. A more general case where each robot can be visited repeatedly over time will be discussed in Section~\ref{sec:method}.

The optimization problem of interest is to find a \textit{valid} path for the supervisor that maximizes the value function~(\ref{eq:value-function-tv}):
\begin{equation}
\label{prob:dynamic-gtp}
\begin{aligned}
\max_{\pi} \quad &Q^\pi \\
\text{s.t.} \quad &v_i^\pi \neq v_j^\pi, \quad \forall \, i,j \in \{0,\dots,|\pi|\}, \, i \neq j \\
&v_0^\pi = 0, \; v_{|\pi|}^\pi = n+1.
\end{aligned}
\end{equation}
Let $\pi^*$ be the optimal path in the optimization problem~(\ref{prob:dynamic-gtp}).

To our knowledge, our work is the first to consider a graph traversal problem with time-varying rewards and costs, and no exact approaches to the \textit{dynamic} GTP~(\ref{prob:dynamic-gtp}) exists other than the enumeration over the space of all paths. In the following section, we approximate the intractable \textit{dynamic} GTP~(\ref{prob:dynamic-gtp}) to a \textit{static} GTP, whose solution can be obtained efficiently using mixed-integer programming~\cite{gurobi}.
\section{Methodology}
\label{sec:method}
In this section, we present an approximation algorithm for the dynamic GTP~(\ref{prob:dynamic-gtp}) based on the solution to the profitable tour problem. The bound on the approximation error is developed and the practical implementation will be detailed.

\subsection{Static GTP Approximation}
We now introduce a \textit{static} graph traversal problem, whose node rewards and edge costs are time invariant. We consider the directed graph $G$ as defined in Section~\ref{sec:problem-formulation}. A \textit{constant} nonnegative reward $r_i \in \mathbb{R}$ is associated with each robot $i \in N$, while a reward $r_0=0$ and $r_{n+1}=0$ is associated with the supervisor and the control center, respectively. A \textit{constant} nonnegative traveling cost $c_{ij} \in \mathbb{R}$ is associated with each arc $(i,j) \in A$. The definition of the node reward and the edge cost are identical to those in Section~\ref{sec:problem-formulation}.

For the \textit{static} graph traversal problem, we define the value of a path $\pi$ as:
\begin{equation}
\label{eq:value-function-static}
Q_\text{s}^\pi = \sum_{k=0}^{|\pi|} \hat{r}_{v_k^\pi} - \sum_{k=0}^{|\pi|-1} \hat{c}_{a_k^\pi},
\end{equation}
where $\hat{r}_i$ and $\hat{c}_{ij}$ are the node rewards and scaled edge costs as defined in equation~(\ref{eq:value-function-tv}). Similar to the value function in the dynamic GTP, the objective is to maximize the reward collected and minimize the path cost. Under the same assumption that the reward of each robot can be collected at most once, the optimization problem for the \textit{static} GTP can be formulated as:
\begin{equation}
\label{prob:static-gtp}
\begin{aligned}
\max_{\pi} \quad &Q_\text{s}^\pi \\
\text{s.t.} \quad &v_i^\pi \neq v_j^\pi, \quad \forall \, i,j \in \{0,\dots,|\pi|\}, \, i \neq j \\
&v_0^\pi = 0, \; v_{|\pi|}^\pi = n+1.
\end{aligned}
\end{equation}
Let $\pi_\text{s}^*$ be the optimal path in the optimization problem~(\ref{prob:static-gtp}).

To overcome the intractability of the original dynamic problem, we approximate the solution to problem~(\ref{prob:dynamic-gtp}) by solving the static GTP~(\ref{prob:static-gtp}) based on the following assumptions:
\begin{assumption}
\label{asm:1}
In the dynamic GTP, the change rate of the node reward and edge cost are bounded above by $|\hat{r}_i(t) - \hat{r}_i(0)| \le \alpha t, \, |\hat{c}_{ij}(t) - \hat{c}_{ij}(0)| \le \beta t, \, \forall \, i,j \in V, \, \forall \, t \ge 0$, where $\alpha$ and $\beta$ are nonnegative real numbers. In the static GTP, the difference between the node reward and the edge cost in the graph is bounded above by $\max_{i,j} |\hat{r}_i - \hat{c}_{ij}| \le \epsilon, \, \forall \, i,j \in V$.
\end{assumption}

\begin{assumption}
\label{asm:2}
The traveling time $\Delta t$ between any two nodes in the graph $G$ is bounded above by $\Delta t \le \overline{\Delta t}$.
\end{assumption}

In practice, $\alpha$ and $\beta$ in Assumption~\ref{asm:1} bound the rates at which the reward and cost can change due to the movement of the robot over time, and Assumption~\ref{asm:2} suggests that the field on which the robots can navigate has a limited size. We construct the \textit{static} graph as the initial condition of the \textit{dynamic} graph, i.e., $\hat{r}_i = \hat{r}_i(0), \, \hat{c}_{ij} = \hat{c}_{ij}(0), \, \forall \, i, j \in V$. We now bound the approximation error of the optimal solution of the static graph traversal problem~(\ref{prob:static-gtp}):
\begin{theorem}
\label{theorem:1}
Consider the dynamic graph traversal problem~(\ref{prob:dynamic-gtp}) and the static graph traversal problem~(\ref{prob:static-gtp}). Let $Q^{\pi^*}$ and $Q_\text{s}^{\pi_\text{s}^*}$ be the maximum value of $Q^{\pi}$ and $Q_\text{s}^{\pi}$ over all paths, respectively. The solution to the static problem approximates the solution to the dynamic problem with the bound:
\begin{equation}
\label{ineq:theorem}
|Q_\text{s}^{\pi_\text{s}^*} - Q^{\pi^*}|
\le
(\alpha + \beta) \frac{n+1}{\lambda e} + \sum_{k=0}^{n} (1 - e^{-\lambda k \overline{\Delta t}}) \epsilon,
\end{equation}
where $n$ is the number of robots.
\end{theorem}
\begin{proof}
For any valid path $\pi$, the value function~(\ref{eq:value-function-tv}) and~(\ref{eq:value-function-static}) can be written as:
\begin{align*}
Q^{\pi}
&=
\sum_{k=0}^{|\pi|-1} e^{-\lambda t_k^{\pi}} \left( \hat{r}_{v_k^{\pi}} (t_k^{\pi}) - \hat{c}_{a_k^{\pi}} (t_k^{\pi}) \right), \\
Q_\text{s}^\pi
&=
\sum_{k=0}^{|\pi|-1} \left( \hat{r}_{v_k^\pi} - \hat{c}_{a_k^\pi} \right),
\end{align*}
by the fact that the terminal node on a valid path must be the control center, whose reward is always zero.

By applying $\pi_\text{s}^*$, which is the optimal solution to~(\ref{prob:static-gtp}), to both the static and dynamic problem, we have:
\begin{equation}
\label{eq:proof-1}
\begin{aligned}
|Q_\text{s}^{\pi_\text{s}^*} - Q^{\pi_\text{s}^*}|
&=
\left| \sum_{k=0}^{|\pi_\text{s}^*|-1} \left( \hat{r}_{v_k^{\pi_\text{s}^*}} - e^{-\lambda t_k^{\pi_\text{s}^*}} \hat{r}_{v_k^{\pi_\text{s}^*}}(t_k^{\pi_\text{s}^*}) \right) \right. \\
&\qquad \quad \, \left. - \left( \hat{c}_{a_k^{\pi_\text{s}^*}} - e^{-\lambda t_k^{\pi_\text{s}^*}} \hat{c}_{a_k^{\pi_\text{s}^*}}(t_k^{\pi_\text{s}^*}) \right) \right|.
\end{aligned}
\end{equation}
By Assumption~\ref{asm:1}, we have
$
\left| \hat{r}_{v_k^{\pi_\text{s}^*}}(t_k^{\pi_\text{s}^*}) - \hat{r}_{v_k^{\pi_\text{s}^*}} \right| \le \alpha t_k^{\pi_\text{s}^*}
$, which is equivalent to:
\begin{equation*}
\left| \hat{r}_{v_k^{\pi_\text{s}^*}} - e^{-\lambda t_k^{\pi_\text{s}^*}} \hat{r}_{v_k^{\pi_\text{s}^*}}(t_k^{\pi_\text{s}^*}) - \hat{r}_{v_k^{\pi_\text{s}^*}} ( 1 - e^{-\lambda t_k^{\pi_\text{s}^*}} ) \right|
\le
e^{-\lambda t_k^{\pi_\text{s}^*}} \alpha t_k^{\pi_\text{s}^*},
\end{equation*}
indicating that the first term on the R.H.S. of the equation~(\ref{eq:proof-1}) is centered around $\hat{r}_{v_k^{\pi_\text{s}^*}} ( 1 - e^{-\lambda t_k^{\pi_\text{s}^*}} )$ within a range of $e^{-\lambda t_k^{\pi_\text{s}^*}} \alpha t_k^{\pi_\text{s}^*}$. Similarly, for the edge cost, we have:
\begin{equation*}
\left| \hat{c}_{a_k^{\pi_\text{s}^*}} - e^{-\lambda t_k^{\pi_\text{s}^*}} \hat{c}_{a_k^{\pi_\text{s}^*}}(t_k^{\pi_\text{s}^*}) - \hat{c}_{a_k^{\pi_\text{s}^*}} ( 1 - e^{-\lambda t_k^{\pi_\text{s}^*}} ) \right|
\le
e^{-\lambda t_k^{\pi_\text{s}^*}} \beta t_k^{\pi_\text{s}^*},
\end{equation*}
indicating that the second term on the R.H.S of the equation~(\ref{eq:proof-1}) is centered around $\hat{c}_{a_k^{\pi_\text{s}^*}} ( 1 - e^{-\lambda t_k^{\pi_\text{s}^*}} )$ within a range of $e^{-\lambda t_k^{\pi_\text{s}^*}} \beta t_k^{\pi_\text{s}^*}$. Therefore, from equation~(\ref{eq:proof-1}) we have:
\begin{equation*}
\begin{aligned}
&|Q_\text{s}^{\pi_\text{s}^*} - Q^{\pi_\text{s}^*}|
\le
\sum_{k=0}^{|\pi_\text{s}^*|-1} \left| \left( \hat{r}_{v_k^{\pi_\text{s}^*}} - e^{-\lambda t_k^{\pi_\text{s}^*}} \hat{r}_{v_k^{\pi_\text{s}^*}}(t_k^{\pi_\text{s}^*}) \right) \right. \\
&\qquad \qquad \qquad \qquad \qquad \qquad \left. - \left( \hat{c}_{a_k^{\pi_\text{s}^*}} - e^{-\lambda t_k^{\pi_\text{s}^*}} \hat{c}_{a_k^{\pi_\text{s}^*}}(t_k^{\pi_\text{s}^*}) \right) \right| \\
&\le
\sum_{k=0}^{|\pi_\text{s}^*|-1} ( 1 - e^{-\lambda t_k^{\pi_\text{s}^*}}) \left| \hat{r}_{v_k^{\pi_\text{s}^*}} - \hat{c}_{a_k^{\pi_\text{s}^*}} \right| + (\alpha + \beta) e^{-\lambda t_k^{\pi_\text{s}^*}} t_k^{\pi_\text{s}^*}
\end{aligned}
\end{equation*}
Consider the function $f(x) = e^{-\lambda x} x, \, x \ge 0$. By taking the derivative to zero, we observe that $f(x)$ reaches a maximum of $1/(\lambda e)$ at $x=1/\lambda$. Therefore, we have:
\begin{equation}
\label{ineq:proof-1}
\begin{aligned}
|Q_\text{s}^{\pi_\text{s}^*} - Q^{\pi_\text{s}^*}|
&\le
(\alpha + \beta) \frac{n + 1}{\lambda e} \\
&\qquad \qquad \quad + \sum_{k=0}^n ( 1 - e^{-\lambda t_k^{\pi_\text{s}^*}}) \left| \hat{r}_{v_k^{\pi_\text{s}^*}} - \hat{c}_{a_k^{\pi_\text{s}^*}} \right| \\
&\le
(\alpha + \beta) \frac{n + 1}{\lambda e} + \sum_{k=0}^n ( 1 - e^{-\lambda t_k^{\pi_\text{s}^*}}) \epsilon \\
&\le
(\alpha + \beta) \frac{n + 1}{\lambda e} + \sum_{k=0}^n ( 1 - e^{-\lambda k \overline{\Delta t}}) \epsilon,
\end{aligned}
\end{equation}
where the second inequality follows from Assumption~\ref{asm:1} and the last inequality follows from Assumption~\ref{asm:2} and the fact that $t_k^{\pi_\text{s}^*} \le k \overline{\Delta t}$.

Similarly, by applying $\pi^*$, which is the optimal solution to~(\ref{prob:dynamic-gtp}), to both the static and dynamic problem, we have:
\begin{equation}
\label{ineq:proof-2}
|Q_\text{s}^{\pi^*} - Q^{\pi^*}|
\le
(\alpha + \beta) \frac{n + 1}{\lambda e} + \sum_{k=0}^n ( 1 - e^{-\lambda k \overline{\Delta t}}) \epsilon.
\end{equation}
Note that $\pi^*$ is suboptimal to the static problem~(\ref{prob:static-gtp}) and $\pi_\text{s}^*$ is suboptimal to the dynamic problem~(\ref{prob:dynamic-gtp}):
\begin{equation}
\label{ineq:proof-3}
Q_\text{s}^{\pi^*} \le Q_\text{s}^{\pi_\text{s}^*}, \quad Q^{\pi_\text{s}^*} \le Q^{\pi^*}.
\end{equation}
From the inequality~(\ref{ineq:proof-1}),~(\ref{ineq:proof-2}), and~(\ref{ineq:proof-3}), we conclude that:
\begin{equation*}
|Q_\text{s}^{\pi_\text{s}^*} - Q^{\pi^*}|
\le
(\alpha + \beta) \frac{n+1}{\lambda e} + \sum_{k=0}^{n} (1 - e^{-\lambda k \overline{\Delta t}}) \epsilon.
\end{equation*}
\end{proof}

An interesting fact that we observe on the bound developed in Theorem~\ref{theorem:1} is that the approximation error is separated into two parts and the discount factor $\lambda$ creates a tension between the two terms on the right hand side of the inequality~(\ref{ineq:theorem}). The first term encapsulates the error generated by the time-varying nature of the rewards and costs in the dynamic problem and can be damped by a large $\lambda$, by applying which the further nodes on the path could make less contribution to the value function compared to the nearer nodes. The second term represents the error originated from the fact that $\pi^*$ is optimized for discounted rewards while $\pi_\text{s}^*$ is optimized for undiscounted rewards and can be damped by a small $\lambda$. Consider a dynamic graph with a change rate of zero, i.e., $\alpha=\beta=0$. The optimal solution to the static and dynamic problem can still be different due to the different definitions of the value function. With an additional condition that $\lambda=0$, however, the value function~(\ref{eq:value-function-tv}) and~(\ref{eq:value-function-static}) of the two problems will be identical and the gap between the optimal solution $Q_\text{s}^{\pi_\text{s}^*}$ and $Q^{\pi^*}$ will be zero, which is also verified by the bound in Theorem~\ref{theorem:1}.

We note that in real-world applications, robots may fail repeatedly, which, in our setting, means that robots can be visited multiple times for reward. Formally, the optimal path may contain loops. However, if the robot autonomy is relatively reliable with rare navigation failures, the second visit to a robot will be necessary only after a long time since the first visit, i.e., $t_{k_1}^{\pi^*} \gg t_{k_2}^{\pi^*}, \, \forall \, k_1, k_2 \in \{0, \dots, |\pi^*|\}, \, k_1 \neq k_2, \, v_{k_1}^{\pi^*} = v_{k_2}^{\pi^*}$. As a result, the discounted reward collected after the time at which the loop is formed is negligible according to equation~(\ref{eq:value-function-tv}). Therefore, $Q_\text{s}^{\pi_\text{s}^*}$ can still approximate the optimal value function of the dynamic graph traversal problem~(\ref{prob:dynamic-gtp}) well with the bound given by equation~(\ref{ineq:theorem}).

\subsection{Profitable Tour Problem}
\label{subsec:ptp}
Although the optimization in the static GTP is still performed over the space of all paths, problem~(\ref{prob:static-gtp}) can be formulated as a profitable tour problem.

The PTP is the problem of finding a route that maximizes the difference between the total collected reward and the total traveling cost. In the remaining part of this section, we first introduce some useful notations and then formulate the static GTP~(\ref{prob:static-gtp}) as a modified PTP.

For any subset of vertices $S \subset V$, we define $\delta^+ (S) = \{ (i, j) \in A: i \in S, j \notin S \}$ and $\delta^- (S) = \{ (i, j) \in A: i \notin S, j \in S \}$. For brevity, we will use the notation $\delta^+ (i)$ and $\delta^- (i)$ when $S=\{ i \}$. We define the variable $y_i$ as a binary variable equal to $1$ if vertex $i \in V$ is visited by the path, and $0$ otherwise. Similarly, we define the variable $x_{ij}$ as a binary variable equal to $1$ if arc $(i, j) \in A$ is traversed by the supervisor, and $0$ otherwise.

The mathematical programming formulation of the static GTP~(\ref{prob:static-gtp}) is the following:
\begin{align}
\label{eq:ptp-obj}
\max &\quad \sum_{i \in V} \hat{r}_i y_i - \sum_{(i, j) \in A} \hat{c}_{ij} x_{ij} \\
\label{eq:ptp-robot-leaving-cons}
\text{s.t.} \quad &\sum_{(i, j) \in \delta^+ (i)} x_{ij} = y_i, \quad \forall \, i \in N, \\
\label{eq:ptp-robot-entering-cons}
&\sum_{(j, i) \in \delta^- (i)} x_{ji} = y_i, \quad \forall \, i \in N, \\
\label{eq:ptp-human-cons}
&\sum_{(i, j) \in \delta^+ (i)} x_{ij} = 1, \sum_{(j, i) \in \delta^- (i)} x_{ji} = 0, \; i = 0, \\
\label{eq:ptp-cc-cons}
&\sum_{(i, j) \in \delta^+ (i)} x_{ij} = 0, \sum_{(j, i) \in \delta^- (i)} x_{ji} = 1, \; i = n + 1, \\
\label{eq:ptp-subtour-elimination-cons}
&\sum_{(i, j) \in \delta^+ (S)} x_{ij} \ge y_b, \quad \forall \, S \subseteq N, \; b \in S, \\
\label{eq:ptp-node-var}
&y_i \in \{ 0, 1 \}, \quad \; \, \forall \, i \in V, \\
\label{eq:ptp-edge-var}
&x_{ij} \in \{ 0, 1 \}, \quad \forall \, (i, j) \in A.
\end{align}
The objective function~(\ref{eq:ptp-obj}) maximizes the difference between collected reward and traveling cost. Constraints~(\ref{eq:ptp-robot-leaving-cons}) and~(\ref{eq:ptp-robot-entering-cons}) ensure that one arc leaves and one arc enters each visited robot, respectively. Constraints~(\ref{eq:ptp-human-cons}) and~(\ref{eq:ptp-cc-cons}) ensure that the path starts from the supervisor and ends at the control center, respectively. Subtours are eliminated through~(\ref{eq:ptp-subtour-elimination-cons}). Finally,~(\ref{eq:ptp-node-var}) and~(\ref{eq:ptp-edge-var}) are variable definitions.

The optimization problem~\cref{eq:ptp-obj,eq:ptp-robot-leaving-cons,eq:ptp-robot-entering-cons,eq:ptp-human-cons,eq:ptp-cc-cons,eq:ptp-subtour-elimination-cons,eq:ptp-node-var,eq:ptp-edge-var} is a variant of the profitable tour problem and can be solved efficiently via mixed-integer programming~\cite{archetti2014chapter}. To retrieve the optimal path, we expand the path from vertex $0$, the supervisor, to vertex $n+1$, the control center, by following the arcs $x_{ij}$ that are assigned with a value of $1$.

To plan actions for the supervisor to complete the task, we solve the PTP problem~\cref{eq:ptp-obj,eq:ptp-robot-leaving-cons,eq:ptp-robot-entering-cons,eq:ptp-human-cons,eq:ptp-cc-cons,eq:ptp-subtour-elimination-cons,eq:ptp-node-var,eq:ptp-edge-var} at each time step, command the supervisor to rescue the first robot on the optimal path, and continue to plan and execute at the next time step following the framework of model predictive control.

\subsection{Practical Considerations}
Each robot in the fleet is assigned independent navigation tasks and the completion of the entire task is declared only when all the robots reach their respective destinations. To increase the efficiency of the robot fleet, higher priority should be given to the robots that are further away from their destinations than to those that are closer to complete the navigation tasks~\cite{wang2011spatio}. In other words, the robots traversing less distance from the starting point should be favored to be rescued earlier than those traversing longer distance. To this end, let $d_i, i \in N$ be the distance that the robot $i$ has traversed. We modify the definition of the scaled edge cost $\hat{c}_{ij}$ in the objective function~(\ref{eq:ptp-obj}) as follows:
\begin{equation}
\label{eq:modified-cost}
\hat{c}_{ij}
=
\mu c_{ij} (t) + \gamma \max (0, d_i - d_j), \quad \forall i, j \in N,
\end{equation}
where $\gamma$ is a weighting factor. For any two robots $i$ and $j$ in the fleet, if robot $i$ has traversed further distance than robot $j$ from the starting point, the traveling cost from $i$ to $j$ will have an additional penalty term of $\gamma (d_i - d_j)$ while the traveling cost from $j$ to $i$ will remain unchanged. As a result, the supervisor will be encouraged to visit robot $j$ before robot $i$.

Although the optimization problem~\cref{eq:ptp-obj,eq:ptp-robot-leaving-cons,eq:ptp-robot-entering-cons,eq:ptp-human-cons,eq:ptp-cc-cons,eq:ptp-subtour-elimination-cons,eq:ptp-node-var,eq:ptp-edge-var} is tractable using modern programming solvers, the number of constraints on the subtour elimination~(\ref{eq:ptp-subtour-elimination-cons}) grows exponentially with the number of robots. To ensure the real-time capability of the algorithm, we use lazy constraints in the replacement of the full set of constraints~(\ref{eq:ptp-subtour-elimination-cons}), i.e., the constraints are included only when they are violated by solutions found during the optimization~\cite{gurobi}.
\section{Case Study}
\label{sec:case-study}
The PTP is known to provide an optimal solution to a static GTP with constant node rewards and edge costs~\cite{kool2018attention}. In this section, we aim to evaluate the performance of the modified PTP~\cref{eq:ptp-obj,eq:ptp-robot-leaving-cons,eq:ptp-robot-entering-cons,eq:ptp-human-cons,eq:ptp-cc-cons,eq:ptp-subtour-elimination-cons,eq:ptp-node-var,eq:ptp-edge-var} on a practical dynamic graph.

We instantiate the dynamic GTP formulated in Section~\ref{sec:problem-formulation} as a one-to-many supervision problem of a robot fleet on an autonomous farm, in which compact agricultural robots are tasked with navigating through rows of crops for plant phenotyping~\cite{mueller2017robotanist}. Due to the environmental complexity and terrain variability in practice, robots may fail the navigation task in the field, and a supervisor is responsible for monitoring and rescuing the robots to complete the task.

\subsection{Simulation Environment}
We developed a simulation environment for the autonomous farm (Figure~\ref{fig:simulation}) to allow simulations of fleet management algorithms for one-to-many supervision in uncertain environments. We assume that the crops are arranged in evenly spaced vertical rows and the farm is surrounded by free space in which the supervisor and the robots can move without failures. The farm is divided evenly for each robot to conduct plant phenotyping through boustrophedon navigation.

\begin{figure}[t]
  \centering
  \includegraphics[width=0.85\linewidth]{Figures/simulation_legend_colorbar.png}
  \caption{\textbf{Simulation environment of an autonomous farm with six robots.} The vertical grey lines mark the places where the crop is planted and thus represent the boundaries of traversable paths for the robots. The dashed cyan line is the history path traversed by the robot from the starting point, while the solid cyan line is the planned path towards the destination. The history and planned path are visualized only for one robot for clarity.}
  \label{fig:simulation}
\end{figure}

\begin{figure}[t]
  \centering
  \begin{subfigure}[b]{0.19\linewidth}
    \includegraphics[width=\linewidth]{Figures/field_1.png}
    \caption{}
  \end{subfigure}
  \begin{subfigure}[b]{0.19\linewidth}
    \includegraphics[width=\linewidth]{Figures/field_2.png}
    \caption{}
  \end{subfigure}
  \begin{subfigure}[b]{0.19\linewidth}
    \includegraphics[width=\linewidth]{Figures/field_3.png}
    \caption{}
  \end{subfigure}
  \begin{subfigure}[b]{0.19\linewidth}
    \includegraphics[width=\linewidth]{Figures/field_4.png}
    \caption{}
  \end{subfigure}
  \begin{subfigure}[b]{0.19\linewidth}
    \includegraphics[width=\linewidth]{Figures/field_5.png}
    \caption{}
  \end{subfigure}
  \caption{\textbf{Agricultural fields used in the case study.} The red cells correspond to a higher probability of robot failure compared to the yellow ones. All the other elements in the simulation environment are omitted.}
  \label{fig:fields}
  \vspace{-3mm}
\end{figure}

In practice, the probability of robot failure is correlated with the navigation difficulty, which may vary over the field due to the presence of weeds, fallen plants, and uneven terrains, to name a few. To incorporate such environmental effects on robot navigation into the simulation, we assign each cell in the farm a nonnegative scalar, which represents the probability of robot failure, based on a bivariate mixed normal distribution with a proper range. Each scalar is further bounded above and below by adjustable thresholds to control the navigation difficulty or the levels of robot autonomy. In Figure~\ref{fig:simulation}, the color of each cell reflects the magnitude of the associated probability of robot failure, i.e., a robot is more likely to fail the navigation task in a red cell than in a yellow cell\footnote{For visualization purposes, the cells that have been traversed by the robots are reassigned with the value of the lower threshold, thus appearing to be yellow in color.}. Upon entering a cell, the robot samples uniformly from the range $[0, 1]$ and takes an action based on the result: proceeds to the next cell if the sampled number is greater than the scalar associated with the current cell or raises a navigation failure otherwise.

The simulation is initialized with the robots at the starting points and the supervisor at the control center. Upon the occurrence of the navigation failure of a robot, the supervisor can approach and rescue the robot to reactivate the autonomy. The robots and the supervisor can both move one cell at a time and can only move along rows of crops, i.e., move vertically, except in the free space. The completion of the task is declared only when all the robots reach the destinations and the supervisor returns to the control center. The expected distance that each robot can travel is computed based on the probability of failure associated with each cell on the planned path, which can be estimated from weed density and/or terrain traversability using aerial systems in practice~\cite{hudjakov2009aerial,sapkota2020mapping}. To plan actions for the supervisor, a directed graph is constructed as described in Section~\ref{sec:problem-formulation} and a receding horizon control strategy is employed as described in Section~\ref{subsec:ptp}.

\subsection{Experimental Setup}
We consider five different fields in the case study (Figure~\ref{fig:fields}), which follow the typical weed density patterns used for weeding robots~\cite{mcallister2020agbots}.

\begin{table}[t]
  \begin{center}
    \caption{Levels of autonomy parameters}
    \label{table:levels-of-autonomy-param}
    \begin{tabular}{ l | c  c  c }
      \toprule
      Levels of autonomy & Low & Mid & High \\
      \midrule
      \rule{-2.5pt}{2ex} Min probability of failure & $0.01$ & $0.01$ & $0$ \\
      Max probability of failure & $0.20$ & $0.15$ & $0.15$ \\
      \bottomrule
    \end{tabular}
  \end{center}
\end{table}

\begin{table}[t]
  \begin{center}
    \caption{Robot fleet size parameters}
    \label{table:robot-fleet-size-param}
    \begin{tabular}{ l | c  c  c }
      \toprule
      Robot fleet size & Small & Mid & Large \\
      \midrule
      \rule{-2.5pt}{2ex} Number of robots & $4$ & $6$ & $9$ \\
      \bottomrule
    \end{tabular}
  \end{center}
  \vspace{-3mm}
\end{table}

We evaluate the performance of the proposed method on the simulated autonomous farm, along with several baseline methods. Let $N_\text{fail} (t) \subseteq N$ be the set of robots that fail the navigation tasks and $v(t) \in V$ be the target of the supervisor given by an algorithm at time $t$. The brief introduction of the baselines is given as follows.
\begin{itemize}
\item
\textit{Greedy-HR (Highest Reward)} assigns the supervisor to the failed robot that generates the highest \textit{one-step} reward:
\begin{equation*}
v(t)
=
\operatorname*{argmax}_j \, \hat{r}_j(t) - \hat{c}_{ij}(t), \; \; i=0, \, j \in N_\text{fail} (t).
\end{equation*}

\item
\textit{Greedy-FTG (Furthest-to-go)} assigns the supervisor to the failed robot that is furthest from the destination:
\begin{equation*}
v(t)
=
\operatorname*{argmin}_j \, d_j, \; \; j \in N_\text{fail} (t).
\end{equation*}

\item
\textit{Greedy-CR} (Closest Robot) assigns the supervisor to the failed robot that is closest to the supervisor:
\begin{equation*}
v(t)
=
\operatorname*{argmin}_j \, c_{ij} (t), \; \; i=0, \, j \in N_\text{fail} (t).
\end{equation*}

\item
\textit{Gittins Index} assigns the supervisor to the failed robot according to the Gittins Index~\cite{weber1992gittins}, which has been applied in weeding algorithms with dynamic rewards~\cite{mcallister2019agbots}:
\begin{equation*}
v(t)
=
\operatorname*{argmax}_j \, \frac{\gamma^{c_{ij}(t)} \hat{r}_j (t)}{\sum_{k=0}^{c_{ij}(t)} \gamma^k}, \; \; i=0, \, j \in N_\text{fail} (t).
\end{equation*}
\end{itemize}
In cases where all the robots are operating normally ($N_\text{fail} (t) = \emptyset$), the above methods assign the supervisor to the control center, i.e., $v(t) = n+1$. To our knowledge, our work is the first to formulate the one-to-many supervision problem as a dynamic GTP, and the above baselines are approaches typically applied in practice to tackle the problem in the absence of a rigorous framework.

Quantitatively, we compare different methods using the following two metrics:
\begin{itemize}
\item
\textit{Task Completion Time}: The time steps elapsed from the start of the simulation until the completion of the task.

\item
\textit{Human Working Time}: The total time steps when the supervisor is not at the control center.
\end{itemize}

The levels of autonomy can affect how much attention and assistance a human supervisor has to provide the robot, while the fleet size has an impact on the difficulty of decision making for multi-robot assistance. To examine the performance of different methods under different conditions, we conduct experiments with varying levels of autonomy and robot fleet size, as described in Table~\ref{table:levels-of-autonomy-param} and Table~\ref{table:robot-fleet-size-param}, respectively. For each combination of field, levels of autonomy, and robot fleet size, each method is evaluated over $10$ trials with different realizations of robot navigation.

\begin{table}[t]
\captionsetup{font=footnotesize}
  \begin{center}
    \caption{Results of fleet management with varying levels of autonomy}
    \label{table:results-mid-fleet-size}
    \begin{tabular}{ l | c  c }
      \toprule
      Methods & Task Completion Time & Human Working Time \\
      \midrule
      \rule{-2.5pt}{2ex} Greedy-HR & $1190.3 \, / \, 1036.1 \, / \, 760.4$ & $1167.0 \, / \, 1014.5 \, / \,725.0$ \\
      Greedy-FTG & $1010.4 \, / \, 868.7 \, / \, 666.2$ & $997.7 \, / \, 854.0 \, / \,641.6$ \\
      Greedy-CR & $929.3 \, / \, 825.5 \, / \, 661.8$ & $900.7 \, / \, 786.6 \, / \, 606.6$ \\
      Gittin's Index & $967.0 \, / \, 817.8 \, / \, 659.9$ & $938.3 \, / \, 776.2 \, / \, 607.0$ \\
      PTP & $\mathbf{905.6} \, / \, \mathbf{788.3} \, / \, \mathbf{626.2}$ & $\mathbf{892.9} \, / \, \mathbf{772.6} \, / \, \mathbf{601.2}$ \\
      \bottomrule
    \end{tabular}
  \end{center}
\end{table}

\begin{figure}[t]
  \centering
  \includegraphics[width=0.9\linewidth]{Figures/resutls_fixed_fleet_size.png}
  \caption{\textbf{Task completion time with varying levels of autonomy.} The robot fleet size is fixed to mid.}
  \label{fig:task-completion-time-fixed-fleet-size}
  \vspace{-2mm}
\end{figure}

\subsection{Results}
\label{subsec:results}
In the first experiment, we fix the robot fleet size to mid and vary the levels of autonomy. The results are presented in Table~\ref{table:results-mid-fleet-size} in the order of \textit{low}/\textit{mid}/\textit{high} autonomy. The task completion time with averages and standard deviations over different fields and trials are visualized in Figure~\ref{fig:task-completion-time-fixed-fleet-size}. As shown, all the methods are able to complete the task in less time with the increase of levels of autonomy as the robots encounter fewer failures. By performing long-horizon planning for the supervisor on the graph, PTP achieves the fastest task completion time and human working time among the five methods under all levels of autonomy. The visualization of human working time reveals similar patterns to those from task completion time and thus omitted for brevity. The observation of longer human working time under lower autonomy also supports the intuition that the supervisor is required to provide more assistance to the robots with more failures occurred.

In the second experiment, we fix the levels of autonomy to low, which generates the smallest margin between PTP and other baselines in the first experiment, and vary the robot fleet size. The results are presented in Table~\ref{table:results-low-autonomy} in the order of \textit{small}/\textit{mid}/\textit{large} fleet size. Similarly, we visualize the task completion time with averages and standard deviations over different fields and trials in Figure~\ref{fig:task-completion-time-fixed-autonomy}. Similar to the findings in the first experiment, PTP outperforms the compared methods in both metrics under most conditions except for a longer human working time with small robot fleet size. As a side note, we observe that the navigation task can be completed in less time with more robots in the team for all methods.

\begin{table}[t]
  \begin{center}
    \caption{Results of fleet management with varying robot fleet size}
    \label{table:results-low-autonomy}
    \begin{tabular}{ l | c  c }
      \toprule
      Methods & Task Completion Time & Human Working Time \\
      \midrule
      \rule{-2.5pt}{2ex} Greedy-HR & $1272.0 \, / \, 1190.3 \, / \, 1049.8$ & $1199.0 \, / \, 1167.0 \, / \, 1037.5$ \\
      Greedy-FTG & $1096.6 \, / \, 1010.4 \, / \, 987.1$ & $1074.6 \, / \, 997.7 \, / \, 978.7$ \\
      Greedy-CR & $1060.0 \, / \, 929.3 \, / \, 858.0$ & $\mathbf{1011.6} \, / \, 900.7 \, / \, 841.4$ \\
      Gittin's Index & $1077.4 \, / \, 967.0 \, / \, 849.1$ & $1021.8 \, / \, 938.3 \, / \, 834.0$ \\
      PTP & $\mathbf{1042.6} \, / \, \mathbf{905.6} \, / \, \mathbf{815.6}$ & $1017.4 \, / \, \mathbf{892.9} \, / \, \mathbf{806.4}$ \\
      \bottomrule
    \end{tabular}
  \end{center}
\end{table}

\begin{figure}[t]
  \centering
  \includegraphics[width=0.9\linewidth]{Figures/resutls_fixed_autonomy.png}
  \caption{\textbf{Task completion time with varying robot fleet size.} The levels of autonomy is fixed to low.}
  \label{fig:task-completion-time-fixed-autonomy}
  \vspace{-3mm}
\end{figure}

To better understand the difference between the effects of the actions planned by the PTP and other baselines, we examine the progress made by the human-robot team against time. The percentage of field covered over time with mid autonomy and mid robot fleet size is plotted in Figure~\ref{fig:covered-field-vs-time}. As shown in Figure~\ref{subfig:covered-field-vs-time-global}, Greedy-CR and Gittins index exhibit better performance than PTP in the first half of the simulation as both baselines encourage the supervisor to rescue the close robots. With shorter robot waiting time, the robot fleet can make faster progress at the initial stage of the navigation task. In contrast, the PTP provides long-term planning for the supervisor and considers robot coordination through the modified cost~(\ref{eq:modified-cost}), thus generating superior global performance on the task compared with other baselines as shown in Figure~\ref{subfig:covered-field-vs-time-local} and the second half of Figure~\ref{subfig:covered-field-vs-time-global}. In other words, each robot is encouraged to wait if the supervisor can benefit from rescuing another robot that either needs more urgent help or can save the distance traveled by the supervisor in the future.

\begin{figure}[t]
  \centering
  \begin{subfigure}[b]{0.49\linewidth}
    \includegraphics[width=\linewidth]{Figures/results_covered_vs_time_final.png}
    \caption{}
    \label{subfig:covered-field-vs-time-global}
  \end{subfigure}
  \begin{subfigure}[b]{0.49\linewidth}
    \includegraphics[width=\linewidth]{Figures/results_covered_vs_time_local.png}
    \caption{}
    \label{subfig:covered-field-vs-time-local}
  \end{subfigure}
  \caption{\textbf{Percentage of field covered over time.} The standard deviations over different trials are omitted for clear presentation. \textbf{(a)} The average percentage of field covered over time across the whole simulation. \textbf{(b)} The details of figure around $405$ time steps when PTP surpasses the second best method in terms of task completion progress.}
  \label{fig:covered-field-vs-time}
  \vspace{-3mm}
\end{figure}
\section{Discussion and Limitations}
The results presented in Section~\ref{sec:case-study} show that compared to baseline methods, the modified PTP provides a promising solution that can enable the human-robot team to complete collaborative tasks with higher efficiency. Despite the advantages, our work also encompasses several limitations, which will be discussed in detail in this section.

One of the main challenges in problem formulation of fleet management is the definition of the reward function $r_i(t)$ for each robot. In this work, the reward is defined as the \textit{net} expected distance that a robot can travel with supervisor intervention, which can change abruptly from $0$ to a positive number at time $t$ when the robot fails. Such discontinuity in time can result in bad performance of the solution obtained at time $t-1$ on the updated dynamic GTP, which can also be seen from the bound~(\ref{ineq:theorem}) as $\alpha$ needs to be large enough to encompass the change in one time step. To resolve the issue, a smooth reward function over time is desired to represent the ``value" of visiting a robot.

In addition, as noted in Section~\ref{subsec:results}, we observe that the modified PTP generates a longer robot waiting time compared to Greedy-CR and Gittins Index, i.e., the robots spend more time on waiting for help from human after a failure occurs. Such a low robot utilization can increase the energy cost in practice when the robots are idle but can be potentially improved by formulating and incorporating the robot waiting time into the objective function of the modified PTP.

Apart from the performance, the real-time capability is another important factor that affects the practical value of an algorithm in real-world applications. To act intelligently, the supervisor in the field requires prompt guidance from the system with small time delays. In our case study, the modified PTP returns the optimal solution within $2.26$, $4.96$, and $24.02$ ms on average in a complete graph with $6$, $8$, and $11$ nodes. Although the algorithm is efficient enough to support the management of robot fleets with moderate size, it is known that the worst-case running time of exact algorithms for PTPs scales superpolynomially with the number of nodes in a graph~\cite{bienstock1993note}. With the recently presented idea of learning heuristics for combinatorial optimization problems~\cite{kool2018attention}, reinforcement learning approaches can be explored to approximate the optimal solution to the dynamic GTP.

Despite the limitations and potential improvements, we hope that this work builds a rigorous framework for fleet management problems with physical assistance, provides a competitive algorithm that enables efficient human-robot collaboration, and can encourage the research on one-to-many supervision from a new perspective of graph traversal problem.
\section{Conclusion}
In this work, we formulate the one-to-many supervision of multi-robot systems as a dynamic graph traversal problem, in which the node rewards represent the value of visiting a robot and the edge costs reflect the traveling cost from one node to another. We approximate the solution to the intractable dynamic problem by solving a static GTP and develop a bound on the approximation error. A practical implementation on optimizing the static GTP is developed based on a modified profitable tour problem, whose optimal solution can be obtained efficiently using mixed-integer programming. Our case study shows that the proposed method outperforms various baselines with faster task completion time and human working time under various conditions in a simulated autonomous farm. Equipped with such an intelligent advising system, the performance of the human-multi-robot team can be potentially enhanced in real-world applications where physical assistance is required. With several possible directions to explore in the future, we hope that this work marks the first step towards formalizing a general supervision problem as a graph traversal problem and can serve as a benchmark for future methods.

\section*{Acknowledgements}
This work was supported by the the USDA National Institute of Food and Agriculture (USDA/NIFA), through the National Robotics Initiative 2.0 (NIFA\#2021-67021-33449), the AI Institute AIFARMS through the Agriculture and Food Research Initiative (AFRI) (USDA/NIFA Award no. 2020-67021-32799), as well as the Illinois Center for Digital Agriculture.

\bibliographystyle{plainnat}


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Those who have severe injuries with big wounds must not trust the Steri Strips, as they won't work for them. Many people recognize the Steri Strips as butterfly bandages due to their structure. The ends of the Steri Strips contain sticky substances, and the middle of the Steri Strips container has no sticky substance.
The wounds which require thin bandages can be suitable for Steri Strips. The Steri Strips can stay for around 2 weeks. Some people may see the Steri Strips getting removed on their own after a few days. The person needs to take some precautions to not let the Steri Strips go away very quickly.
Steri Strips Time
In weeks 2 weeks
In days 14 days
There are many types of Steri Strips that people can find in the market. Not all the Steri Strips would look exactly similar, but they would be thin. The lasting time of Steri Strips depends on how they are put and maintained. The person needs to stay away from water if they want to keep the Steri Strips for a long time.
The main mechanism behind the healing of wounds by Steri Strips is to heal the wound without touching it. The Steri Strips would close the ends of the wounds and this would help in faster healing of the wounds. The Steri Strips would help in preventing the wounds from the bacteria and viruses present in the environment.
The best part about the Steri Strips is that they can be removed anytime whenever the person wants. The person can take off the Steri Strips before one week if the wounds are completely healed. Unlike the stitches, the Steri Strips won't require any special method. Not all wounds are suitable for using the Steri Strips.
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The wounds which are small in size and have straight ends are a better fit for the Steri Strips. If the wounds are bleeding continuously, then the person should avoid putting the Steri Strips on them. Any type of liquid near the wounds can remove the Steri Strips as the sticky substance would get weak after moisture contact.
The length of the wound is a big concern for knowing their suitability for Steri Strips. The wounds which are longer than half-inch would not be suitable for the application of Steri Strips. If someone tries to apply the Steri Strips on the bigger wounds, then it may cause the wound to go worse by pressurizing the wounds.
The person should avoid putting Steri Strips on the wounds which would not get in touch with the middle part of the Steri Strips. If the person wants to maintain proper hygiene, then they can change the Steri Strips every 2 to 4 days.
If the Steri Strips are applied on the part of the body which doesn't move a lot, then it would not get removed before 2 weeks. Everyone should apply the Steri Strips with proper hygiene to not get them removed quickly. Sometimes, people apply the Steri Strips with dirty hands and this would cause problems such as bacterial infection.
To make the Steri Strips last more than one week, everyone should try to apply them to the dry area. The edges of the Steri Strips should be tightly stuck. The strips would get separated or fall off the wound when they are no more effective. The person may not have to remove the Steri Strips all the time.
Everyone needs to avoid removing and sticking the Steri Strips many times, as it may affect the condition of the wound.
The lasting time of the Steri Strips would be around 2 weeks. The Steri Strips would come out on their own when the wounds are completely healed. The surgeons may apply the Steri Strips when the wounds are about to heal.
The people should avoid applying the Steri Strips on the wound from which the liquid is coming out continuously as they won't allow the Steri Strips to stay for a long time. The quality of the Steri Strips would affect how long the Steri Strips would last. People should try to apply the high-quality Steri Strips to allow it to stay for more than 2 weeks.
https://journals.lww.com/plasreconsurg/fulltext/2004/03000/THE_APPLICATION_OF_STERI_STRIPS.88.aspx
https://emj.bmj.com/content/19/5/405.short
How Long Do Accidents Stay On Your Record (And Why)?
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How Long Do Points Stay On Your License (And Why)?
How Long Do Droplets Stay In The Air (And Why)?

redpajama_set_name: RedPajamaCommonCrawl


text:
Counties Isiolo
Isiolo activist murdered where husband and son were killed 11 years ago
Isiolo gender activist and peace ambassador Elizabeth Ibrahim, who was stabbed to death at Kambi Garba in Isiolo on January 3, 2022, during a past interview with Nation.Africa in Isiolo town.
Photo credit: Waweru Wairimu | Nation Media Group
By Waweru Wairimu
An Isiolo-based gender activist and peace ambassador Elizabeth Ibrahim was on Monday evening killed over a suspected land dispute.
The mother of five was stabbed to death at Kambi Garba allegedly by Patrick Nawit, 45, who narrowly escaped death after police officers rescued him from an irate mob that had descended on him with kicks and blows, badly injuring him.
The suspect is currently hospitalised at the Isiolo Referral Hospital in critical condition under the watch of police officers.
Isiolo women receive Head of State Commendation awards
Gender Jan 04
Eyes on Borana elders in Isiolo governor's race
Isiolo Jan 04
Isiolo County Commissioner Geoffrey Omoding said preliminary investigations showed that the suspect attacked Ms Ibrahim over a land dispute.
It, however, remains unclear where the actual incident happened with reports indicating that Mr Nawit attacked the woman at a burial ceremony and police saying both were walking by the roadside when the man turned on the woman.
"They were walking together when the man attacked the woman with a knife and bled to death. The public descended on the suspect but he was rescued (by our officers) and taken to hospital," County Police Commander Joseph Kigen told Nation.Africa.
The police boss said investigations had been launched to establish what transpired before the incident.
Husband and son had been hiding
In a sad coincidence, the widow was killed within the same area where her husband and son were killed 11 years ago following clashes pitting two communities living in Isiolo that left 10 people dead and over 20 houses torched.
Armed attackers set ablaze her house where her husband and son had been hiding on the morning of October 22, 2011.
Her husband was shot dead while he struggled to get out of the house while the Form Four student succumbed to burn injuries.
After the Monday evening incident, a section of Isiolo leaders condemned the incident and called on the security agencies to expedite the probe and ensure justice is served to the bereaved family.
County Woman Rep Rehema Jaldesa and Nominated MCA Mumina Konso eulogised Ms Ibrahim as a selfless person who had immense love and dedication to the community.
"I am very saddened by the death of Ms Ibrahim. I condemn the inhumane act," Ms Konso shared.
Having borne the brunt of insecurity, Ms Ibrahim was involved in peacebuilding and conflict management through community sensitisation and awareness.
"I have been passionate about peacebuilding and leading peace initiatives. I know how important peace is because I lost my husband due to fights. I am a victim of ethnic violence and I am committed to ensuring the improved relationship among Isiolo residents and neighbouring counties," she told Nation.Africa in a past interview.


text:
Q: Do any programming languages or package managers support coherence/confluence/global uniqueness of installed packages? When npm installs packages, it produces a tree of dependencies, where each package in the tree has its own tree of dependencies. As a result, the same package may occur in the tree multiple times. When obtaining an object that is re-exported through transitive dependencies, different objects may be returned based on the specific path of exports that were followed.
This causes problems in some cases, so peer dependencies exist, which allow the top-level of an application to specify a single version of a package, which sub-dependencies share in common.
If every dependency were marked as a peerDependency, then a single, global version of each package would exist in an application.
My question is: are there any languages or package managers which enforce a similar behavior everywhere, such that any two packages which share a dependency will share the exact same version of this dependency? And as a bonus, what costs or benefits have said languages/ecosystems encountered as a result of this?

redpajama_set_name: RedPajamaStackExchange


- Help people in the bus.
There is an abandoned bus in the jungle that is being assaulted by zombies. The quest automatically begins when you drive by and are prompted to help the poor couple trapped inside.
Peel the zombies off the bus and off Carlos and speak to him afterward to finish this quick sidequest.


text:
Weather Setting
Results of the past season
This season, a new greenhouse was built for tomatoes on our site, in which we planted completely new varieties of tomato for us. And it was necessary to build the greenhouse itself, and to build a high ridge in it in the spring. For this reason, we were delayed with planting seedlings, but the ridge justified itself. Fruiting in it continued until October. The place for the greenhouse was chosen correctly, and the varieties of tomatoes were selected well. In the greenhouse, many bushes of delicious "beef-tomatoes" grew and bore abundantly. The end result is long-term fruiting and extremely tasty, delicious fruits at the end of the season.
Tomatoes, and weighty …
Melons in the open field: the first ridge - we got 66 melons from two plants of Serezhkina love melons. They turned out to weigh from 0.5 to 1.5 kilograms, the fruiting of the variety lasted until the very frost, but the taste of the fruit, let's say, is not for everybody. On the second street ridge, measuring 3.5 x 0.8 meters, we placed four plants. They set up and ripened 82 fruits weighing from 1.5 to 2 kg. Roksolana melon bore especially abundantly. The quality of the pods of this hybrid turned out to be very high.
Watermelons in the open field. On a ridge measuring 1.2 x 1 meter with a ridge height of 80 centimeters, we grew 16 watermelons on three plants. Particularly pleased with the watermelon Gift of the North - the weight of the largest fruit was 10 kg. And the taste of watermelons in the open field turned out to be better than in a greenhouse.
And the peppers did not fail
In the greenhouse, both watermelons and melons developed well, as they both grew on completely new, vertical ridges constructed for the first time. The area of the ridges was small, but the harvest of fruits harvested from these areas was high. We got 15 fruits from five watermelon plants. The watermelons were quite large - 10 kg and more. For all fruits, special hard shelves were made. The largest watermelon of the Lezheboka variety pulled 18 kilograms! The fruits of the Hybrid Gift to the North were ready for harvest in mid-August, and the Lezhebok variety was ripe by the end of the month.
The biggest problem in growing watermelon fruit in a greenhouse was that it was difficult to design the shelves for the fruit. Some of the shelves were made to hang like a swing. And during watering, it happened that we touched this shelf with our head, and then the fruits fell. For this reason, three watermelons fell from a height of 2 meters and split.
Melons in the greenhouse. Basically, the Gerd hybrid was planted in the greenhouse. Developed well, but the problem was the same - falling fruits and breaking the whips. From each melon plant in the greenhouse, we received 18 fruits, their average weight was about 2 kg.
Pumpkin Khutoryanka
The past year was successful for cucumbers, pumpkins and zucchini. The main thing in the success of growing these crops in hot summer is to fulfill the motto: "Do not forget, water!" Among the new products, pumpkins were attracted by their beauty and productivity of the varieties Burger and Khutoryanka. Last season, butternut pumpkins also bore abundant fruit: we collected 17 fruits from two plants. Flowers on the site this summer also pleased us with friendly and long flowering, but for this we had to spend an unusually long time and effort on watering.
Apple and plums gave us a bountiful harvest. But berry crops in our area gave a smaller yield than a year ago. Garden strawberries not only did not please with a large harvest, but their fruiting was short-lived. The lack of harvest of this culture is also due to the fact that our strawberry plantings were very actively attacked by flocks of thrushes. Apparently, this was a consequence of the hot summer, we think that there was less food for birds in the forests.
Our young plants of edible honeysuckle bore fruit very well last summer. The first signal of ripening of its berries was the flocks of the same blackbirds. They were so bold that they were not even afraid of the owners of the garden passing by, apparently, they liked the berry. Of the plant pests, slugs worried us the most. One gets the impression that their army is growing every year. The method of dealing with them on our site is manual collection plus processing of plants with ash.
The eggplants were also good
What is the result of the past horticultural season? For us, it turned out to be successful in terms of harvest, but we admit that the irrigation was thoroughly worn out. If someone of those gardeners who were left without a crop last year wants to know the secrets of high yields on our site, then here we can say this: our method of growing plants is that we try to carefully lay food in the ridges even before planting plants, we mulch the soil during the period of abundant fruiting and take care of plant health during the growing season. We do not carry out pest control by chemical methods, as we create healthy land, healthy conditions for growth and fruit setting. We try to avoid disease. If some plant got sick, then this is an "emergency" for us, which means that somewhere we made a mistake in preparing the habitat for it and overlooked something.


text:
Arts Review: Expensive Shit
qmunicate 19/04/2017 arts and culture, arts review, Uncategorized
Dir, Adura Onashile, Tron Theatre, 30th March – 1st April
I walk into the auditorium not sure what to expect. A toilet attendant? Two clubs in different continents? Dreams of dancing? I am not sure this is going to work. Yet what I encountered is an intelligent, thought-provoking and sensitive performance. Somehow, it manages to connect two seemingly separate worlds by focusing on the universality of themes like dreams, power and the rights of women's bodies.
Expensive Shit works by playing on the similarities and differences of the two settings, a Nigerian nightclub and a Scottish club based on Glasgow's Shimmy Club. The stage is used ingeniously to reflect such nuances. The props and setting remain identical, which underlines the idea that the structures of each place essentially function in the same way. Yet, subtle changes in lights, to illuminate a different club name, and sound variation in the form of changing background music, reveals the simultaneous cultural differences.
The setting is brought alive by the insightful acting and passionate dancing of the four performers, three of whom each take on two roles (one for each setting) whilst the protagonist remains the same. Yet even she is revealed as having gone through experiences that changed her. In the later-set location of Glasgow, the toilet attendant is shown at first as cynical, beaten, accepting of her subjugation. In comparison, her younger self seems to live off of her hopeful dreams for the future of becoming a dancer in the revolutionary band of the late Nigerian musician Fela Kuti.
Throughout the play, however, dark undercurrents begin to emerge as implications of the abuse of men's power appear. Poverty pushing women into the arms of abusing men, date rape and the male gaze become apparent features of the play. I thought it was incredible the way in which I was pulled along with the actors in their slow realization of the covert powers that were controlling their lives and their bodies.
Yet what truly inspired me was the ending. Rather than leaving me with a bitter taste in my mouth and a sense of powerlessness, it empowered me, as the actors managed to find a way to retake control each in their own way.
[Kirsty Campbell]
expensive shit, Kirsty Campbell, tron theatre, University of Glasgow
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An independent survey was conducted with positive airway pressure patients from the United States, United Kingdom, Germany, France and Australia, including patients who have used more than one different brand of positive airway pressure mask. The survey was conducted by a third party, DVL Smith, at ResMed's request and expense. Based on the collective survey results, of those expressing a preference, the data demonstrates, at the 95% confidence level, that ResMed is the preferred mask brand. The detailed results of the survey are proprietary to ResMed. This survey was conducted between August 14 and September 6, 2012.


text:
Dębnicka Dolina – dolina w Górach Opawskich, w środkowej części Lasu Prudnickiego, na wschód od wsi Dębowiec, na terenie administracyjnym miasta Prudnik. Położona między wzniesieniami Kobylica, Święta Góra, Zbylut, Wróblik i Długota. Przepływa przez nią potok Trzebinka (Dębnicki Potok), dopływ Prudnika.

Dolina mieści się w granicach Parku Krajobrazowego Góry Opawskie. Jest to ostoja zwierzyny od pozostałej części lasu. Przebywają tu sarny i dziki. Znajduje się tu daglezja, ustanowiona pomnikiem przyrody.

Historia
W Dębnickiej Dolinie znajduje się grodzisko, zaznaczane na niemieckich mapach pod nazwą "Schlossplatz", czyli "miejsce zamku", "plac zamkowy". Jest to typowe średniowieczne, dobrze zachowane grodzisko stożkowe. Na kwadratowej wyniosłości prawdopodobnie znajdowała się drewniana wieża, a na otaczających ją z trzech stron wałach palisada. Od czwartej strony gród chronił strumień.

W latach 30. XX wieku w dolinie znajdowało się miejsce odpoczynku z ławkami, nazywane Reimannsruh. Prowadził tędy szlak z sanktuarium św. Józefa do Dębowca. Pozostałością po nim jest kamienna tablica. Wyraźna ścieżka prowadząca z dna Dębnickiej Doliny przez stok Świętej Góry wyznaczała fragment granicy między lasem, który był własnością Prudnika, a Lasem Trzebińskim. Obecnie biegnie tędy granica między miastem i gminą Prudnik a wsią Trzebina w gminie Lubrza. Na przedłużeniu granicznej ścieżki znajduje się podłużny i spłaszczony kamień, który według Andrzeja Derenia mógł pełnić funkcję kamiennej kładki na pobliskim strumieniu, albo był jednym z kamieni granicznych Królewskiego Miasta Prudnik.

Przed 1837 w Dębnickiej Dolinie powstał staw, który służył jako rezerwuar wody na wypadek pożaru w Lesie Prudnickim. Na jego miejscu w 2018 Nadleśnictwo Prudnik utworzyło większy zbiornik wodny o powierzchni 0,4 ha. Miał on poprawić bilans wodny lasu, zmniejszyć zagrożenie pożarowe i zwiększyć odporność lasu na susze poprzez uwilgotnienie mikroklimatu.

Turystyka

Szlaki turystyczne
W rejonie Dębnickiej Doliny przebiegają szlaki turystyczne:
  Główny Szlak Sudecki im. Mieczysława Orłowicza (440 km): Prudnik – Świeradów-Zdrój
  Szlak Historyczny Lasów Królewskiego Miasta Prudnik (17,5 km): Park Miejski w Prudniku – stare dęby w Prudniku – Kapliczna Góra – Kobylica – Dębowiec – rozdroże pod Trzebiną – sanktuarium św. Józefa w Prudniku-Lesie – Prudnik–Lipy – Park Miejski w Prudniku

Szlaki rowerowe
W rejonie Dębnickiej Doliny przebiegają szlaki rowerowe:
  Wokół Lasu Prudnickiego – Pętla II (13,5 km): Prudnik – sanktuarium św. Józefa w Prudniku–Lesie – rozdroże pod Trzebiną – Dębowiec – Prudnik

Przypisy

Dębowiec (województwo opolskie)
Doliny Polski
Geografia Prudnika
Góry Opawskie

redpajama_set_name: RedPajamaWikipedia


The International Commission for the Conservation of Atlantic Tunas (ICCAT), which ended its annual meeting on Nov. 17, has agreed to increase fishing quotas for Atlantic bluefin tuna.
"The increased quotas for Atlantic bluefin tuna are risky and threaten to undo recent gains," said Amanda Nickson, who directs tuna conservation efforts for The Pew Charitable Trusts. "Significant concerns remain about the ability of these fish to fully recover from a long history of overfishing."
In addition, delegations to the meeting in Genoa, Italy, took no action on proposed shark protections and decided to again delay implementation of an electronic bluefin catch documentation system intended to better track fishing in the Atlantic Ocean waters under the commission's jurisdiction.
"This year's ICCAT decisions have been overwhelmingly disappointing. Several species, including bluefin tuna and porbeagle sharks, remain at serious risk from unsustainable fishing. Despite the last few years of progress from ICCAT countries, the decisions this year have shown that this commission is not accounting for critical vulnerabilities highlighted by science," said Paulus Tak, who led Pew's delegation to ICCAT. "Instead of continuing progress toward adopting precautionary, science-based catch limits in some of these fisheries, member countries put in place very risky quotas that could lead to declines in bluefin populations."
Pew had recommended that ICCAT follow the scientific advice and maintain current quotas for both populations through 2016.
Not all commission actions were negative. "Commission members took positive steps toward ending illegal fishing, which is good, but, overall, the outcome this week underscores the need to keep the international spotlight fixed on this body," Tak said.
For western Atlantic bluefin tuna, members of ICCAT raised the quota to 2,000 metric tons, a 14 percent increase over last year's. According to scientific assessments, although there has been measurable growth in this population, it is just as likely that increasing catch limits will reverse the positive trajectory as maintain it. In addition, the eastern bluefin tuna quota is set to increase by roughly 20 percent, to 15,821 metric tons, with certain member countries allowed an additional 321 metric tons as catch. The quota will increase by about 20 percent again in 2016 and for a third time in 2017.
With next year's increased quotas, the need for tighter controls on undocumented and illegal catch and trade is more important than ever. Despite this, ICCAT members delayed the upcoming March deadline to implement a new system that would electronically track all catch and major sources of trade of Atlantic bluefin tuna.
"Despite ongoing reports of seizures of illegally caught fish, for the fourth straight year, governments are delaying the implementation of an electronic tracking system that would improve their ability to shrink the black market for Atlantic bluefin tuna," Nickson said.
Although ICCAT members did not act on illegal fishing of bluefin tuna, they did take steps to eliminate some illegal fishing that goes undetected. They agreed to set up a special fund to assist in the implementation of port inspection requirements. The use of International Maritime Organization numbers will also be increased and will now be mandatory for all vessels that are at least 20 meters long and fish for bigeye and yellowfin tuna.
ICCAT will also work to enhance the effectiveness of vessel monitoring systems (VMS), which use satellites to transmit information on a vessel's location and fishing activities to aid authorities in monitoring, control, and surveillance efforts. Countries agreed that fishing vessels over 24 meters long will be required to transmit location data to any ICCAT coastal state when in its waters. The location will now be relayed every four hours, instead of the current six, a decision that was made by consensus.
Member countries could not reach agreement on proposals that would have protected porbeagle and shortfin mako sharks, continuing to leave these populations at risk.
"Once again, ICCAT members ignored calls to sustainably manage shark populations. Porbeagle and shortfin mako sharks in the Atlantic Ocean will continue to be fished without limit, despite clear scientific advice that overfishing is depleting these populations," said KerriLynn Miller, an expert with Pew's global shark conservation program. "Failure to act goes against the recommendations of precautionary science and will only speed the decline of these top predators."


Inspired by that very photo on Pinterest, I did it about a month ago and love it! Our box spring had been scratched to heck by the cats. I used some dark brown microfiber fabric, 2 yards for a Queen size bed.
The bottom was really easy to attach, I just used my electric staple gun to attach the fabric. The top was trickier as it doesn't have wood on that side, so I used Stitch-witch! It worked wonderfully and has held up.
Another tricky part was figuring out where to have my ends line up since the fabric wasn't long enough to go around each side, just around the ends. So I wrapped the ends (foot, head) first and put the fabric over the sides last.


text:
IDMN: International Design Media Network
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TALKING DESIGN: DESIGN AND PROGRESSIVE CHANGE
Brisbane (Australia) - The Australian Graphic Design Association (AGDA) Queensland is hosting a Talking Design Public Lecture supported by the Queensland Government through Arts Queensland and the State Library of Queensland. Don Ryun Chang (Korea) and David Berman (Canada) will talk about the role of design in a changing world.
The role of designers in a changing world
What role will design and designers play in delivering a positive future?
And what is the role of businesses in forging this future?
Don Ryun Chang
Seoul (Korea)
Don Ryun Chang was born to diplomat parents and grew up on five continents - Asia, Europe, North and South America and Africa. He was educated at the University of British Columbia in Canada, the Parsons School of Design, and received his MFA from the California Institute of the Arts. Don then worked for several organizations such as Nara Advertising, Design Focus in Korea, Steiner & Co. in Hong Kong, and was Creative Director for the Infinite Group. Don founded DC&A in 1991, which later became one of the leading identity companies in Asia. The company merged with Interbrand in July 1999 and has developed acclaimed identities for the 2002 FIFA World Cup, Korea Telecom, Shinhan Bank and Korea Tourism Office.
Don has received numerous international design awards from prestigious organisations such as the Brno and Warsaw Poster Biennale, and the Type Directors Club of New York. Don lectures widely on branding and is currently Dean of the Graduate School of Advertising at Hongik University in Seoul. He has served as Vice President of the Visual Information Design Association of Korea (VIDAK) and is the current President of the Icograda Executive Board. Don advises for many institutions including the Korean Olympic Committee, Seoul Metropolitan Government and is the author of five books including How to succeed in business with design and Brand Media Innovation.
David Berman has over 20 years of experience in graphic design and communications and has worked extensively in the adaptation of printed materials for electronic distribution, including web design and software interface development. As an expert speaker, graphic designer, communications strategist, public speaker, typographer and consultant, his professional work has brought him to over 10 countries in the past few years. His clients include IBM, the International Space Station, the Canadian Government, the World Bank, and the Aga Khan Foundation. David's work includes award winning projects in the application of plain writing and design.
David has worked to establish a code of ethics that embraces social responsibility for graphic designers throughout Canada. The Society of Graphic Designers of Canada (GDC) ratified his draft nationally in May 2000. He served as President of the first elected board of the Association of Graphic Designers of Ontario (RGD), North America's first accredited graphic design organisation, from 1997 to 1999. He led the development of the association's General Bylaw and Rules of Professional Conduct and authored Ontario's accreditation examination section on ethics and professional responsibility. He has served as the National Ethics Chair for the GDC since 2002. David has served as Treasurer of the Icograda Executive Board since 2005. He published Do Good Design— How designers can change the world in January 2009.
Venue: slq Auditorium 1, Level 2, State Library of Queensland
Admission is free but RSVP is required by Thursday 9 July 2009 to with the subject 'Talking Design'. Seating is strictly limited.
About AGDA
The Australian Graphic Design Association (AGDA) is the national association for professional graphic designers. It was founded in 1988 to facilitate the advancement of the graphic design profession in Australia. AGDA is a Professional Member of Icograda.
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A star is born !!!!!!!!!!
Actually,there are two hydros in my basement Rec. Room. The "America" boat is a ASH hull,just to the left you can see another hull,its our new 15SSH hull.We will do a photo shoot for JOMS in early spring 2019.
Absolutely gorgeous! Hope 2019 is a great season for Team Sees. Please let us know what we can do to help!
Well God speed Evel Knievel. I like it.
Just wondering,did any one notice our over worked boat bottom inspector taking a well deserved break,he is under the boat to the right in the picture?My son didn't notice him when he took the photo,but there he is,doing his job.
Should we include "Tender Vittles" in our sponsorship for next year?
Yes,along with a JOMS flea collar.I will consult with his agent,see if he requires anything else.


Leaders of Australia's General Aviation (GA) Advisory Group has this week presented a plan to Government to help ensure the sector's future.
Deputy Prime Minister and Minister for Infrastructure and Transport Michael McCormack said he received the General Aviation Flight Plan when he met with sector leaders in Canberra.
"The GA Advisory Group was established by the then-Minister Darren Chester in October 2016, to provide the very diverse GA sector with a forum to advise the Government on its priorities," Mr McCormack said.
The GA Flight Plan has identified three key priorities to ensure a strong future for the sector.
"I welcome the establishment of the GA Flight Plan and I have asked the Department of Infrastructure, Regional Development and Cities and the Civil Aviation Safety Authority (CASA) to work with the Group in responding to these priorities," Mr McCormack said.
GA Advisory Group Chair and Royal Flying Doctor Service of Australia CEO Dr Martin Laverty thanked the Deputy Prime Minister for his strong backing of the GA industry.
"The Deputy Prime Minister has given the GA Advisory Group freedom to identify our own opportunities for growth and to present its ideas on solutions to some of our challenges," Dr Laverty said.
CASA Chief Executive Officer and Director of Aviation Safety Shane Carmody welcomed the opportunity to work closely with the GA Advisory Group and to strengthen the safety regulator's ties with General Aviation.
"I'm pleased to have met with the GA Advisory Group, and to plan to use it as an ongoing reference group on safety regulatory issues relating to the GA sector," Mr Carmody said.


Whether you are new to Android phones or you've been around for a while, you may be surprised to learn about the multiple hidden features that Google has put into the Android platform. Perhaps one of the best-kept secrets that many Android users aren't aware of are the Android Easter Eggs.
From the time Android started, Android users have always loved to explore and discover what they can do with their phone. This lead to Android developers putting in some occasional surprises in the system which only those who love tinkering with their phone can discover. These surprises are referred to as Android Easter Eggs, and the best known – and most fun – Android Easter Eggs are the mini games.
Of course, not all of us have the time or interest to go digging through every little menu in our Android device's settings, so I'm going to just show you how to access your Android Easter Egg mini game.
Scroll down and look for the "System" option and open it.
Look for the "About Phone" option and open it.
Find the "Android Version" tab.
Rapidly press the "Android Version" tab until something pops up. Usually what pops up is the icon of your latest Android Version.
Android 8.0 – The latest version allows you to play around and control some sea creatures on your phone.
Android 7.0 – A spin-off based on a popular Japanese mobile game, Neko Atsume – Android Neko. The game is pretty cute, and you can even feed the cats.
Android 6.0 and 5.0 – A spin-off to Flappy Bird that is fun and addictive.
Android Easter Eggs, like regular Easter eggs, are hard to find, but finding one is worth it because it's a treat. Once you have unlocked them you have a gift waiting in front of you.
Still need help finding your mini game Easter Egg? Know of another Android Easter Egg? Let us know in the comments, then share this post with your friends to help them find their own Android Easter Eggs!
Seems like a waste of space? …….
Hi Feebz, thanks for sharing your thoughts to us. Congratulations on finding the easter egg for Android Oreo. True, it can be a waste of space but it's designed to be a reward system for those who like tinkering their devices. Furthermore, such easter egg wouldn't take that much space. In our opinion, it should be taking less than 1MB of space.


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The 2018 Race Might Be the Last Big Democratic Stand Against Coffman
Chris Bianchi
Congressman Mike Coffman
Buckley Air Force Base.
Chris Bianchi | February 26, 2018 | 8:31am
It's the beginning of an even-numbered year, which means we're only months away from being bombarded by Republican Congressman Mike Coffman's amazing/terrible TV ads and photos of politicians glad-handing through Aurora, Centennial and the rest of the 6th District. Millions of dollars are already being thrown at Colorado's most expensive House race (by far).
But could this be the last biannual money and TV ad-athon in the 6th? If Coffman is able to pull off a fourth consecutive victory in this suburban swing district that includes much of Adams, Arapahoe and Douglas counties, it would cement him as an entrenched congressman, and perhaps take him out of Democratic targets in future election cycles.
If he does it again, you just might have to call him Iron Mike.
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"Coffman has been semi-officially endangered since his seat was redistricted in 2011. Since then, he's survived three challenges," says University of Denver political science professor Seth Masket. "[This year] is shaping up to be possibly the strongest Democratic tide since 2006. If Coffman can survive this, he can probably survive whatever the Democrats throw at him."
Not so fast, though, say Democrats. There's plenty of reason to believe that 2018 in particular could be different, and operatives on both sides of the aisle acknowledge that this year presents a completely different challenge for the fifth-term Aurora native.
An unpopular Republican president is tweeting on Pennsylvania Avenue in a national political environment that's expected to heavily favor Democrats. A record number of congressional Republicans have announced their retirements as they brace for a potential Democratic wave.
Though they're a few months old at this point, early polls have pointed to a tight race in the 6th, and Democrats are fielding a different type of candidate: Former Army Ranger Jason Crow, who's never held office, is the leading contender to win his party's primary and battle Coffman, who has never run with a Republican in the White House.
"This is the toughest environment Coffman has run in, in a district that is trending away from him," says Rachel Irwin, regional spokeswoman for the Democratic Congressional Campaign Committee, which has labeled the 6th District as one of its 24 "red to blue" target flip seats. "You have the perfect storm of an electorate that is well educated and diverse. We fully expect to flip this seat this cycle."
Should Coffman prevail on November 6, though, it could validate his own political brand, which goes against the general party tilt, similar to Democratic Senator Joe Manchin in deep-red West Virginia or longtime Republican Congressman Frank LoBiondo of traditionally Democratic New Jersey. Coffman has built an image of a moderate centrist — an image that Democrats fiercely contest by pointing to his voting record in Congress that they argue falls in line with Trump's priorities.
"I think that's the message on Coffman: He's not Trump, but he enables Trump by voting for Trump's agenda 95 percent of the time in Washington," says Eric Walker, the Colorado Democratic Party's communication director.
But perhaps more successfully than fellow GOP member Senator Cory Gardner, Coffman has been able to separate himself from the mainstream Republican brand, one that would doom more conventional candidates in a Democratic-tilting district such as the 6th.
"Despite Mike increasing his raw vote margin of victory every cycle since 2012, Dem Super PACs (specifically two Pelosi-affiliated groups — the DCCC and House Majority PAC) have only increased their spending in negative attack ads on the airwaves and in the mailboxes," writes Coffman spokesman Tyler Sandberg in an email. "We're ready for the fight."
Why does this congressional race matter so much? Colorado's other six congressional districts are about as competitive as a beer-in-hand kickball game. The 6th District, which voted for Hillary Clinton by a convincing nine-point margin but turned around and elected Coffman by around eight, is Colorado's only truly competitive House race each cycle. Another win by Coffman could cement this race as a likely Republican hold in future elections — or at least until redistricting after the 2020 Census.
"If Nancy Pelosi and her liberal donors want to continue wasting their money trying to take out Coffman, so be it," Sandberg writes. "Voters in the sixth district know that Mike fights for them, not (Democratic House minority leader) Nancy Pelosi, and they have long appreciated his willingness to stand up to both sides."
After squeezing out a two-point victory in his first election after 2011 re-districting moved him from a safe Republican seat to a much more competitive one, Coffman jumped his margin of victory to nearly ten points in each of his last two campaigns. Coffman defeated Democrat Andrew Romanoff by 8.9 points in 2014, and he followed that up by defeating Democrat Morgan Carroll by 8.3 points in what was generally expected to be a closer race. Coffman's popularity in immigrant communities in particular is believed to be a major part of his bipartisan appeal, and some of Coffman's harshest rhetoric against Donald Trump is often saved for immigration issues.
Probable re-districting after the 2020 Census, including the high possibility of Colorado receiving another congressional district, will make this all moot in three years, by which point Coffman will be 65 and potentially approaching retirement.
Chris Bianchi is a Westword contributor interested in politics.
Twitter: @bianchiweather
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