diff --git a/src/year2/distributed-autonomous-systems/img/safety_control.png b/src/year2/distributed-autonomous-systems/img/safety_control.png new file mode 100644 index 0000000..536d48c Binary files /dev/null and b/src/year2/distributed-autonomous-systems/img/safety_control.png differ diff --git a/src/year2/distributed-autonomous-systems/img/safety_control_multi.png b/src/year2/distributed-autonomous-systems/img/safety_control_multi.png new file mode 100644 index 0000000..47ad406 Binary files /dev/null and b/src/year2/distributed-autonomous-systems/img/safety_control_multi.png differ diff --git a/src/year2/distributed-autonomous-systems/img/safety_control_single.png b/src/year2/distributed-autonomous-systems/img/safety_control_single.png new file mode 100644 index 0000000..c0f1500 Binary files /dev/null and b/src/year2/distributed-autonomous-systems/img/safety_control_single.png differ diff --git a/src/year2/distributed-autonomous-systems/sections/_safety_controllers.tex b/src/year2/distributed-autonomous-systems/sections/_safety_controllers.tex index e60501b..94ff786 100644 --- a/src/year2/distributed-autonomous-systems/sections/_safety_controllers.tex +++ b/src/year2/distributed-autonomous-systems/sections/_safety_controllers.tex @@ -25,6 +25,11 @@ The goal is to design a feedback control law $\kappa^s: X \rightarrow \mathbb{R}^m$ for a control-affine non-linear dynamical system such that the set $X^s$ is forward invariant (i.e., any trajectory starting in $X^s$ remains in $X^s$). + \begin{figure}[H] + \centering + \includegraphics[width=0.25\linewidth]{./img/safety_control.png} + \end{figure} + \begin{remark} The time derivative of $V^s(\x(t))$ along the system trajectories is given by: \[ @@ -116,6 +121,11 @@ \item[Single-robot obstacle avoidance] \marginnote{Single-robot obstacle avoidance} Task where the goal is to keep an agent to a safety distance $\Delta > 0$ from an obstacle. + \begin{figure}[H] + \centering + \includegraphics[width=0.35\linewidth]{./img/safety_control_single.png} + \end{figure} + A control barrier function to solve the task can be: \[ V^s(\x) = \Vert \x - \x_\text{obs} \Vert^2 - \Delta^2 @@ -152,6 +162,11 @@ \item[Multi-robot collision avoidance] \marginnote{Multi-robot collision avoidance} Task with $N$ single integrator agents that want to keep a safety distance $\Delta > 0$ among them. + \begin{figure}[H] + \centering + \includegraphics[width=0.35\linewidth]{./img/safety_control_multi.png} + \end{figure} + The local control barrier function to solve the task can be defined as: \[ V^s_{i,j}(\x_i, \x_j) = \Vert \x_i - \x_j \Vert^2 - \Delta^2