Flocking of Linear Parameter Varying Agents: Source Seeking Application with Underwater Vehicles

Distributed control for complex missions: Quasi‐linear parameter varying approach

“…In particular, we are interested in a flock of autonomous mobile agents with the task to find level sets (surfaces) corresponding to a given concentration level and distribute themselves over the surface (level surface tracking), and to patrol the level surface by moving in flocks around it (level surface monitoring). For simplicity we make the following assumptions: 21,23 …”

“…Assumption There exist $$$ {c}_{\Psi}>0 $$$ that satisfies the Lipschitz condition on the gradient $$$$ \left\Vert \mathrm{\nabla \Psi }(q)-\mathrm{\nabla \Psi}\left(\tilde{q}\right)\right\Vert \le {c}_{\Psi}\left\Vert q-\tilde{q}\right\Vert, \kern1em \forall q,\tilde{q}\in {\mathbb{R}}^m. $$$$ A two‐layered control architecture for a network of LPV agents will be used here, based on work in Reference 23, see Figure 1. A virtual layer consists of a flocking filter and represents the dynamics of the information flow in the network, and a second layer represents the dynamics of physical agents.…”

“…The overall coupled network dynamics can be written as $$$$ {\displaystyle \begin{array}{ll}\dot{q}& =p,\\ {}\dot{p}& =-\nabla V(x)-\left({\mathcal{L}}_{(m)}(x)+ cI\right)v+{u}^{\gamma}\left(x,v\right)=U\left(x,v\right),\end{array}} $$$$ and $$$$ {\displaystyle \begin{array}{ll}\left[\begin{array}{c}\dot{x}\\ {}\dot{v}\end{array}\right]& ={A}_{cl}\left(\rho \right)\left[\begin{array}{c}x\\ {}v\end{array}\right]+{B}_{cl}\left(\rho \right)q,\\ {}y& =\left[\begin{array}{c}x\\ {}v\end{array}\right].\end{array}} $$$$ The following theorem summarizes the main results in Reference 23.…”

“…tracking), and to patrol the level surface by moving in flocks around it (level surface monitoring). For simplicity we make the following assumptions: 21,23 Assumption 1. The scalar field Ψ(q) is time invariant and twice differentiable.…”

“…In Reference 23, an underwater source seeking scenario with a swarm of autonomous underwater vehicles is considered. For this purpose an LPV model of the Hippocampus autonomous underwater vehicle, developed at TUHH, 24 is used for controller design and simulation.…”