We consider the optimal coverage problem where a multi-agent network is deployed in an environment with obstacles to maximize a joint event detection probability. We first show that the objective function is monotone submodular, a class of functions for which a simple greedy algorithm is known to be within 1-1/e of the optimal solution. We then derive two tighter lower bounds by exploiting the curvature information of the objective function. We further show that the tightness of these lower bounds is complementary with respect to the sensing capabilities of the agents. Simulation results show that this approach leads to significantly better performance relative to previously used algorithms.

We address the problem of multiple local optima commonly arising in optimization problems for multi-agent systems, where objective functions are nonlinear and nonconvex. For the class of coverage control problems, we propose a systematic approach for escaping a local optimum, rather than randomly perturbing controllable variables away from it. We show that the objective function for these problems can be decomposed to facilitate the evaluation of the local partial derivative of each node in the system and to provide insights into its structure. This structure is exploited by defining “boosting functions” applied to the aforementioned local partial derivative at an equilibrium point where its value is zero so as to transform it in a way that induces nodes to explore poorly covered areas of the mission space until a new equilibrium point is reached. The proposed boosting process ensures that, at its conclusion, the objective function is no worse than its pre-boosting value. However, the global optima cannot be guaranteed. We define three families of boosting functions with different properties and provide simulation results illustrating how this approach improves the solutions obtained for this class of distributed optimization problems.

A multiagent coverage problem is considered with energy-constrained agents, where a charging station is used to replenish an agent’s energy as it becomes depleted while performing the coverage task. The objective of this article is to compare the coverage performance between centralized and decentralized approaches. To this end, a centralized coverage control method is developed to switch agents between an optimal coverage formation and an optimal charging formation. We design a controller for agent trajectories that include dwell times at the optimal coverage locations, and charging times at the charging station to maximize a coverage metric over a finite time interval. Our controller guarantees that at any time there is at most one agent leaving the team for energy repletion. We also derive a tight bound, which allows us to quantify the gap between the coverage performance of the proposed strategy and the unknown globally optimal coverage performance.

A robust control approach is proposed to solve the asymptotic stabilization problem of networked control systems, where the data transmission is mediated by a triggering function, and is subject to time-varying transmission delays. We show that the triggering mechanism and the delay effects could be regarded as uncertain components interconnected with a stable linear time-invariant system. We then use two operators to describe the uncertainties, and find the corresponding integral quadratic constraints of the operators. The stability of the networked control system is analyzed from a robust control point of view. Beyond the stability analysis, a co-design algorithm is devised to design the control gain and detection parameters jointly to maximize the inter-event interval as well as the maximum allowable time-delay. Theoretically, the proposed scheme guarantees that out-of-order packet delivery does not happen. The robust control framework allows the algorithm developed for time-varying delays to be applied to the constant delay and the delay free cases. Finally, the theoretical results are demonstrated and verified by numerical simulations.

We address the optimal dynamic formation problem in mobile leader-follower networks where an optimal formation is generated to maximize a given objective function while continuously preserving connectivity. We show that in a convex mission space, the connectivity constraints can be satisfied by any feasible solution to a mixed integer nonlinear optimization problem. When the optimal formation objective is to maximize coverage in a mission space cluttered with obstacles, we separate the process into intervals with no obstacles detected and intervals where one or more obstacles are detected. In the latter case, we propose a minimum-effort reconfiguration approach for the formation which still optimizes the objective function while avoiding the obstacles and ensuring connectivity. We include simulation results illustrating this dynamic formation process.