Distributed source seeking in a 3-dimensional environment without explicit estimation of the gradient of the field is challenging. Nevertheless, for a swarm of an arbitrary number of agents, we develop a strategy to perform a source seeking behavior by requiring agents to synchronize their direction of motion using only local interactions while modulating their speed based only on the field value measured by each agent. The agents collectively move toward the source without estimating gradient and without sharing measurements of the field. We formulate a cascaded input-to-state stability problem from which we obtain Lyapunov-based convergence and robustness results. We validate the convergence of the swarm to the minimum of the field through simulated source seeking behavior in a 3-dimensional scalar field.

The problem of online parameter identification for spatially distributed systems using a mobile sensor network is investigated in this brief. Inspired by the passive identifier developed for boundary control of partial differential equations (PDEs) using a static sensor network, we propose a distributed online passive identifier that is able to estimate the unknown diffusion coefficient of the advection-diffusion PDE using data collected by a mobile sensor network moving in the field. To enable the online passive identifier, we develop a distributed cooperative Kalman filter run by each sensing agent that provides state estimates of the field. Optimal trajectory for the mobile sensor network in the advection-diffusion field is found, and distributed control laws to control the mobile sensor network to estimate and follow the trajectory while keeping a desired formation are designed. We prove that the parameter estimation errors are bounded and achieve parameter consensus. In addition, by generating a persistence of excitation condition, we further verify the asymptotic parameter convergence. Numerical simulations for 2-D and 3-D cases demonstrate the effectiveness of the proposed online passive identifier.

This article presents an online parameter identification scheme for advection–diffusion processes using data collected by a mobile sensor network. The advection–diffusion equation is incorporated into the information dynamics associated with the trajectories of the mobile sensors. A constrained cooperative Kalman filter is developed to provide estimates of the field values and gradients along the trajectories of the mobile sensors so that the temporal variations in the field values can be estimated. This leads to a co-design scheme for state estimation and parameter identification for advection–diffusion processes that is different from comparable schemes using sensors installed at fixed spatial locations. Using state estimates from the constrained cooperative Kalman filter, a recursive least-square (RLS) algorithm is designed to estimate unknown model parameters of the advection–diffusion processes. Theoretical justifications are provided for the convergence of the proposed cooperative Kalman filter by deriving a set of sufficient conditions regarding the formation shape and the motion of the mobile sensor network. Simulation and experimental results show satisfactory performance and demonstrate the robustness of the algorithm under realistic uncertainties and disturbances.

SUMMARY: In this article, we investigate the problem of parameter identification of spatial–temporal varying processes described by a general nonlinear partial differential equation and validate the feasibility and robustness of the proposed algorithm using a group of coordinated mobile robots equipped with sensors in a realistic diffusion field. Based on the online parameter identification method developed in our previous work using multiple mobile robots, in this article, we first develop a parameterized model that represents the nonlinear spatially distributed field, then develop a parameter identification scheme consisting of a cooperative Kalman filter and recursive least square method. In the experiments, we focus on the diffusion field and consider the realistic scenarios that the diffusion field contains obstacles and hazard zones that the robots should avoid. The identified parameters together with the located source could potentially assist in the reconstruction and monitoring of the field. To validate the proposed methods, we generate a controllable carbon dioxide (CO₂) field in our laboratory and build a static CO₂ sensor network to measure and calibrate the field. With the reconstructed realistic diffusion field measured by the sensor network, a multi-robot system is developed to perform the parameter identification in the field. The results of simulations and experiments show satisfactory performance and robustness of the proposed algorithms.

Field coverage is a representative exploration task that has many applications ranging from household chores to navigating harsh and dangerous environments. Autonomous mobile robots are widely considered and used in such tasks due to many advantages. In particular, a collaborative multirobot group can increase the efficiency of field coverage. In this paper, we investigate the field coverage problem using a group of collaborative robots. In practical scenarios, the model of a field is usually unavailable and the robots only have access to local information obtained from their on-board sensors. Therefore, a Q-learning algorithm is developed with the joint state space being the discretized local observation areas of the robots to reduce the computational cost. We conduct simulations to verify the algorithm and compare the performance in different settings.

In the realm of real-time environmental monitoring and hazard detection, multi-robot systems present a promising solution for exploring and mapping dynamic fields, particularly in scenarios where human intervention poses safety risks. This research introduces a strategy for path planning and control of a group of mobile sensing robots to efficiently explore and reconstruct a dynamic field consisting of multiple non-overlapping diffusion sources. Our approach integrates a reinforcement learning-based path planning algorithm to guide the multi-robot formation in identifying diffusion sources, with a clustering-based method for destination selection once a new source is detected, to enhance coverage and accelerate exploration in unknown environments. Simulation results and real-world laboratory experiments demonstrate the effectiveness of our approach in exploring and reconstructing dynamic fields. This study advances the field of multi-robot systems in environmental monitoring and has practical implications for rescue missions and field explorations.