We design a control law for two agents to successfully track a level curve in the plane without explicitly estimating the field gradient. The velocity of each agent is decomposed along two mutually perpendicular directions, and separate control laws are designed along each direction. We prove that the formation center will converge to the neighborhood of the level curve with the desired level value. The algorithm is tested on some test functions used in optimization problems in the presence of noise. Our results indicate that in spite of the control law being simple and gradient-free, we are able to successfully track noisy planar level curves fast and with a high degree of accuracy.

We develop a plume tracking algorithm for a swarm of mobile sensing agents in turbulent flow. Inspired by blue crabs, we propose a stochastic model for plume spikes based on the Poisson counting process, which captures the turbulent characteristic of plumes. We then propose an approach to estimate the parameters of the spike model, and transform the turbulent plume field detected by sensing agents into a smoother scalar field that shares the same source with the plume field. This transformation allows us to design path planning algorithms for mobile sensing agents in the smoother field instead of in the turbulent plume field. Inspired by the source seeking behaviors of fish schools, we design a velocity controller for each mobile agent by decomposing the velocities into two perpendicular parts: the forward velocity incorporates feedback from the estimated spike parameters, and the side velocity keeps the swarm together. The combined velocity is then used to plan the path for each agent in the swarm. Theoretical justifications are provided for convergence of the agent group to the plume source. The algorithms are also demonstrated through simulations.

Biological inspirations have lead us to develop a switching strategy for a group of robotic sensing agents searching for a local minimum of an unknown noisy scalar field. Starting with individual exploration, the agents switch to cooperative exploration only when they are not able to converge to a local minimum at a satisfying rate. We derive a cooperativeH∞filter that provides estimates of field values and field gradients during cooperative exploration and give sufficient conditions for the convergence and feasibility of the filter. The switched behavior from individual exploration to cooperative exploration results in faster convergence, which is rigorously justified by the Razumikhin theorem, to a local minimum. We propose that the switching condition from cooperative exploration to individual exploration is triggered by a significantly improved signal-to-noise ratio (SNR) during cooperative exploration. In addition to theoretical and simulation studies, we develop a multiagent testbed and implement the switching strategy in a lab environment. We have observed consistency of theoretical predictions and experimental results, which are robust to unknown noises and communication delays.

We design a switching strategy for a group of robots to search for a local minimum of an unknown noisy scalar field. Starting with individual exploration, the robots switch to cooperative exploration only when they are not able to locate the field minimum based on the information collected individually. In order to test and demonstrate the switching strategy in real-world environment, we implement the switching strategy on a multi-robot test-bed. The behaviors of a group of robots are compared when different parameters for exploration are adopted. Especially, we observe the effect of memory lengths on the switching behaviors as predicted by theoretical results. The experimental results also justify the effects of different formation sizes and noise attenuation levels on the performance of the cooperative H∞filter that are utilized in the cooperative exploration phase.