Cooperative Exploration

Cooperative Exploration of Level Surfaces in 3D Scalar Field

We develop strategies for a group of mobile sensing agents to cooperatively explore the level surfaces of an unknown 3D scalar field. To measure the field, a cooperative Kalman filter is constructed to combine the sensor readings from all agents and give the estimates of the field value and gradient. To reveal the structure of the field, the formation formed by the agents is controlled to track curves on a level surface in the field. We design steering control laws that are applied to the formation center to control the trajectory of the formation so that any curve with known curvature and torsion can be followed. In particular, we track lines of curvature on a desired level surface and the formation trajectory reflects the 3D geometry of the surface. The Taubin’s algorithm is applied so that a line of curvature can be detected and estimated. We prove the sufficient and necessary conditions that ensure the reliable estimates of the lines of curvature. We also investigate the problem of utilizing the minimum number of agents to accomplish the exploration tasks. Simulation results demonstrate that with the minimum number of agents, the lines of curvature on a desired level surface can be detected and traced successfully.

Robust Cooperative Exploration with a Switching Strategy

It has been observed that certain fish species switch between individual exploration behaviors and cooperative exploration behaviors based on different levels of food concentration in the ambient environment. Inspired by the biological observations, this paper develops a switching strategy for a group of robotic sensing agents to search 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 speed using the information collected individually. We derive a cooperative H infinity filter to provide estimates of the field value and the field gradient 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 to the local minimum, which is rigorously justified by the Razumikhin theorem. 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. The agents switch back to individual exploration when noises in the time-varying field has significantly reduced, which provides possibility for successful individual exploration. In addition to theoretical and simulation studies, we develop a multi-agent testbed and implement the switching strategy in a lab environment. We evaluate the exploration performance of a group of mobile robots sensing a light field under different sets of parameters. We have observed consistency between theoretical predictions and experimental results. In addition, the experiments demonstrate that the switching strategy is robust to perturbations resulting from unknown noises and communication delays. (see summary)


Figure 1.


Figure 2. Experimental setting


Figure 3. Trajectories of the robots in the experiment (from individual exploration to cooperative exploration)