In this work inspired by flocking of birds or fish communities traveling together in the nature, we have developed a novel dynamically reformable mobile formation algorithm for the navigation of wheeled mobile robot (WMR) groups operating in complex and/or obstacle dense environments. The proposed method is formed via the combination of simple and computationally efficient tools such as (i) a mobile network of a small number of WMR sensors for detecting obstacles; (ii) cardinal cubic splines or least squares fits for modeling the formation boundaries based on this small network; and (iii) reference frames to ensure uniform spacing and velocity profiles along the ensemble. By these components a simple geometrical formation is developed for real time flock path planning of relatively large groups of small agents. To our best knowledge the proposed approach is novel and its effectiveness is verified by simulations in complex environments.

Path planning for formations of wheeled mobile robots (WMRs) has been an active research topic of robotics in the recent years. The methods of route generation for WMRs usually utilize complex algorithms, which require global information of the workspace or mapping of the nearby environment. Hence they are not very efficient for formation based motion of large collections of small entry-level agents. In this work a path generation method is developed for synthesizing non-holonomic paths for small unicycle WMRs, and then is integrated into simple geometrical formations for extension to navigation of relatively large groups of small agents. Our technique is based on a computationally low-cost algorithm; and works effectively for transfer of many robots in obstacle cluttered environments. The efficiency of our technique is verified by simulation results.

Linear fitting of implicit algebraic models to data usually suffers from global stability problems. Complicated object structures can accurately be modeled by closed-bounded surfaces of higher degrees using ridge regression. This paper derives an explicit formula for computing a Euclidean invariant 3D ridge regression matrix and applies it for the global stabilization of a particular linear fitting method. Experiments show that the proposed approach improves global stability of resulting surfaces significantly