Modified Newton's method applied to potential field-based navigation for nonholonomic robots in dynamic environments

This paper is to investigate inherent oscillations problems of potential field methods (PFMs) for nonholonomic robots in dynamic environments. In prior work, we proposed a modification of Newton's method to eliminate oscillations for omnidirectional robots in static environment. In this paper, we develop control laws for nonholonomic robots in dynamic environment using modifications of Newton's method. We have validated this technique in a multi-robot search-and-forage task. We found that the use of the modifications of Newton's method, which applies anywhere C2 continuous navigation functions are defined, can greatly reduce oscillations and speed up the robot's movement, when compared to the standard gradient approaches.