Modified Newton´s method applied to potential field navigation

In this paper, we propose the use of a modification of Newton´s method for potential field navigation. The use of the modified Newton´s method, which applies anywhere C₂ continuous navigation functions are defined, greatly improves system performance in the presence of obstacles, when compared to the standard gradient descent approaches. To illustrate the technique, we also propose a hierarchical software architecture for robots that supports multi-robot coordination and can be easily extended for other applications. Simulations show that a robot team can accomplish a cooperative material-handling task in an initially unknown environment while avoiding collision with static obstacles and other team members. We derive a control law based on the modified Newton method that guarantees team stability for all time.