Motion in potential field and navigation function

This chapter introduces motion-planning methods that do not assume knowledge of global coordinates, but, instead, are based on the artificial potential field specified over the domain and implement the navigation function (NF) scheme. Following the approach of navigation using potential field, the NF is defined as a particular continuous smooth potential function that takes zero value at the target point and unity value on the boundaries of the environment and the obstacles. Moreover, in order to ensure a solution, it is required that all critical points of the navigation function are nondegenerated in such a sense that there are no such “plateau” areas where the gradient of the navigation function vanishes. The chapter presents NF variants using three different scenarios: navigation in static deterministic environment, navigation in static uncertain environment, and finally, navigation in dynamic environment.