Kinematics-Based Navigation Functions

Abstract

In this paper, we introduce a new family of navigation laws which are based on analytic navigation functions derived using the kinematics equations. These navigation laws combine local and global aspects, and can be used for both indoor and outdoor navigation. The robot's kinematics model is represented in polar coordinates. The analytic navigation functions suggested here are functions of the line-of-sight angle between the robot and the goal, and depend on one or more navigation parameters. The navigation parameters allow us to control the navigation law and, thus, the path of the robot. The choice of the navigation function and its parameters is important, and must satisfy some conditions. Different paths are obtained for different navigation functions and different parameters. This property is used to avoid collision with obstacles. Under this formulation, the number of navigation functions allowing the robot to reach a given goal is infinite. An extensive simulation study shows the effectiveness of the method.