Autonomous navigation and obstacle avoidance using navigation laws with time-varying deviation functions

In this paper we introduce a new family of navigation functions for robot navigation and obstacle avoidance. The method can be used for both path finding and real-time path planning. Each navigation function is composed of three parts: a proportionality term, a deviation function and a deviation constant. Deviation functions are time-varying functions satisfying certain conditions. These functions and parameters are updated in real-time to avoid collision with obstacles. Our strategy uses polar kinematics equations to model the navigation problem in terms of the range and direction between the robot and the goal. The obstacles are mapped to polar planes, and represented by the range and the direction from the robot or the final goal in polar coordinates. This representation gives a certain weight to the obstacles based on their relative position from the robot and facilitates the design of the navigation law. There exists an infinite number of navigation functions obtained by changing the proportionality constant, the deviation constant or the deviation function. This offers an infinite number of possibilities for the robot's path. Our navigation strategy is illustrated using an extensive simulation where different navigation parameters are used.