Autonomous Mobile Robots and Multi-Robot Systems

4Motion in Potential Field and Navigation Function

Nir Shvalb and Shlomi Hacohen

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 scheme. Similar to general gradient descent techniques, the main idea of potential field and navigation function (NF) methods is to construct a “surface” over which the robot “slides” from initial configuration to the goal configuration. In addition, the chapter presents the novel method of path planning in uncertain environment with probabilistic potential.

4.1 Problem Statement

In general, the problem of motion planning for a mobile robot requires determination of an optimal path in two‐ or three‐dimensional domain without colliding with static or dynamic obstacles, where optimality refers to minimal length of the path, minimal energy consumption, or similar parameters that are interpreted as a cost of the motion. Obstacles in this framework depend on the considered mission of the robot and may be walls, furniture, other players, or agents that move in the robot's environment, or even the regions where the robot cannot communicate with the base station or cannot maneuver.

The methods and techniques for solving the problem of motion planning are usually determined as the motion‐planning scheme, which formally is aimed to provide a path of the robot and minimizes a definite ...