Journal of Intelligent & Robotic Systems

, Volume 93, Issue 3–4, pp 687–697 | Cite as

Rapid Navigation Function Control for Two-Wheeled Mobile Robots

  • Wojciech KowalczykEmail author
Open Access


This paper presents a kinematic controller for a differentially driven mobile robot. The controller is based on the navigation function (NF) concept that guarantees goal achievement from almost all initial states. Slow convergence in some cases is a significant disadvantage of this approach, especially when narrow passages exist in the environment and/or specific values of design parameters are set. The main reason of this phenomenon is that the velocity control strongly depends on the slope of the NF. The algorithm proposed in this paper is based on a method introduced in Urakubo (Nonlin. Dyn. 81(3): 1475–1487 2015), that extends NF to nonholonomic mobile platforms and allows stabilizing not only the position of robots but also their orientation. This algorithm is used as a reference in experimental performance comparison. In the new algorithm, the gradient of the NF is used to generate motion direction but the velocity is computed as a function of position and orientation errors. This approach results in much better state converge. Analysis of the convergence shows how the location of the eigenvalues of linearized system affects time of goal achievement. The paper describes saddle point detection and avoidance methodology and presents their experimental verification. It also shows what happens in practice if initial position is located exactly in the saddle point and its detection/avoidance procedures are turned off.


Mobile robot control Navigation function Set point control Obstacle avoidance Saddle point detection 



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© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Institute of Automation and Robotics, Faculty of ComputingPoznan University of TechnologyPoznanPoland

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