Homotopy Path Planning for Terrestrial Robots Using Spherical Algorithm

Abstract

Autonomous and semiautonomous mobile robots play an important role in making tasks in environments considered hostile or dangerous for a human being. In order to execute many of the required tasks, robots need, in its architecture, a module of navigation with an appropriate path planning algorithm. This paper presents the development and implementation of a methodology for path planning of a mobile robot using a spherical algorithm and homotopy continuation methods (HCMs). The first section is a brief introduction about HCMs. Subsequently, the homotopy path planning method and spherical path tracking algorithm are explained, as well as the upgraded version and its main features. Then, the main contributions of this paper are presented and the effectiveness of the proposed method is proved. Besides, numerical examples, implementation results in multiple platforms including a 32-b microcontroller and robot operating system, are displayed. Finally, some favorable results from a comparative between the proposed methodology against sampling-based planners using the open motion planning library are presented. Note to Practitioners —This paper presents a numerical routine for homotopy path planning that can be implemented easily using different programming languages or programs like C, C++, and Maple CAS software, among many others. The aim of this paper is to introduce a numerical algorithm suitable to be implemented in different platforms even with low hardware resources. The main advantage of this method is that it is not probabilistic and it is easy to implement by any engineer with basic knowledge of numerical methods. The numerical simulations show that it is possible to resolve in milliseconds environment maps composed by several hundreds of obstacles.