Collision-Free Path Planning Applied to Multi-Degree-of-Freedom Robotic Arms Using Homotopy Methods

Robotic arms are extensively employed across various disciplines, within both structured and unstructured workspaces, as well as across numerous applications. These components serve to address a multitude of challenges, thus enabling their integration into collaborative tasks with humans. In order to address these emerging challenges, there is a growing demand for more efficient path-planning algorithms. Hence, this study introduces a technique based on homotopy continuation methods, offering a distinctive and innovative approach to tackling these issues. The methodology proposed in this study enables the modeling of robotic arms with multiple degrees of freedom. It is proficient in operating within narrow corridors and achieves a collision-free path, provided the workspace allows for it. Due to its deterministic nature, the solution path is consistently reproducible. Furthermore, the computation times and RAM memory consumption achieved for hyper-redundant robotic arms fall within the range of seconds and kilobytes (KB). For anthropomorphic or classical robotic arms, computation times are on the order of milliseconds, as evidenced by the case studies presented in this paper. The method was validated using a Thermo Electron robotic arm, specifically the CRS CataLyst-5 model. This validation demonstrated its potential for application in the field of industrial robotics.