UFMG researchers' algorithm speeds up robot navigation distance calculations

Vector-field-based methods are widely used for robotic path-tracking, but they often require repeatedly computing the distance between the robot's configuration and a reference curve. When extended to Lie groups (such as SE(3) for 3D motion), this computation becomes expensive for embedded systems with high control frequencies. A new paper by Vinicius M. Gonçalves, João Baião, Felipe Bartelt, and colleagues from UFMG and other institutions tackles this challenge by introducing an efficient algorithm that exploits the structure of G-polynomial curves—a generalization of polynomials to matrix Lie groups.

The method reformulates the distance problem as a small set of polynomial root-finding operations, drastically reducing computational load while preserving accuracy. Simulation results show significant time savings compared to existing optimization-based approaches. The researchers also provide practical formulas for the special Euclidean group SE(3) and validate the algorithm experimentally on a real robotic manipulator. An open-source computational package is available online, making the technique immediately applicable for robotics practitioners working on real-time navigation and control.