Humanoid Robot Kinematics Modeling Using Lie Groups.

This paper presents new analytical methods, using techniques from the theory of Lie Groups and tools from Computational Geometry, to de-velop algorithms for kinematics modeling and path-planning of humanoid robots. We introduce deterministic solutions, geometrically meaningful and numerically stable, based on the PoE (Product of Exponentials for-mula), which allows us to develop algorithms to solve the humanoid me-chanical problem, even for real-time applications. Besides, to solve the path-planning problem, we introduce a close-form solution based on the FMM (Fast Marching Methods) used to study interface motion. The first development of this paper is a new approach for the analysis of the hu-manoid model; this is the humanoid SKD (Sagital Kinematics Division). The second development is the construction of the new FM3 (Fast Marching Method Modified) algorithm for the humanoid collision-free WBT (Whole Body Trajectory) calculation. In addition, the third main goal of this work is to build a general and analytical solution for the hu-manoid kinematics problem (direct and inverse); this is the new human-oid OSG (One Step to Goal) algorithm. The works are presented along with computed examples using both simulated and experimental results with the humanoid robot RH0 at the University Carlos III of Madrid