Modeling robot geometries like molecules, application to fast multi-contact posture planning for humanoids

Traditional joint-space models used to describe equations of motion for humanoid robots offer nice properties linked directly to the way these robots are built. However, from a computational point of view and convergence properties, these models are not the fastest when used in planning optimizations. In this paper, inspired by Cartesian coordinates used to model molecular structures, we propose a new modeling technique for humanoid robots. We represent robot segments by vectors and derive equations of motion for the full body. Using this methodology in a complex task of multi-contact posture planning with minimal joint torques, we set up optimization problems and analyze the performance. We demonstrate that compared to joint-space models that get trapped in local minima, the proposed vector-based model offers much faster computational speed and a suboptimal but unique final solution. The underlying principle lies in reducing the nonlinearity and exploiting the sparsity in the problem structure. Apart from the specific case study of posture optimization, these principles can make the proposed technique a promising candidate for many other optimization-based complex tasks in robotics.