Theoretical and Algorithmic Aspects of Generating Pre-Control form of the gCBHD Formula

摘要

The generalized Campbell-Baker-Hausdorff-Dynkin formula is a powerful tool in nonholonomic motion planning. It allows to construct a map from controls to displacements in a configuration space, primarily hidden behind differential equations. The formula is complex in its basic form and also when driftless nonholonomic systems substitute a general (even nonautonomous) form. Therefore it needs to be simplified to be useful. In this paper its pre-control form will be the main subject. The pre-control form means that the mapping is from general controls (not in a parametric form) to local configuration shifts. In this paper it will be proven that coefficients of the pre-control form satisfy a nice property. An algorithm will also be presented to compute coefficients of pre-control form much faster than algorithms designed for this task and known in the robotic literature. Appropriate simulation comparisons will be provided.