STRATIFIED INVARIANTS FOR KINEMATIC SINGULARITIES
Abstract
Motion planning and optimal control form substantial endeavors across theoretical and practical aspects of research and development in inverse kinematics. Both are hindered by singularities, i.e., those regions of configuration space where the mechanism at hand loses at least one degree of freedom. Equivalently, singularities are those regions where the derivative of the kinematic map fails to attain full rank. The prevailing wisdom in kinematics research is that such singularities should be quickly identified and steadfastly avoided. Here we suggest a fundamentally different approach: a deeper geometric and topological understanding of singularities will be enormously beneficial to inverse kinematics. The ability to efficiently probe the fibers of a kinematic map at (or even near) a singularity allows us to properly catalog safe directions as well as prohibited ones in the configuration space. The knowledge of such directions will, in turn, facilitate far more efficient solutions to standard motion planning problems by removing superfluous constraints: we could safely pass through singularities rather than forcing ourselves to bypass them. For a wide and practically relevant class of kinematic maps, we aim to algorithmically decompose the configuration and state spaces into sub-manifolds so that the kinematic map in question (a) sends sub-manifold to sub-manifold, and (b) has a constant rank derivative when restricted to each sub-manifold. This stratification serves as an essential starting point for a thorough analysis of various kinematic singularities, their computable invariants, and hence, of their mechanical passability.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Apr 20, 2023
- Source ID
- FA95502210462
Entities
People
- Martin Helmer
Organizations
- Air Force Office of Scientific Research
- North Carolina State University
- United States Air Force