A differential-geometric approach for 2D and 3D object grasping and manipulation

摘要: Abstract This article presents an expository work on a differential-geometric treatment of fundamental problems 2D and 3D object grasping manipulation by pair robot fingers with multi-joints under holonomic or nonholonomic constraints. First, Lagrange’s equation motion fingers-object system whose is confined to vertical plane derived constraints when rolling contacts between finger-ends surfaces are permitted. Then, class control signals called “blind grasping” constructed without knowing the kinematics using any external sensing like vision tactile sensation shown realize stable in dynamic sense. Stability its convergence equibrium manifold treated basis differential geometry solution trajectories closed-loop dynamics constraint manifolds. Second, mathematical model multi-joint assumption that spinning rotation around opposing axis contact points does no more arise. It that, differently from case, instantaneous time-varying, which induces expressed as linear rotational pinched object. there sensings can Finally, it proposed geometric stability naturally cope redundancy resolution surplus degrees-of-freedom (d.f.) overall system, closely related Bernstein’s d.f. problem.