A Differential-Geometric Approach for Bernstein's Degrees-of-Freedom Problem

摘要: This article challenges Bernstein’s problem of redundant degrees freedom (DOF) that remains unsolved from the control-theoretic point view as well standpoint both neuro-physiology and robotics. Firstly, a rather simpler but mysterious control movements human-like multi-joint reaching with excess DOFs is analyzed Newtonian mechanics differential geometry. Secondly, another illustrative seems to be sophisticated complicated tackled, which find sensory coordinated signal for 3-Dimensional stable grasping object manipulation by pair robot fingers multiple joints under effect gravity nonholonomic constraints. In each problem, it possible simple renders corresponding closed-loop dynamics on its equilibrium-point manifold. It claimed, however, convergences solutions an manifold can not using Lyapunov’s direct method, because Lyapunov-like energy form positive definite due redundancy DOFs. Instead, novel definition called “stability manifold” based upon concept Riemannian distance constraint introduced in problems used analysis convergence solution trajectories. also shown finiteness metrics plays important role evaluation performance problems.