The Admissible Set for a Robotic System with Unilateral Constraint
This paper focuses on investigating systematically the phenomenon of the bouncing motion when a robotic manipulator slides on a rough surface. From the viewpoint of rigid body dynamics, this phenomenon is related to the dynamical properties of a multi-rigid-body system subject to unilateral constraints with friction. Applying the LCP (Linear Complementary Problem) theory, we can classify the bouncing motion into two cases: one that is due to the action of inertia of system; the other that is due to the singularities of rigid-body model induced by friction forces. As an example of a planar multibody system with single unilateral constraint, the admissible set for a two-link manipulator is studied in detail. Meanwhile, The numerical results show that the paradoxes in rigid body model can occur even if the value of coefficient of friction is very small.
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