The shape Jacobian of a manipulator with hyper degrees of freedom

Abstract

The Shape Jacobian which is the counterpart of the manipulator Jacobian plays a key role to control the shape of a manipulator with extraordinarily many degrees of freedom. In this paper, we show some significant properties of the Shape Jacobian; the structure, boundedness, determinant and singularity, in geometric pavor.

Sliding mode control of manipulators using first-order equations of motion with diagonal mass matrix

“…It is because each 'decoupled link' (i.e. a link which also contains couplings among the kth link and others) has kinetic energy expressed as 1 2 N k u 2 k À Á :…”

“…Trajectory tracking for robot manipulators, in the non-adaptive case, is usually realized using an inverse dynamics control scheme or sliding mode controller [1][2][3][4][5][6][7][8].…”

Output Track Controller with Gravitational Compensation for a Class of Hyper-Redundant Robot Arms

“…In [1][2][3][4], were analyzed the kinematic models by the "backbone curve". The papers [5][6][7] derived a new kinematic model by using the differential geometry, [8,12] studied the manipulability of continuum robots. Cable-driven continuum robot control with variable stiffness was studied in [13].…”

Non-Adaptive Sliding Mode Controllers in Terms of Inertial Quasi-Velocities

“…; Moreno-Valenzuela & Kelly (2006). One of known applications of the sliding mode approach allows one to control a shape Mochiyama et al (1999). In order to design various versions of control laws strict Lyapunov functions for a class of global regulators for robot manipulators are introduced Santibanez & Kelly (1997); Spong (1992) or in terms of the IQV also in Herman (2009b).…”