A Hierarchical Structure Control Strategy Based on MPC for a Six-DOF Flexible Joint Manipulator

Table 1

Notations.

Notation	Meaning
	Link angle vector,
	Link velocity vector,
	Link acceleration vector,
	-th link angle
	Joint angle vector,
	Joint acceleration vector,
	-th joint angle
	Joint driving torque vector,
	Torque acting on the -th link
	Inertia matrix for the rigid links,
	Torque vector caused by Coriolis force and
	centrifugal forces,
	Torque vector caused by gravity,
	Diagonal matrix of actuator inertias reflected
	to the link side of gears,
	Diagonal matrix containing the joint stiffness
	coefficients,
	-th joint stiffness coefficients