Online Trajectory Tracking Control Based on the Explicit Form of the Equations of Motion for Serial Manipulator Using the New Formulation

Table 1

Notations for the new formulation.

Symbols	Designations
	The i-th body or link
	The i-th subsystem
	The N-dimensional generalized coordinates.
,	The N-dimensional velocities and accelerations vectors of the joints.
,	The i-th joint type, is zero if the i-th joint type is a revolute, is one if the i-th joint type is a prismatic.
	The i-th joint center.
	The centeroid of the link
	The position vector of relative to joint center
	The i-th joint axis.
	The downward unit vector specifying the gravity direction.
	The i-th base that is attached to body
	The frame attached to body
	The mass of body .
	The 3 × 3 inertia tensor associated with body defined in
	The 3 × 3 pseudoinertia tensor associated with body defined in
I	The 3 × 3 identity matrix
	The N-vector of the joint generalized forces.
	The rotation matrix of base with respect to base