An approach to nonlinear feedback control with applications to robotics

A control problem involving a mechanical system with generalized coordinates
q
∈
R
^m
is considered. The error in tracking a desired input
y
^d
∈
R
^p
is
e
=
E
(q,y
^d
)∈
R
^m
. If
E
satisfies simple conditions, it leads to a nonlinear control law that assures
e
(t)→0 as
t
→∞. The law is robust in that small changes in it do not produce large steady-state errors or loss of stability. In this theory a unified framework is presented for treating a number of problems in the control of mechanical manipulators.