A new class of robust control algorithms is proposed for the trajector
y following problem of a robot manipulator It is shown that every prop
osed control can guarantee three kinds of global stability results bas
ed on the designer's choice: uniformly and ultimately bounded stabilit
y, asymptotic stability, and exponential stability. Exact knowledge of
robot dynamics is not required except that unknown dynamics must be b
ounded in Euclidean norm by a second-order polynomial function with kn
own coefficients.