This note addresses the problem of adaptive hybrid controller design f
or constrained robots with the consideration of computational efficien
cy. Two efficient control schemes respectively based on Lagrange and N
ewton-Euler dynamics formulation are presented. Detailed analyses on t
racking properties of joint positions, velocities, and constrained for
ces are derived for both the Lagrange approach and the Newton-Euler ap
proach. Although control laws in these two approaches are developed in
dependently, a tight connection between them is signified, which highl
ights a possible bridge over different general adaptive approaches res
pectively based on the two dynamics formulations.