The problem of adaptive hybrid controller design for constrained roots with the consideration of computational efficiency is addressed. Two efficient control schemes based, respectively, on Lagrange and Newton-Euler dynamics formulation are presented. Detailed analyses on tracking properties of joint positions, velocities, and constrained forces are derived for both the Lagrange approach and the Newton-Euler approach. Although control laws in these two approaches are developed independently, a tight connection between them is found, indicating a possible bridge between general adaptive approaches based, respectively, on the two dynamics formulations.
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