Modified virtual decomposition control for robotic mechanisms with mixed kinematic chains: a fully decentralized control algorithm

Whole-Body Anti-Input Saturation Control of a Bipedal Robot

“…( 12), and the associated update adaptive laws in Eq. ( 13) are all stable in light of Barbalat's lemma [27].…”

“…The key idea is that every uncertain term can be represented using orthogonal basis functions such as Chebyshev polynomials, Fourier series, neural network approximators, etc. ; see the studies [27][28][29][30] for more details. The adaptive law for the weighting coefficients is designed using Lyapunov theory to ensure stability based on the passivity condition.…”