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This article applies high-order differential estimation to the motion planning of humanoid robots for the first time. A multiobjective optimization model and the corresponding optimal policy are designed from the perspective of solving time-varying linear equations. This method can avoid the calculation of the Jacobian matrix pseudo-inverse and its derivative, reduce energy consumption, and achieve smooth human-like robot motions. High-order differential estimation is realized by cascading multiple integration-enhanced differentiators, which estimate the first derivative based on hybrid error and quasi-sliding mode techniques. The merits of the differentiator include high accuracy in estimating high-order derivatives and the elimination of chattering. Theoretical analyses verify that the proposed differentiator and the differentiator-based solver have asymptotic convergence. Simulations prove that the integration-enhanced differentiator and the differentiator-based method have excellent performance. Experiments illustrate that the designed solver for the motion planning of a humanoid upper-body robot can track desired trajectories and perform carrying tasks.
Yin et al. (Wed,) studied this question.