Adaptive approximation control of biped robots: a low-level tracking control layer

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Abstract

The adaptive approximation control is a powerful tool for controlling robotic systems with unmodeled dynamics. The local (partitioned) approximation-based adaptive control includes representation of the uncertain matrices and vectors in the robot model as finite combinations of basis functions. Update laws for the weighting matrices are obtained by the Lyapunov-like design. However, one of the inherent limitations of this category of approximation is curse dimensionality associated with the approximation of uncertain matrix. There are three possible representations for the approximation of the uncertain matrix: Kronecker product, sparse matrices, and GL operator. Both Kronecker product and sparse matrices can grow exponentially with the dimension of the target matrix, whereas GL operator can grow linearly but without the use of conventional operations of matrices. In light of the above, this report proposes a simple representation for the approximation of the uncertain matrix. The proposed representation is directly linear concerning the dimension of the target matrix using the conventional operations of matrices. Two case studies are simulated which are: two-link manipulator and 6-link biped robots during the complete gait cycles (single support phase SSP and double support phase DSP). Biped robot has different configurations during the walking cycle; it is considered as an open-chain mechanism with a fixed-base stance foot during the SSP and as a closed constrained mechanism during the DSP.The results show that for low dimension robotic manipulators, all representations can be conducted equivalently. There is no large difference in simulation time, whereas for higher degrees of freedom robots the GL operator and the proposed representation are superior in simulation time.

Authors 2

1. Hayder F. N. Al-Shuka

   University of Baghdad

   Affiliation as printed

   Department of Aeronautical Engineering, University of Baghdad

2. Burkhard J. Corves Aachen

   RWTH Aachen University

   Affiliation as printed

   Rheinisch-Westfälische Technische Hochschule Aachen University