Robust Decentralized Formation Tracking Control for Stochastic Large-Scale Biped Robot Team System Under External Disturbance and Communication Requirements

Abstract

In this study, a robust decentralized stochastic H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> tracking control design is proposed to deal with the team formation tracking problem for a large-scale biped robot team system with external disturbance and communication requirement on biped robots and leader. Under the concept of virtual leader and the decentralized control approach, biped robots walking in a large-scale team formation are controlled to track their own reference paths with the robust stochastic H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> tracking performance. Consequently, the original robust decentralized stochastic H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> large-scale biped robot team formation tracking control design problem can be transformed to a set of independent Hamilton-Jacobi inequality (HJI)-constrained optimization problems for each biped robot. To cope with the difficulties in solving the HJIs for the robust decentralized stochastic H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> team formation tracking control design, a numerical framework is introduced to approximate the walking biped robot systems. Based on the tensor-product model transformation technique, the set of independent HJI-constrained optimization problems for the robust decentralized stochastic H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> team formation tracking control design is converted into a set of independent linear-matrix-inequality-constrained optimization problems, which can be solved efficiently by the convex optimization methods. Since the robust decentralized stochastic H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> team formation tracking control can be designed individually, the magnitude of a biped robot team can be easily increased to a very large scale. Finally, a simulation example of decentralized H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> formation tracking control design for a 30-scale biped robot team is given to validate the effectiveness of the proposed scheme.