Analysis and control of the chaotic turbulence of nonholonomic constraints on humanoid robots

This paper presents the chaotic issue of flexible arms on the wheeled humanoid robot. A chaotic attractor may be induced from the unpredictable turbulence and unstable periodic orbits (UPO) embedded in the internal dynamics. Based on differential geometry, the proposed nonholonomic system can be decomposed into subsystems using the normal-form methodology. However, the high-order nonlinearities of the internal dynamics resulted from the unconstrained subsystem can induce unpredictable chaos in high-frequency circumstances. This paper is dedicated to the modeling, analysis and control of such a nonholonomic system with chaotic problem. A chaotic/sliding-mode composite controller using the piecewise algorithm instead of the tedious point-wise algorithm for the coordinate transformation is proposed. Finite element method is also applied to model the flexible beam under the assumption of small perturbation. It is shown that the proposed algorithm can achieve predetermined performance and attenuate the steady-state error to avoid the chaotic phenomenon. A self-fabricated humanoid robot and the computer simulation are successfully accomplished to justify the realistic implementation of the proposed algorithm.