A neuro-sliding-mode control (NSMC) strategy was developed to handle the complex nonlinear dynamics and model uncertainties of flexible-link manipulators. A composite controller was designed based on a singularly perturbed model of flexible-link manipulators when the rigid motion and flexible motion are decoupled. The NSMC is employed to control the slow subsystem to track a desired trajectory with a traditional sliding mode controller to stabilize the fast subsystem which represents the link vibrations. A stability analysis of the flexible modes is also given. Simulations confirm that the NSMC performs better than the traditional sliding-mode control for controlling flexible-link manipulators. The control strategy not only gives good tracking performance for the joint angle, but also effectively suppresses endpoint vibrations. The simulations also show that the control strategy has a strong self-adaptive ability for controlling manipulators with different parameters.

Mutual information (MI) is a basic concept in information theory. Therefore, estimates of the MI are fundamentally important in most information theory applications. This paper provides a new way of understanding and estimating the MI using the copula function. First, the entropy of the copula, named the copula entropy, is defined as a measure of the dependence uncertainty represented by the copula function and then the MI is shown to be equivalent to the negative copula entropy. With this equivalence, the MI can be estimated by first estimating the empirical copula and then estimating the entropy of the empirical copula. Thus, the MI estimate is an estimation of the entropy, which reduces the complexity and computational requirements. Tests show that the method is more effective than the traditional method.

Humanoid walking planning is a complicated task because of the high number of degrees of freedom (DOFs) and the variable mechanical structure during walking. In this paper, a planning method for 3-dimensional (3-D) walking movements was developed based on a model of a typical humanoid robot with 12 DOFs on the lower body. The planning process includes trajectory generation for the hip, ankle, and knee joints in the Cartesian space. The balance of the robot was ensured by adjusting the hip motion. The angles for each DOF were obtained from 3-D kinematics calculation. The calculation gave reference trajectories of all the DOFs on the humanoid robot which were used to control the real robot. The simulation results show that the method is effective.