Design, analysis, and control of a cable-driven parallel platform with a pneumatic muscle active support

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.The neck is an important part of the body that connects the head to the torso, supporting the weight and generating the movement of the head. In this paper, a cable-driven parallel platform with a pneumatic muscle active support (CPPPMS) is presented for imitating human necks, where cable actuators imitate neck muscles and a pneumatic muscle actuator imitates spinal muscles, respectively. Analyzing the stiffness of the mechanism is carried out based on screw theory, and this mechanism is optimized according to the stiffness characteristics. While taking the dynamics of the pneumatic muscle active support into consideration as well as the cable dynamics and the dynamics of the Up-platform, a dynamic modeling approach to the CPPPMS is established. In order to overcome the flexibility and uncertainties amid the dynamic model, a sliding mode controller is investigated for trajectory tracking, and the stability of the control system is verified by a Lyapunov function. Moreover, a PD controller is proposed for a comparative study. The results of the simulation indicate that the sliding mode controller is more effective than the PD controller for the CPPPMS, and the CPPPMS provides feasible performances for operations under the sliding mode control

Positive curvature property for some hypoelliptic heat kernels

In this note, we look at some hypoelliptic operators arising from nilpotent rank 2 Lie algebras. In particular, we concentrate on the diffusion generated by three Brownian motions and their three Lévy areas, which is the simplest extension of the Laplacian on the Heisenberg group $\mathbb{H}$. In order to study contraction properties of the heat kernel, we show that, as in the case of the Heisenberg group, the restriction of the sub-Laplace operator acting on radial functions (which are defined in some precise way in the core of the paper) satisfies a non negative Ricci curvature condition (more precisely a $CD(0, \infty)$ inequality), whereas the operator itself does not satisfy any $CD(r,\infty)$ inequality. From this we may deduce some useful, sharp gradient bounds for the associated heat kernel