This paper addresses fixed-time trajectory tracking for a dual-arm free-floating space robot (FFSR) with the large initial errors and bounded uncertainty. A wrist-based trajectory planning method is improved by fixed-time stability to fast eliminate the error caused by singularity. Then, a novel low-chattering and global-nonsingular fixed-time terminal sliding mode control strategy is studied by state approaching angle and switching sliding mode; the practical fixed-reachable Lyapunov stability analysis is presented for a mechanical control system. In the end, the proposed trajectory planning method and controller are combined to improve the tracking accuracy of end-effector to the nanoscale. Simulation results validate the effectiveness of the proposed methodologies.

In this paper, some new coincidence point theorems in continuous function spaces are presented. We show the hybrid mapping version and multivalued version of both Lou’s fixed point theorem (Proc. Amer. Math. Soc.127 (1999)) and de Pascale and de Pascale’s fixed point theorem (Proc. Amer. Math. Soc.130 (2002)). Our new results encompass a number of previously known generalizations of the theorems. Two examples are presented.

Single crystals of KBeBO3F (KBBF) up to 2 mm in thickness were grown by using a spontaneous nucleation method. The flux was composed of KF and B2O3, and the optimal ratio for growing KBBF single crystal thicker than 1 mm is suggested to be (1.0–1.5):(5.0):(0.7–1.2) (KBBF:KF:B2O3) in molar ratio. The ideal morphology of.KBBF is two sets of tabular facets and a set of rhombic facets. Surface morphology.was characterized both by optical microscopy and atomic force microscopy. Transmission spectra showed that high transmission was maintained up to 170 nm. Based on refractive index measurements, phase matching curves for types I and II were determined. Using a prism coupling method, the effective fourth harmonic generation for an Nd:YAB laser was realized in an 0.6-mm-thick KBBF sample. The output energy of the 266-nm beam was 0.282 mJ, and the conversion efficiency was 11.8%. A 183.6-nm laser over 1 mW was obtained from a Ti:sapphire second harmonic generation beam in an 0.8-mm KBBF sample. The conversion efficiency reached 2.3%. A 179.4-nm laser was also observed from a 358.7-nm laser by directly frequency doubling. This is the shortest wavelength obtained through nonlinear optical processes in a solid-state laser.

ZnO has high piezoelectric coupling coefficient and acoustic velocity; therefore, it is an attractive material candidate for high frequency and low loss filters. Piezoelectric ZnO thin film based RF devices offer the advantages such as low power consumption, circuit miniaturization and cost reduction through integration with main stream MMIC technology. We report CVD growth of epitaxial ZnO thin films on R-sapphire substrates. X-ray diffraction techniques have been used to study the crystallinity and orientation of the films, as well as the epitaxial relationship between the films and the substrate. High-resolution cross-sectional TEM reveals the atomically sharp interface structure. As grown ZnO films exhibit dominant n-type conductivity due to the oxygen vacancies. Excellent piezoelectricity has been achieved through a multi-step Li diffusion under oxygen ambient. Surface Acoustic Wave (SAW) filters with 10-micron wavelength have been fabricated. Low insertion loss and high piezoelectric coupling coefficient have been observed.