An approach to the dynamic modeling and sliding mode control of the constrained robot is proposed in this article. On the basis of the Udwadia-Kalaba approach, the explicit equation of the constrained robot system is obtained first. This equation is applicable to systems with either holonomic or non-holonomic constraints, as well as with either ideal or non-ideal constraint forces. Second, fully considering the uncertainty of the non-ideal force, that is, the dynamic friction in the constrained robot system, the sliding mode control algorithm is put forward to trajectory tracking of the endeffector on a vertical constrained surface to obtain actual values of the unknown constraint force. Moreover, model order reduction method is innovatively used in the Udwadia-Kalaba approach and sliding mode controller to reduce variables and simplify the complexity of the calculation. Based on the demonstration of this novel method, a detailed robot system example is finally presented.

A reduced-order approach to the adaptive fuzzy sliding mode control of the constrained manipulator is proposed. Based on the Udwadia–Kalaba motion constraint equation, the dynamic equation of the constrained manipulator with both ideal and non-ideal constraints is obtained. Considering the uncertainty of the terminal non-ideal constrained force and the chattering phenomenon of sliding mode control, the adaptive fuzzy and the sliding mode control method are combined to control the constrained manipulator. Because the system is constrained, the model order reduction method is innovatively used in the control algorithm. The stability of the system is proved by Lyapunov theorem. For demonstrating the effectiveness of the control algorithm, the 2-degree-of-freedom manipulator is taken as the research object. Finally, the high-precision control of the manipulator is achieved and the chattering phenomenon caused by the sliding mode control is weakened.

Optical polyimide (PI) membrane is a promising substrate material for diffractive lens applied in future large-aperture space based imaging system because of its light weight, environmental adaptability and deployable feature. In this letter, we put forward a facile large-area uniform photolithography technique using vacuum assisted self contact method to fabricate large-aperture membrane diffractive lens. We fabricated a φ 400 mm aperture membrane off-axis 2-levels Fresnel Zone Lens (FZL) based on the method and achieved uniformly distributed photoresist morphology as well as over 36.6% average diffraction efficiency in full aperture. The results demonstrated that vacuum assisted self contact method effectively eliminates considerable air gaps caused by unevenness of large area photomask and substrate, thus facilitates uniform light field distribution in photoresist. This work provides reference to fabrication techniques of large aperture membrane diffractive lens, and offers feasible methods for future large area flexible electronics manufacturing.

Large aperture high diffraction efficiency off-axis Fresnel lens is one of the most important optical elements in future 10m scale aperture transmissive space telescope systems. Improving diffraction efficiency and effective aperture are long-term goals and bottlenecks for engineering applications. A 4-level off-axis fresnel lens with Ф350 mm effective aperture and 2 µm critical dimension was fabricated through overlay etching technique bylaser direct writing system. Average diffraction efficiency of 75.9% was achieved and certain distribution pattern was observed. Influence of alignment errors on diffraction efficiency distribution was analysed and discussed in detail. This work presented the best results to our knowledge among the same field with similar aperture and critical dimension in open publications, and layed a solid foundation for future large aperture diffractive telescope development.