Pipe routing can be briefly formulated as seeking the shortest collision-free pipe paths while meeting certain engineering constraints. This article presents a new rectilinear pipe routing algorithm called Manhattan visibility graph (MVG) by extending the Visibility Graph method used for finding the shortest collision-free paths in Euclidean spaces to Manhattan spaces. Subsequently, the article proves that MVG can theoretically guarantee an optimal solution. Further, the article extends MVG algorithm to surface cases to meet requirements of routing pipes in aero-engine rotational spaces. Unlike previous graph methods that commonly yield more than n nodes (where n is the total number of terminals and obstacle vertices), MVG significantly reduces computation complexity because of containing only n nodes. Finally, numerical computations on a developed pipe routing system are performed to demonstrate the effectiveness and efficiency of the proposed method.
This paper puts forward realizing the synchronous control of spacecraft attitude and micro-vibration by taking advantage of magnetic suspension rotor deflection of magnetically suspended control and sensitive gyro. A disturbance-observer is designed to estimate the complex micro vibration which is hard to measure, and an adaptive robust sliding mode controller is designed as an integrated controller and its stability is proven by Lyapunov stability criterion. The band-pass filters are introduced to separate low frequency and high frequency control signals and takes them as input commands of gyro frame and magnetic suspension rotor, respectively. The semi-physical simulation results testify that the proposed method has good vibration suppression effect as well as improves the attitude convergence rate.
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