With the rapid development of space science projects,large deployable mechanisms have been widely used.However,due to the effects of mechanical friction and gravitational acceleration,on-orbit mechanisms cannot be alw...With the rapid development of space science projects,large deployable mechanisms have been widely used.However,due to the effects of mechanical friction and gravitational acceleration,on-orbit mechanisms cannot be always deployed to the expected pose.For some precision optical mechanisms,even a minor deviation can result in significant error,so it needs to be measured and corrected.In this paper,the deployment process was modeled and simplified as rotation under single-rotation-axis constraint and translation under single-direction constraint.To solve the problem,a method based on cross-ratio invariability was proposed.The proposed method does not rely on camera calibration techniques,as well as artificial marking points,both of which are necessary in PnP.Instead,only three calibration images before launch and a measurement image on orbit were required.Simulations and experiments demonstrated that the proposed method is more accurate than PnP.In addition,experiments also proved that the feasibility of the proposed method under dark conditions with the aid of a light source and some reflective marking points.展开更多
A natural compactification of the virtual configuration space of N points on the Riemann sphere C is constructed by using cross-ratios. We show that this compactification is homeomorphic to the Bers＇ compactification...A natural compactification of the virtual configuration space of N points on the Riemann sphere C is constructed by using cross-ratios. We show that this compactification is homeomorphic to the Bers＇ compactification of the virtual moduli space of a punctured Riemann sphere of type N. In particular, the system of global and explicit coordinates of this standard compactification is given by cross-ratios.展开更多
Let QS* (S 1) be the space of quasisymmetric homeomorphisms of the unit circle such that the corresponding subspace of the universal Teichmu¨ller space has Weil-Petersson metric.In this paper we give a necessary ...Let QS* (S 1) be the space of quasisymmetric homeomorphisms of the unit circle such that the corresponding subspace of the universal Teichmu¨ller space has Weil-Petersson metric.In this paper we give a necessary condition for a quasisymmetric homeomorphism to belong to QS *(S 1) from the aspect of cross-ratio distortion.展开更多
基金Supported in part by the National Natural Science Foundation of China(No.62271148).
文摘With the rapid development of space science projects,large deployable mechanisms have been widely used.However,due to the effects of mechanical friction and gravitational acceleration,on-orbit mechanisms cannot be always deployed to the expected pose.For some precision optical mechanisms,even a minor deviation can result in significant error,so it needs to be measured and corrected.In this paper,the deployment process was modeled and simplified as rotation under single-rotation-axis constraint and translation under single-direction constraint.To solve the problem,a method based on cross-ratio invariability was proposed.The proposed method does not rely on camera calibration techniques,as well as artificial marking points,both of which are necessary in PnP.Instead,only three calibration images before launch and a measurement image on orbit were required.Simulations and experiments demonstrated that the proposed method is more accurate than PnP.In addition,experiments also proved that the feasibility of the proposed method under dark conditions with the aid of a light source and some reflective marking points.
基金supported by Grants-in-Aid for Scientific Research (C) (Grant No. 23540202)Grant-in-Aids for Scientific Research (B) (Grant No. 20340030)
文摘A natural compactification of the virtual configuration space of N points on the Riemann sphere C is constructed by using cross-ratios. We show that this compactification is homeomorphic to the Bers＇ compactification of the virtual moduli space of a punctured Riemann sphere of type N. In particular, the system of global and explicit coordinates of this standard compactification is given by cross-ratios.
文摘Let QS* (S 1) be the space of quasisymmetric homeomorphisms of the unit circle such that the corresponding subspace of the universal Teichmu¨ller space has Weil-Petersson metric.In this paper we give a necessary condition for a quasisymmetric homeomorphism to belong to QS *(S 1) from the aspect of cross-ratio distortion.
