Flight Vehicle Attitude Determination Using the Modified Rodrigues Parameters

There are two attitude estimation algorithms based on the different representations of attitude errors when modified Rodrigues parameters are applied to attitude estimation. The first is multiplicative error attitude estimator （MEAE）, whose attitude error is expressed by the modified Rodrigues parameters representing the rotation from the estimated to the true attitude. The second is subtractive error attitude estimator （SEAE）, whose attitude error is expressed by the arithmetic difference between the true and the estimated attitudes. It is proved that the two algorithms are equivalent in the case of small attitude errors. It is possible to describe rotation without encountering singularity by switching between the modified Rodrigues parameters and their shadow parameters. The attitude parameter switching does not bring disturbance to MEAE, but it does to SEAE. This article introduces a modification to eliminate the disturbance on SEAE, and simulation results demonstrate the efficacy of the presented algorithm.

Statistical Analysis of Thunderstorms on the Eastern Tibetan Plateau Based on Modified Thunderstorm Indices

The Tibetan Plateau, with an average altitude above 4000 m, is the highest and largest plateau in the world. The frequency of thunderstorms in this region is extremely high. Many indices are used in operational forecasting to assess the stability of the atmosphere and predict the probability of severe thunderstorm development. One of the disadvantages of many of these indices is that they are mainly based on observations from plains. However, considering the Plateau＇s high elevation, most convective parameters cannot be applied directly, or their application is ineffective. The pre-convective environment on thunderstorm days in this region is investigated based on sounding data obtained throughout a five-year period（2006–10）.Thunderstorms occur over the Tibetan Plateau under conditions that differ strikingly from those in plains. On this basis,stability indices, such as the Showalter index（including SI and SICCL）, and the K index are improved to better assess the thunderstorm environments on the Plateau. Verification parameters, such as the true-skill statistic（TSS） and Heidke skill score（HSS）, are adopted to evaluate the optimal thresholds and relative forecast skill for each modified index. Lastly, the modified indices are verified with a two-year independent dataset（2011–12）, showing satisfactory results for the modified indices. For determining whether or not a thunderstorm day is likely to occur, we recommend the modified SICCLindex.

Distributed attitude consensus of spacecraft formation flying

The consensus problem of the distributed attitude synchronization in the spacecraft formation flying is considered.Firstly,the attitude dynamics of a rigid body spacecraft is described by modified Rodriguez parameters（MRPs）.Then global stable distributed cooperative attitude control laws are proposed for different cases.In the first case,the control law guarantees the state consensus during the attitude synchronization.In the second case,the control law ensures both the attitudes synchronizing to a desired constant attitude and the angular velocities converging at zero.In the third case,an attitude consensus control law with bounded control input is proposed.Finally,the effectiveness and validity of the control laws are demonstrated by simulations of six rigid bodies formation flying.

Comparison of two Nd:YAG laser posterior capsulotomy: cruciate pattern vs circular pattern with vitreous strand cutting

AIM： To investigate the effects and safety of neodymium： yttrium-aluminium-garnet（Nd：YAG） laser posterior capsulotomy with vitreous strand cuttingMETHODS： A total of 40 eyes of 37 patients with symptomatic posterior capsular opacity（PCO） were included in this prospective randomized study and were randomly subjected to either cruciate pattern or round pattern Nd：YAG posterior capsulotomy with vitreous strand cutting（modified round pattern）. The best corrected visual acuity（BCVA）, intraocular pressure（IOP）, refractive error, endothelial cell count（ECC）, anterior segment parameters, including anterior chamber depth（ACD） and anterior chamber angle（ACA） were measured before and 1 mo after the laser posterior capsulotomy. RESULTS： In both groups, the BCVA improved significantly（P〈0.001 for the modified round pattern group, P=0.001 for the cruciate pattern group）; the IOP and ECC did not significantly change. The ACD significantly decreased（P〈0.001 for both） and the ACA significantly increased（P=0.001 for the modified round pattern group and P=0.034 for the cruciate group）. The extent of changes in these parameters was not significantly different between the groups.CONCLUSION： Modified round pattern Nd：YAG laser posterior capsulotomy is an effective and safe method for the treatment of PCO. This method significantly changes the ACD and ACA, but the change in refraction is not significant. Modified round pattern Nd：YAG laser posterior capsulotomy can be considered a good alternative procedure in patients with symptomatic PCO.

Fully-Actuated System Approach Based Optimal Attitude Tracking Control of Rigid Spacecraft with Actuator Saturation

In this paper,a fully-actuated system approach(FASA)based control method is proposed for rigid spacecraft attitude tracking with actuator saturation.First,a second-order fully-actuated form of spacecraft attitude error model is established by modified Rodrigues parameters(MRPs).The unknown total disturbance caused by inertial uncertainty and external disturbance is estimated by using extended state observer,then an FASA based controller is developed.Further,a control parameterization method is adopted to optimize the parameter matrices of FASA based controller with the actuator saturation.Finally,a numerical example is carried out to validate the effectiveness of the proposed scheme.

On analytical solution of system of nonlinear fractional boundary value problems associated with obstacle

In this paper,we use the modified variation of parameters method(MVPM),an elegant coupling of variation of parameters method(VPM)and Adomian’s decomposition method(ADM),for finding the analytical solution of system of nonlinear fractional boundary value problems associated with obstacle.Caputo sense of fractional derivative is used to coup up with fractional term.The results are calculated in terms of series with easily computable components.The used technique is quite easy and convenient for such type problems because it has been previously applied over several nonlinear obstacle systems.