No abstract

The deflection of the vertical (DOV), the angle at a given point on the Earth between the vertical and the direction of the normal to the reference ellipsoid through that point (Herrmann and Bucksch, 2014), is critical to different directions (Barzaghi et al., 2016) in geodesy, for example, the transformation between astronomical and geodetic results including coordinates and azimuth angles, the transformation between different height systems, the reduction of horizontal and vertical angles to an ellipsoid surface, geodetic net calculations and geoid detection. Some critical applications of the DOV and its variation, that is, plumb line variations (Li and Li, 2009;Li et al., 2001;Tanaka et al., 2001), probably are national defense, aerospace applications, and geophysics research. In particular, geophysics can reveal the migration of materials underground, which has a significant impact on embodied earthquake signal analysis and could contribute to earthquake monitoring. Both the International Astronomical Union and the International Association of Geodesy pay considerable attention to studying the DOV.The methods for determining the DOV include astro-and geodetic observations. For example, the observation equipment has been updated from traditional astronomical theodolite or zenith tubes to digital zenith telescopes in recent years (which have an absolute axis pointing error of 1  E 2ʺ and 0.2ʺ observing internal coincidence, respectively); other methods include early global navigation satellite system (GNSS) and leveling measurements (e.g., 0.7ʺ calculation accuracy could be obtained using the geoid in an accuracy level of several centimeters), which are available for small and linear terrain features (Ceylan, 2009), and gravitational methods (e.g., the mean accuracy of the DOV in the 2000 China gravitational field and quasi-geoid system ([CGGM] could reach up to 1.5ʺ [Sun et al., 2005]).

This paper investigates the application of particle swarm optimization (PSO) algorithm to plan joint trajectories of the space modular reconfigurable satellite (SMRS). SMRS changes its configuration by joint motions to complete various space missions; its movement stability is affected by joints motions because of the dynamic coupling effect in space. To improve the movement stability in reconfiguration progress, this paper establishes the optimization object equation to characterize the movement stability of SMRS in its reconfiguration process. The velocity-level and position-level kinematic models based on the proposed virtual joint coordinate system of SMRS are derived. The virtual joint coordinate system solves the problem of asymmetric joint coordinate system resulted by the asymmetric joint arrangement of SMRS. The six-order and seven-order polynomial curves are chosen to parameterize the joint trajectories and ensure the continuous position, velocity, and acceleration of joint motions. Finally, PSO algorithm is used to optimize the trajectory parameters in two cases. Consistent optimization results in terms of the six-order and seven-order polynomial in both cases prove the PSO algorithm can be effectively used for joint trajectory planning of SMRS.

Space modular self-reconfigurable satellites (SMSRSs) are a new type of satellite with reconfigurable structures and adjustable functions. The inverse kinematics of the hyper-redundant structure of SMSRSs are difficult to solve by traditional methods. In this paper, the inverse kinematics of SMSRS is transformed into an optimization problem and solved using the optimization method. Moreover, the avoidance of self-collision is implemented in the optimization process. Firstly, the kinematic model of SMSRS is established. Then, to find the more accurate inverse kinematics solutions, a novel Segmented Hybrid CMA-ES and PSO (SHCP) algorithm is proposed. The algorithm is used for three cases of inverse kinematic problems, and the optimization results prove the optimization method is effective to solve the inverse kinematic problem with self-collision avoidance. Compared to the results of PSO variants, meta-heuristic algorithms, and hybrid algorithms, the novel algorithm has higher accuracy, proving its better performance on the inverse kinematics problem of SMSRS.