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The purpose of this study is to obtain the differential geometric analysis of autonomous wheel-legged robots and their trajectories on the terrain.

The author uses a wheel using the osculating sphere of the curve on rough terrain. Additionally, the author expresses a triple osculating sphere wheel by taking advantage of differential geometry. Moreover, the author examined the consecutive wheel center-curves to obtain the optimum posture of a micro-hydraulic toolkit (MHT) robot.

The author examined the terrain path, which is crucial for trajectory planning in terms of the geometric perspective. The author designed the triple MHT wheel using the osculating sphere of the MHT robot trajectory by taking advantage of local differential geometric properties of this curve on the terrain. The consecutive wheel center-curves were expressed and studied based on differential geometry.

The author provides a novel approach for the optimum posture of an MHT robot using consecutive wheel-center curves and provides an original perspective to MHT robot and its trajectory by using differential geometry.

The purpose of this paper is to develop a discrete element (DE) and multiscale modeling methodology to represent granular media at their particle scale as they interface solid deformable bodies, such as soil‐tool, tire, penetrometer, pile, etc., interfaces.

A three‐dimensional ellipsoidal discrete element method (DEM) is developed to more physically represent particle shape in granular media while retaining the efficiency of smooth contact interface conditions for computation. DE coupling to finite element (FE) facets is presented to demonstrate initially the development of overlapping bridging scale methods for concurrent multiscale modeling of granular media.

A closed‐form solution of ellipsoidal particle contact resolution and stiffness is presented and demonstrated for two particle, and many particle contact simulations, during gravity deposition, and quasi‐static oedometer, triaxial compression, and pile penetration. The DE‐FE facet coupling demonstrates the potential to alleviate artificial boundary effects in the shear deformation region between DEM granular media and deformable solid bodies.

The research is being extended to couple more robustly the ellipsoidal DEM code and a higher order continuum FE code via overlapping bridging scale methods, in order to remove dependence of penetration/shear resistance on the boundary placement for DE simulation.

When concurrent multiscale computational modeling of interface conditions between deformable solid bodies and granular materials reaches maturity, modelers will be able to simulate the mechanical behavior accounting for physical particle sizes and flow in the interface region, and thus design their tool, tire, penetrometer, or pile accordingly.

A closed‐form solution for ellipsoidal particle contact is demonstrated in this paper, and the ability to couple DE to FE facets.

Interstellar gas passing through the solar system may effect the interplanetary gas, planetary atmospheres and satellite orbits. Interaction of the interstellar and interplanetary gases is considered; a solar system corona may be formed.

The purpose of this paper is to design a solar sail heliocentric transfer orbit which can meet the requirements of control system and capture orbit, and to provide the change of angles for attitude control system.

Aiming at the problem of solar sail heliocentric transfer orbits design, this paper addresses the derivation of analytical optimal control law. The control laws can realize the combination of the control of each orbit element, but they can only give local optimal solution to meet the practical needs of mission. In order to solve this problem and meet the capture orbit and the attitude control system requirements, the modified genetic algorithm based on the analytical control law is introduced.

The algorithm addressed by this paper includes results closer to the global optimization, and also can meet the engineering constraints.

The analytical optimal control law can be applied to the future onboard sail control systems. The blending optimal algorithm is demonstrated to be suitable as a method of preliminary design for solar sail deep space exploration mission.

A blending optimal algorithm combining the analytical control law and genetic algorithm is proposed; the algorithm can search for global optimization based on the local optimal results of analytical control law.

The purpose of this paper is to study the effect of J₃ perturbation of the Earth’s oblateness on satellite orbit compared with J₂ perturbation.

Based on the parametric variation method in the time domain, considering more accurate Earth potential function by considering J₃-perturbation effect, the perturbation equations about satellite’s six orbital elements (including semi-major axis, orbit inclination, right ascension of the ascending node, true anomaly, eccentricity and argument of perigee) has been deduced theoretically. The disturbance effects of J₂ and J₃ perturbations on the satellite orbit with different orbit inclinations have been studied numerically.

With the inclination increasing, the maximum of the semi-major axis increases weakly. The difference of inclination disturbed by the J₂ and J₃ perturbation is relative to orbit inclinations. J₃ perturbation has weak effect on the right ascension and argument of perigee. The critical angle of the right ascension and argument of perigee which decides the precession direction is 90° and 63.43°, respectively. The disturbance effects of J₂ and J₃ perturbations on the argument of perigee, right ascension and eccentricity are weakened when the eccentricity increases, simultaneously, the difference of J₂ and J₃ perturbations on argument of perigee, right ascension and argument of perigee decreases with eccentricity increasing, respectively.

In the future, satellites need to orbit the Earth much more precisely for a long period. The J₃ perturbation effect and the weight compared to J₂ perturbation in LEO can provide a theoretical reference for researchers who want to improve the control accuracy of satellite. On the other hand, the theoretical analysis and simulation results can help people to design the satellite orbit to avoid or diminish the disturbance effect of the Earth’s oblateness.

The J₃ perturbation equations of satellite orbit elements are deduced theoretically by using parametric variation method in this paper. Additionally, the comparison studies of J₂ perturbation and J₃ perturbation of the Earth’s oblateness on the satellite orbit with different initial conditions are presented.

The purpose of this paper is to establish a paint deposition pattern model applied to robotic air spray painting in order to achieve the accuracy and uniformity of paint film thickness on free‐form surface.

The paper opts for an exploratory study using the curvature circle method for air spray painting on free‐form surface to construct a spray gun model. First, a paint deposition pattern model of ellipse dual‐β distribution is fitted on the basic of experimental data from robotic air spray painting. Second, a spray gun model is proposed using the curvature circle method for air spray painting on free‐form surface. The theoretical result is coincident with the film thickness in verification experiment spraying a cylinder surface. The biggest error of the sample points between the theoretical and experimental results is less than 4 μm, thereby the correctness and effectiveness of the proposed model is validated.

The paper provides a specific theoretical and methodological support for the realization of process planning and simulation system in surface spray manufacturing. It will make the future developed system meet the actual processing requirement. At the same time, it is more representative.

The paper finds an approach to solve paint deposition pattern model suitable to free‐form surface. The present method can be applied to the complex reality of topological relation for actual workpiece surface to be painted.