In this paper a unified control-oriented modeling approach is proposed to deal with the kinematics, linear and angular momentum, contact constraints and dynamics of a free-flying space robot interacting with a target satellite. This developed approach combines the dynamics of both systems in one structure along with holonomic and nonholonomic constraints in a single framework. Furthermore, this modeling allows considering the generalized contact forces between the space robot end-effecter and the target satellite as internal forces rather than external forces. As a result of this approach, linear and angular momentum will form holonomic and nonholonomic constraints, respectively. Meanwhile, restricting the motion of the space robot end-effector on the surface of the target satellite will impose geometric constraints. The proposed momentum of the combined system under consideration is a generalization of the momentum model of a free-flying space robot. Based on this unified model, three reduced models are developed. The first reduced dynamics can be considered as a generalization of a free-flying robot without contact with a target satellite. In this reduced model it is found that the Jacobian and inertia matrices can be considered as an extension of those of a free-flying space robot. Since control of the base attitude rather than its translation is preferred in certain cases, a second reduced model is obtained by eliminating the base linear motion dynamics. For the purpose of the controller development, a third reduced-order dynamical model is then obtained by finding a common solution of all constraints using the concept of orthogonal projection matrices. The objective of this approach is to design a controller to track motion trajectory while regulating the force interaction between the space robot and the target satellite. Many space missions can benefit from such a modeling system, for example, autonomous docking of satellites, rescuing satellites, and satellite servicing, where it is vital to limit the contact force during the robotic operation. Moreover, Inverse dynamics and adaptive inverse dynamics controllers are designed to achieve the control objectives. Both controllers are found to be effective to meet the specifications and to overcome the un-actuation of the target satellite. Finally, simulation is demonstrated by to verify the analytical results.

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This paper presents a unified control-oriented modeling of a free-flying space robot interacting with a target satellite. The purpose of the modeling is to design a controller to track motion trajectory while regulating the force interaction between the space robot and the target satellite. Many space missions can benefit from such a modeling system, for example, autonomous docking of satellites, rescuing satellites, and satellite servicing, where it is vital to limit the contact force during the robotic operation. A unified dynamics model is developed by combining equations of motions of the space-robot and the target satellite all together with the constraint equations of the contact geometry and those of the conservation of linear momentum and angular momentum. The former constraint is imposed due to constrained motion of the space-robot end-effecter, while the later exists because all force/moment, including the contact force and joint torques, are considered as internal force/moment for the combined system of the space robot and the target satellite. Finally, simulation is demonstrated by using a PD controller to verify the analytical results. J J J J J

Abstract. This paper presents a proposal of the fourth law of thermodynamics, the nature of the Universe Dark Energy and the potential to generate such an energy. Recent astronomical observation of Ia supernovae indicates that the Universe is expanding at accelerating rate and composed of around 70% dark energy; 25% dark matter; and 5% Hydrogen, Helium and stars. In this paper a physical interpretation of the dark energy is presented. This interpretation is based on geometric modeling of space-time as a phase fluid and the momentum generated by the time. In this modeling the time is considered to have a mechanical nature so that the momentum associated with it is equal to the negative of the universe total energy. Based on this analysis and by the virtue of the classical thermodynamics, the fourth law of thermodynamics is proposed to account for the dominating energy in the universe. It states that "Considering time as mechanical variable, for a closed system with moving boundaries composed of homogenous isotropic cosmic fluid, the system will have a negative pressure equal to the energy density that causes the system to expand at an accelerated rate. Moreover, the momentum associated with the time is equal to the negative of the system total energy". Such a law is very important to account for the dominating component of the universe, the 70% dark energy that is behind the accelerated expansion of the Universe. The possibility to generate such dark energy is then discussed utilizing macro or micro/nano systems. Finally, simulation results are demonstrated to verify the proposed results.

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