Abstract

In the thesis 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. A physical interpretation of holonomy/nonholonomic constraints is analyzed based on d'Almberts-Lagrange dynamics and reveals geometric conditions that generate such a behavior. Moreover, a nonholonomy criterion is proposed to verify the integrability of momentum constraints by using a linear transformation via orthogonal projection techniques and singular value decomposition. This criterion can be used to verify the holonomy of a free-flying space robot with or without interaction with a target satellite and to check whether these constraints or their initial conditions are violated. 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.