Nonholonomic control of coupled spatial multibody systems

This dissertation is concerned with dynamic modeling, controllability and control synthesis of coupled multibody systems. The systems are configured as open kinematic chain and with large angle motions in three dimensional space. Angular momentum preserving reorientation problem is of interest here. This has applications in multibody satellites and space robotics, and, in the understanding of the classical cat fall problem. A coordinate free representation of dynamics for a multibody system, composed of rigid bodies connected by ball-in-socket joints without kinematic loops, is derived. The conservation of angular momentum results in a nonholonomic constraint. Important properties of nonholonomic system are discussed. Controllability is explored in a coordinate free form. Local coordinate results can then be easily derived. A sufficient condition for strong accessibility and small time local controllability (STLC) is derived. We give a nonsmooth feedback control law to control the absolute orientation of two-body system. This synthesis approach based on a path planning method: multi-cycle joint motion. We prove that the applicability of the control synthesis using linear motions along a closed relative angle path requires controllability condition to be satisfied. The computer simulation results illustrate the convergent property of this control design. Results presented here are a nontrivial extension of previous work on planar systems. All results can be extended to tree connected multibody systems and can be applied to many mechanical system with nonholonomic constraint.