Contact dynamics and force control of flexible multi-body systems

A detailed modelling of contact dynamics involving general flexible multi-body systems of arbitrary kinematic architecture is considered. The components undergoing direct contact (e.g., the end-effector of a manipulator and a satellite) are modelled using the finite element method and the Lagrange multiplier technique. Special attention is paid to dynamic fidelity of contact dynamics. Contact geometric constraints and corresponding contact forces are analysed and incorporated into the dynamical equations. This model takes into account structural deformations and oscillations, friction, time-varying contact area, and repeated contact/impact. Multi-body systems, on the other hand, are handled by a modified Euler-Lagrange method based on the Natural Orthogonal Complement (NOC). Thus, the system dynamics is composed of a set of differential equations (either multi-body formulations or finite element nodal displacement formulations) subjected to sets of algebraic equations expressing kinematic or contact constraints. A systematic procedure for solving this system of equations is formulated with special emphasis on computational efficiency.This dynamic model is then used to design a composite controller which must simultaneously achieve three goals: (1) trajectory tracking, (2) force control, and (3) stabilization of the flexible degrees of freedom of the multibody system. The singular perturbation method is used to obtain two reduced order models. Subsequently, the slow subsystem is used to design a simultaneous position/force controller based on impedance control, where an optimization method is incorporated to accommodate manipulator redundancy. The fast subsystem is used to design a Linear Quadratic Regulator (LQR) to suppress structural vibrations.A simulation environment is developed based on the above procedures and formulations for the planar case. It is used to perform dynamic and control simulations of a variety of contact scenarios involving multi-body systems. A comparative study of the results indicates that a detailed contact dynamics model may be essential for a realistic simulation of contact/impact, capture, and force control operations