| Algorithms for the control and simulation of multibody systems are created in this dissertation to aid in the design of controlled mechanical systems. A multibody system is a collection of rigid bodies connected by joints and serves as a basis for many models of mechanical systems. A procedure is created to construct mechanical integrators for Lagrangian systems with holonomic constraints. Mechanical integrators are numerical integrators that respect the structure of mechanical systems and conserve energy, momentum, and/or are symplectic. The construction procedure creates symplectic-momentum integrators based on a discrete variational principle and discretizes the principles of mechanics rather than the equations of motion. The method is applied to the double spherical pendulum and the free rigid body, and numerical results are given. A 3D balancing controller is designed for a multibody model of a human biped. The controller utilizes recursive multibody dynamics algorithms, forms a workspace model, efficiently calculates kinematics and joint torques, and coordinates the degrees of freedom of the two legs. The controller is designed to serve as a basis for more complicated motions: walking, running, jumping, changing direction, and adapting to loads. Simulation results are presented of the controlled model reacting to disturbances. Recursive multibody algorithms for forward kinematics, inverse dynamics, and forward dynamics of tree-structured multibody systems are derived using Lie group notation. Components of a multibody simulator specifically designed for real-time simulation of human biped models interacting with the ground are designed. A simple contact model is developed, and the mechanical integrators with external forces are used. Simulation results of a rigid body colliding with the ground are given. Discrete-time equations of motion for tree-structured multibody systems are derived, and a method is developed to solve the equations with a computational cost that grows linearly with the number of joints. The dissertation concludes with a discussion of future work. |
