Distributed Dynamics of Systems with Closed Kinematic Chains

Abstract The simulation of mathematical models of mechanical systems with closed kinematic chains involves the solution to a system of highly coupled differential-algebraic equations. The numerical stiffness of these systems calls for small time steps in order to insure accuracy. Real-time and interactive forward simulations tend to be difficult to achieve for such systems, especially for large multi-body systems with multiple links and many kinematic loops. One way to overcome the time constraint is to distribute the load onto several processors. The modular formulation of mathematical models is attractive because existing models may be assembled to create different topologies, e.g. cooperative robotic systems. Conversely, a given robotic topology may be broken into smaller topologies with simpler dynamics. Moreover, parallel-kinematics machines bear inherent spatial parallelism. This feature is exploited in this thesis, in which we examine the formulation of such modular and distributed models and evaluate their performance as applied to mechanical systems with closed kinematic chains. Three general undistributed formulation methods are specialized to cope with distribution and modularity and applied to a three-degree-of-freedom planar parallel manipulator to generate distributed dynamics models. Finally, the results of case studies are reported, and a comparison is made to highlight the salient features of each method.The simulation of mathematical models of mechanical systems with closed kinematic chains involves the solution to a system of highly coupled differential-algebraic equations. The numerical stiffness of these systems calls for small time steps in order to insure accuracy. Real-time and interactive forward simulations tend to be difficult to achieve for such systems, especially for large multi-body systems with multiple links and many kinematic loops. One way to overcome the time constraint is to distribute the load onto several processors. The modular formulation of mathematical models is attractive because existing models may be assembled to create different topologies, e.g. cooperative robotic systems. Conversely, a given robotic topology may be broken into smaller topologies with simpler dynamics. Moreover, parallel-kinematics machines bear inherent spatial parallelism. This feature is exploited in this thesis, in which we examine the formulation of such modular and distributed models and evaluate their performance as applied to mechanical systems with closed kinematic chains. Three general undistributed formulation methods are specialized to cope with distribution and modularity and applied to a three-degree-of-freedom planar parallel manipulator to generate distributed dynamics models. Finally, the results of case studies are reported, and a comparison is made to highlight the salient features of each method.