Solving equations of motion on a virtual tree machine

The dynamic equations of motion for rigid links connected at hinges to form a tree are amenable to a parallel solution. Such a solution can potentially provide a real-time simulation of the dynamic behavior of a broad class of objects used in animation and robotics even when the number of links is large. However, the design of a parallel algorithm poses problems not encountered in the sequential, one-processor case, such as assignment of links to processes, allocation of processes to physical processors, synchronization of processes, and the reduction of communication losses. The computation time using a parallel algorithm and an unlimited number of processors is shown to grow with the height of the tree rather than with its number of links. Increased communication costs degrade performance by a factor at most equal to the fanout. The facility used to investigate these problems is a Virtual Tree Machine (VTM) multi-computer implemented on a network of autonomous VAX-11/780 computers and SUN-2 workstations, each running a UNIX operating system.‡ Although the VTM is physically connected via a local area network, its performance in this study reflects what would occur in a point-to-point interconnection of processors in a tree configuration which would be much more expensive to build and test.