@TechReport{Dartmouth:TR2006-576,
author = {Anne Loomis},
title = {{Computation Reuse in Statics and Dynamics Problems for Assemblies of Rigid Bodies}},
institution = {Dartmouth College, Computer Science},
address = {Hanover, NH},
number = {TR2006-576},
year = {2006},
month = {June,},
URL = {http://www.cs.dartmouth.edu/reports/TR2006-576.pdf},
comment = {
Master's thesis.
},
abstract = {
The problem of determining the forces among contacting rigid bodies is
fundamental to many areas of robotics, including manipulation
planning, control, and dynamic simulation. For example, consider the
question of how to unstack an assembly, or how to find stable regions
of a rubble pile. In considering problems of this type over discrete
or continuous time, we often encounter a sequence of problems with
similar substructure. The primary contribution of our work is the
observation that in many cases, common physical structure can be
exploited to solve a sequence of related problems more efficiently
than if each problem were considered in isolation.
We examine three general problems concerning rigid-body assemblies:
dynamic simulation, assembly planning, and assembly stability given
limited knowledge of the structure's geometry.
To approach the dynamic simulation and assembly planning applications,
we have optimized a known method for solving the system dynamics. The
accelerations of and forces among contacting rigid bodies may be
computed by formulating the dynamics equations and contact constraints
as a complementarity problem. Dantzig's algorithm, when applicable,
takes n or fewer major cycles to find a solution to the linear
complementarity problem corresponding to an assembly with n contacts.
We show that Dantzig's algorithm will find a solution in n - k or
fewer major cycles if the algorithm is initialized with a solution to
the dynamics problem for a subassembly with k internal contacts.
Finally, we show that if we have limited knowledge of a structure's
geometry, we can still learn about stable regions of its surface by
physically pressing on it. We present an approach for finding stable
regions of planar assemblies: sample presses on the surface to
identify a stable cone in wrench space, partition the space of
applicable wrenches into stable and unstable regions, and map these
back to the surface of the structure.
}
}