DEADLINE: Monday, October 28, 2013 IN-CLASS DEMO DAY: Tuesday, October 29, 2013
In this assignment you will implement a simulator from scratch for a
tree-structured rigid or elastic body system. Your simulator will
make use of efficient recursive algorithms for forward dynamics (or
quasi-statics) to estimate the motion of the structure. To support a
wider range of student projects, you can choose to do one of
Implement forward robot dynamics using RNEA and CRBA:
This combination leads to an O(N^3) algorithm for
forward-dynamics of rigid-body systems, which is very fast for
small N. Use this approach to build a fast simulator for a
simple robot mechanism. Your interactive system should support
the application of external forces, such as contact (modeled via
penalty forces), or user-applied forces.
Implement forward robot dynamics using Featherstone's
algorithm: This option produces an O(N) forward-dynamics
implementation, that is faster than option 1 for large systems.
If you implement this version, you should apply it to a very
Implement a quasi-static elastic rod simulation using the
STRANDS algorithm [Pai 2002]: Implement a single
quasi-static elastic rod solver for the "standard BVP" discussed
in that paper. You may assume either that the rod is
inextensible, or allows extension. In your interactive
implementation, you should manipulate the free end of the rod
using an applied wrench, which may be estimated by using a
virtual coupling (a generalized 6-dof spring) to your animated
Implement a dynamic elastic rod simulation: As a final
and more challenging option, one can attempt an implementation
of "Discrete Elastic Rods" [Bergou et al. 2008].
Simplifications should be taken to avoid implementing all
features given the limited time frame, e.g., a good target is to
implement an isotropic, naturally straight rod.
Modeling component: The main two tasks of this
assignment are to (1) implement the core algorithm, and (2) apply it
to a nontrivial example that you will model. The simplest example
for robot dynamics algorithms (option 1 or 2) is a non-branching
chain (or serial manipulator) with single-dof revolute joints, and
should be used to debug your implementation. Please also try
at least one nontrivial, creative example of your choosing.
Depending on what you attempt to model, you may decide to use rigid
body links of various shapes. You can find the inertia tensors of
common primitives, such as spheres, ellipsoids, boxes, cylinders,
available in common rigid-body dynamics texts.
Benchmark your results:Run examples with varying
number of links/nodes, N, to determine its performance. Verify that
your algorithm achieves the expected theoretical performance.
Groups: You must may not form groups to complete this
assignment. You are free and encouraged to discuss equations and
ideas with other students, however all software implementations must
be conducted on your own.
Programming language: You are free to use any programming
language and environment that you like for this project (C++, Java,
Matlab, python, processing, etc.).
Animate your results: Use 3D (or 2D) graphics to generate an
interactive animation of your simulation results. Demonstrate the
response of your simulator to user-controlled forces. Feel free to
use existing low-level graphics libraries, such as OpenGL, GLUT, or
DirectX, or a more high-level graphics library, such as SFML (Simple and Fast
Multimedia Library), Processing,
Qt, etc. Building the graphical component first, even if it is
simple, is also an excellent way to debug your implementation.
In cases where the simulation runs very slowly (such as for very
large models, e.g., of a large botanical tree), you can dump frames
and generate a video offline.
External library usage: Feel free to use external libraries
for basic matrix-vector computations, as well as matrix solvers,
e.g., a Cholesky solver for factoring the joint-space inertia matrix
in option 1. You may not use external libraries for simulation,
e.g., of robot dynamics, elastic rods, etc.
Written report and videos: You should submit a brief report
detailing the approach that you took, including implementation
challenges encountered. Your report should also describe any
findings, performance analyses, and creative artifacts generated.
Video artifacts are also strongly encouraged to demonstrate findings
and creative artifacts. Videos can be generated using screen capture
software, videos made from dumped frames, or even video shot off the
screen using a hand-held video recorder.
Document external sources: You should list all significant
external sources that you used to arrive at your final submission.
This includes webpages, technical papers, other software
implementations, as well as discussions with other students in the
Live demonstration: You will get the chance to demonstrate
your results in a show-and-tell class on Tuesday, October 29.
A demonstration is especially important for cases in which the
results of your algorithm are not easily demonstrated in print or
video. Note that although you are required to submit your software
implementation, you are responsible for providing evidence that your
project works via your report, videos, and live demonstration. The
grader should not be required to run and interrogate your code to
determine that your implementation works.
Hand-in using CMS: Please submit via CMS a brief written
report (in txt or PDF format) describing your approach and any
findings, in addition to your implementation, simulation artifacts,
On collaboration and academic integrity: You are allowed to
collaborate on the assignments to the extent of formulating ideas as
a group, and derivation of physical equations. However, you must
conduct your programming and write up completely on your own, and
understand what you are writing. Please also list the names of
people that you discussed the assignment with. You are expected to
maintain the utmost level of academic integrity in the course. Any
violation of the code of academic integrity will be penalized