Estimate the CoM of a spinning 2D disk moving due to gravity using only world-frame observations of points on the disk.
Equivalently: learn the rigid body transforms from points on a body to the center of mass using ballistic motion.
$ git clone https://github.com/lowdrant/ballisticukf.git --recurse-submodules
$ python3 main.py
Requires: matplotlib, numpy, scipy, my custom state estimator library (included as a submodule).
How could we estimate the center-of-mass (CoM) of a rotating rigid body undergoing ballistic motion? Since ballistic objects rotate about their CoM (neglecting air resistance), it should be straightforward to estimate the CoM from world-frame position measurements of points on the body. However, I have yet to find an explicit treatment of this problem.
For simplicity, I'm going to work with a spinning disk in moving in 2D.
- Generate rigid body transforms from CoM to points on body
- Simulate disk motion, tracking CoM and angle
- Compute point motion after simulation using RBTs and disk motion (simpler code)
- Feed point motion time series into filter (selected at CLI)
- profit
Our disk has mass m and radius r and experiences gravitational acceleration g. We can choose units of mass, length, and time so that m = r = g = 1. Then all results are dependent on ratios, primarily initial velocity to g. That way I can focus on actually working without worrying about confounding details, i.e. accidentally making mass negative.
- UKF implementation
- KF implementation (for illustration)
[1] Thrun, Sebastian, et al. Probabilistic Robotics. MIT Press, 2010. ISBN 10: 0262201623ISBN
Marion Anderson - lmanderson42@gmail.com