CDM

The comprehensive Dynamics motion (CDM) is a library built on top of COMA library to run algorithms along N-CMTM tool.

Table of contents

1. Installation
2. Results
3. Reference

Installation

The V1 is still in WIP. The V0 is an executable used for RSS2021 that has working algorithms, tests and benchmarks.

Dependencies

To compile you need the following tools:

• Git
• CMake >= 3.8.2
• doxygen
• g++ >= 8.3 (for C++17 support)
• Eigen >= 3.2
• coma
• RBDyn

For v0:

• CppAD
• benchmark

Building

git clone --recursive https://github.com/vsamy/coma
cd cdm
mkdir build
cd build
cmake [options] ..
make -j8 install

Building V0

git clone --recursive https://github.com/vsamy/coma
cd cdm
mkdir build
cd build
cmake -DBUILD_V0=ON ..
make -j8

Results

Some comparison results

V0

Here are some benchmarks made with google benchmarks and a i7-7700HQ@2.80GHz.

The next graph is the FK computation time of 100-DoF model (CDM vs RBDyn) depending on the order of the N-CMTM. CDM is 2 to 5 times slower.

The next graph is the computation time of the FK (CDM VS AD) depending on the number of DoF of the system. At 200-DoF, CDM is more than 100 times faster. In this case, with use AD to compute the second-order derivative of the acceleration (snap).

Here are comparison of CDM with different methods for different orders.

order	RBDyn	dv_p(t)	ddv_p(t)	AD
velocity	5.18703e-16	/	/	2.28878e-16
accel...	1.75542e-15	1.08502e-7	/	88578e-16
jerk	/	2.83273e-7	15.6074	1.50195e-15
snap	/	5.10762e-7	54.8067	2.27058e-15
crackle	/	8.10141e-7	150.261	/

Next table is a comparison between CDM and different methods for the ID

order	RBDyn	dv_p(t)
0 (momentum)	5.62864e-16	/
0 (torque)	4.33414e-15	/
1	/	1.04706e-6
2	/	1.2258e-6
3	/	2.0509e-6

Finally, the next table represents the max error of Jacobian (*1e-16) computation where A stands fot eh aleph (the comprehensive motion) and J, K, N, B, Q and R are respectively the link Jacobian, the link momentum Jacobian, the link force Jacobian, the joint momentum Jacobian, the joint force Jacobian and the joint torque Jacobian.

order	JA	KA	NA	BA	QA/RA
1	1.49629	1.49629	1.49629	23.5579	23.5579
2	15.6296	22.2720	20.1281	143.064	99.2641
3	87.0878	87.6064	76.7999	148.885	120.504
4	193.816	209.061	163.068	842.994	944.174
5	766.013	547.351	887.600	2277.34	3241.04

Reference

Related paper is freely accessible here

Citation

@inproceedings{samy2021generalized,
  title={Generalized Comprehensive Motion Theory for High-Order Differential Dynamics},
  author={Samy, Vincent and Ayusawa, Ko and Yoshida, Eiichi},
  journal={Robotics: Science and Systems XVII},
  year={2021}
}