Symbolic Dynamics

Can machines beat humans in the symbolic space?
Some documentation is on the Notion page.

Important Notes

• The Casadi version of the forward dynamics function is about 10000 times faster than the original matlab version!
• Currently only support urdf that satisfy the following condition:
  1. There are only revolute joints or fixed joints.
  2. The transformations between joints in the home configuration are orthognal (the rotations are multiple of $\pi/2$). This simplifies the symbolic calculation.
  3. There is no branched links.
• Running this code requires the symbolic toolbox and the robotics toolbox.
• DynamicsSym.SaveFunction() may take tremendous amout of time. Avoid using it if you can.
• The animation part is currenly irrelavent.

Instruction

Run startup.m to set path. Run test_casadi.m to see the comparison between the symbolic dynamics and the ground truth.

Results

The comparison between the calculation of the symbolic function (using substitution) and the matlab toolbox is shown here.

1. Mass matrix

2. Transformation matrix

3. Gravitation torque matrix

4. Forward dynamics

Reference

1. Robot Modeling and Control