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If you need the symbolic Jacobian of your robot you should calculate it in symbolic form using Matlab for example. It allows symbolic calculation as exemplified in this page. Moreover, the Matlab Robotic Toolbox has a C code generator useful to directly output the calculated symbolic quantities in C format.

On the other hand, KDL library allows you to numerically compute the matrices of the robot dynamic model (e.g. Inertia, Coriolis, Gravity) starting from robot state (joint positions, velocities). You can find the detailed implementation here.

Hope this can help.