Some aspects in the bond graph modelling of robotic manipulators: angular velocities from symbolic manipulation of rotation matrices

The paper discusses certain issues involved in the modelling of robotic manipulators using bond graphs. The time rates of joint variables are related to the rates of Cartesian variables using modulated transformers, which are obtained from respective Jacobian matrices. A symbolic approach to derive these matrices is presented, with derivations. The Jacobian relating the angular velocities with joint rates can be derived directly from the rotation matrix for the corresponding link. In the literature, the only method used is the recursive method, which is computationally more intensive. We present another approach, which is simpler and computationally efficient and amenable to symbolic derivation. An example of a two link spatial manipulator is presented. Expressions of its Jacobian are derived using the proposed method, and its bond graph model is presented along with simulation results.