Lagrangian model, simulation and control of a spherical robot

The derivation of the Lagrangian for different configurations of spherical robots is explored through the use of the Euler Lagrange equations and additional constrains for the generalized velocities. The degrees of freedom are specified with rotation matrices and linear displacement vectors, allowing to determine the necessary elements for all the models in a procedural way, and to obtain the dynamics of the system. One of the thus obtained models is used for simple velocity control tests with two approaches, using the torque and velocity of the rotatory actuators as control inputs, with successful results for a simplified system with one degree of freedom, and satisfactory results for the general system.