Spherical Robot Control with Internal Actuation: A Variational Approach

In this research work, we propose an optimal control law based on a variational approach for a spherical robot system with internal actuation. This system is particularly significant because it is nonlinear and has nonholonomic constraints. Furthermore, full Lie group symmetry is not available and is broken due to advection parameters arising out of subgroup symmetry. We address two control objectives: a contact position stabilization problem with zero angular velocities and that with constant spin. The control objective is defined through a cost functional encompassing both stabilization error and control effort. Energy optimal control law is deduced from a control Hamiltonian function using a variational approach, and finally, optimal state and costate dynamics are calculated. The performance of the proposed optimal controller is evaluated through simulation analysis.