A nonlinear optimal control approach for the spherical robot

<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> A nonlinear H-infinity (optimal) control approach is developed for the problem of the control of the spherical rolling robot. The solution of such a control problem is a nontrivial case due to underactuation and strong nonlinearities in the system's state-space description. The dynamic model of the robot undergoes approximate linearization around a temporary operating point which is recomputed at each timestep of the control method. The linearization relies on Taylor series expansion and on the computation of the system's Jacobian matrices. For the linearized dynamics of the spherical robot an H-infinity controller is designed. To compute the controller's feedback gains an algebraic Riccati equation in solved at each iteration of the control algorithm. The global asymptotic stability properties of the control method are proven through Lyapunov analysis. Finally, for the implementation of sensorless control for the spherical rolling robot, the H-infinity Kalman Filter is used as a robust state estimator.