We report on the design and analysis of a controller which can achieve dynamical self-righting of our hexapedal robot, RHex. We present an empirically developed control procedure which works reasonably well on indoor surfaces, using a hybrid energy pumping strategy to overcome torque limitations of its actuators. Subsequent modeling and analysis yields a new controller with a much wider domain of success as well as a preliminary understanding of the necessary hybrid control strategy. Simulation results demonstrate the superiority of the improved control strategy to the first generation empirically designed controller.