In this paper, two nonlinear methods for stabilizing the orientation of a Four-Wheel Independent Drive and Steering (4WIDS) robot while in the air are analyzed, implemented in simulation, and compared. AGRO (the Agile Ground Robot) is a 4WIDS inspection robot that can be deployed into unsafe environments by being thrown, and can use the reaction torque from its four wheels to command its orientation while in the air. Prior work has demonstrated on a hardware prototype that simple PD control with hand-tuned gains is sufficient, but hardly optimal, to stabilize the orientation in under 500ms. The goal of this work is to decrease the stabilization time and reject disturbances using nonlinear control methods. A model-based Feedback Linearization (FL) was added to compensate for the nonlinear Coriolis terms. However, with external disturbances, model uncertainty and sensor noise, the FL controller does not guarantee stability. As an alternative, a second controller was developed using backstepping methods with an adaptive compensator for external disturbances, model uncertainty, and sensor offset. The controller was designed using Lyapunov analysis. A simulation was written using the full nonlinear dynamics of AGRO in an isotropic steering configuration in which control authority over its pitch and roll are equalized. The PD+FL control method was compared to the backstepping control method using the same initial conditions in simulation. Both the backstepping controller and the PD+FL controller stabilized the system within 250 milliseconds. The adaptive backstepping controller was also able to achieve this performance with the adaptation law enabled and compensating for offset noisy sinusoidal disturbances.