We previously developed a novel composite wheel-leg-track explosive ordnance disposal (EOD) robot with high mobility, able to switch between a track or a self-balancing motion mode according to environmental conditions, named Scorpio. In this paper, we propose an adaptive nonlinear control algorithm for improving the stability of the robot in the self-balancing mode. First, a model of the dynamics of the robot was established, with which we designed the nonlinear cascade controller for combined balance and motion control. With our system, the attitude of the robot is estimated using a Kalman filtering algorithm. Based on this, an adaptive adjustment algorithm amends the parameters of the controller in real time according to the state of the robot, for improved stability. In addition, we formulated an adaptive zero-offset angle identification algorithm to compensate for deviations caused by changes to the robot's center of gravity (due to changes to its mechanical structure), ensuring that this stability could be maintained. Results of experiments conducted to verify their operation show that self-balancing control of Scorpio can be achieved with the proposed algorithms.