Experimental Comparison of PID, LQR-Based, and PDD²-LQR Control for Stationary Balancing of a Full-Scale Bicycle Robot Using a Scissored-Pair Control Moment Gyroscope

This paper studies the stationary balancing of a full-scale bicycle robot using a scissored-pair control moment gyroscope (CMG). The test robot weighs 60 kg and includes two counter-rotating flywheels, a 20:1 geared gimbal system, an inertial measurement unit (IMU), and an embedded controller. For controller design, a simplified nonlinear model of the roll and CMG dynamics is derived and linearized around the upright position. The main contribution of this work is the experimental testing of a PDD2-LQR controller. This controller keeps the standard LQR state-feedback baseline and adds feedback from the roll error, roll rate, and filtered roll acceleration. Instead of redesigning the whole controller, the same LQR gains are used in both the baseline LQR and PDD2-LQR setups. This allows us to directly evaluate the benefit of the extra PDD2 terms on the same hardware under the same actuator limits. Experiments were carried out using PID, LQR, and PDD2-LQR controllers. The PDD2-LQR controller reached an average RMSE of 0.660 degrees and an average MAE of 0.477 degrees. These values represent improvements of about 51.8% and 43.2%, respectively, compared with the standard LQR controller. Overall, the results show that adding roll-motion feedback to the baseline controller significantly improves stationary balancing performance.