Moving Horizon Estimation and Constrained Model Predictive Control for Balancing a Wheel-Legged Robot Under Unknown Disturbances

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Article Summary

Wheel-legged robots balance on two wheels while using articulated legs to change height, absorb impacts, and cross uneven terrain. On hardware, the balance controller must rely on noisy inertial and encoder measurements, and it must reject disturbances that are not known in advance, such as payloads and wind, without exceeding motor torque limits. This paper presents a moving horizon estimator (MHE) combined with an offset-free, constrained model predictive controller (MPC) for the sagittal balance of a 9.95 kg wheel-legged robot. The estimator uses a virtual-leg model augmented with a horizontal hip force, a body pitch torque, and a gyroscope bias. Its accelerometer model removes the predicted hip acceleration, and its process noise is increased when an impact is detected. We evaluate the approach in MuJoCo with simulated sensor noise, bias, quantization, and delay, and compare it with LQR baselines that use ground-truth state, a complementary filter, or the same MHE. In a driving, squatting, reversing, and bowing sequence, MPC with MHE reduced the RMS speed error to 0.11 m/s, compared with 0.24 m/s for LQR with ground-truth state. Under an unknown 2 kg payload and a 10 N headwind, the mean position error in wind was 6 cm, compared with 81 cm for LQR with ground-truth state. Across a 3 $\times$ 4 grid of payloads and headwinds, LQR with the same estimator fell in 3 of 12 combinations, compared with 1 of 12 for MPC. These results are limited to simulation on flat ground, and experimental validation on hardware remains future work.

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