Adaptive Model Predictive Control with Data-driven Error Model for Quadrupedal Locomotion

TL;DR

Quadruped MPC performance degrades when the reduced-order model cannot fully capture real dynamics or disturbances. The paper introduces an ARMAV-based data-driven error model that forecasts state errors from sensor residuals and compensates future MPC predictions via $\tilde{x}_{t+1} = x_{t+1} + S\hat{e}_{t+1}$, while leaving MPC laws unchanged. Key contributions include (i) deriving and validating an ARMAV error model from real data, (ii) integrating it with MPC for improved future-state estimation and ground reaction force planning, and (iii) hardware validation on Sirius-Belt with a heavy un-modeled payload, showing reduced CoM vibration and more stable trotting. The approach demonstrates practical viability for payload-bearing quadrupeds by mitigating model imperfections and maintaining robust locomotion in the presence of disturbances.

Abstract

Model Predictive Control (MPC) relies heavily on the robot model for its control law. However, a gap always exists between the reduced-order control model with uncertainties and the real robot, which degrades its performance. To address this issue, we propose the controller of integrating a data-driven error model into traditional MPC for quadruped robots. Our approach leverages real-world data from sensors to compensate for defects in the control model. Specifically, we employ the Autoregressive Moving Average Vector (ARMAV) model to construct the state error model of the quadruped robot using data. The predicted state errors are then used to adjust the predicted future robot states generated by MPC. By such an approach, our proposed controller can provide more accurate inputs to the system, enabling it to achieve desired states even in the presence of model parameter inaccuracies or disturbances. The proposed controller exhibits the capability to partially eliminate the disparity between the model and the real-world robot, thereby enhancing the locomotion performance of quadruped robots. We validate our proposed method through simulations and real-world experimental trials on a large-size quadruped robot that involves carrying a 20 kg un-modeled payload (84% of body weight).

Figures (7)

• Figure 1: The forward trotting with un-modeled payload experiment. (a) Baseline: the mean of body height is 0.367 m (desired value is 0.4 m) and its STD (Standard Deviation) is 0.0035 m; (b) Proposed: the mean of body height is 0.397 m and its STD is 0.0011 m.
• Figure 2: Overview of proposed control framework. The state error data from the robot are collected to construct a data-driven error model including modeling (Section \ref{['modeling']}) shown in grey, determining model order (Section \ref{['checking']}) shown in blue and making prediction (Section \ref{['Model_structure']}) shown in orange. Then the Predicted values of future robot state from MPC based on the reduced-order model (ignoring dynamic of legs) are adjusted by muti-steps ahead prediction of error model then outputs desired robot states ${\bm x_d}$ and GRFs (Ground Reaction Forces) ${\bm u_d}$ by optimization for WBC (Whole-body Control). WBC is also adjusted by one-step ahead prediction from the error model and uses the full-order model to calculate joint torque ${\bm \tau _d}$ and joint position ${\bm q_d}$ for a quadruped robot.
• Figure 3: The vibration of body height during trotting in place. In these two cases, the desired body height is 0.38 m.
• Figure 4: GRFs (Ground Reaction Forces) of one leg in the vertical direction in simulation. The data are from the left front leg of the robot and the other legs have a similar trend. In the case of inaccurate mass, it is obvious that baseline MPC generates larger GRFs (red line) due to the defect model while the propose controller has a great effect in adjusting it (blue line).
• Figure 5: The simulation results of the robot with an un-modeled 8 kg payload. In this simulation, the desired height of CoM is also 0.38 m.