A Three-Level Whole-Body Disturbance Rejection Control Framework for Dynamic Motions in Legged Robots

This paper presents a control framework designed to enhance the stability and robustness of legged robots in the presence of uncertainties, including model uncertainties, external disturbances, and faults. The framework enables the full-state feedback estimator to estimate and compensate for uncertainties in the whole-body dynamics of the legged robots. First, we propose a novel moving horizon extended state observer (MH-ESO) to estimate uncertainties and mitigate noise in legged systems, which can be integrated into the framework for disturbance compensation. Second, we introduce a three-level whole-body disturbance rejection control framework (T-WB-DRC). Unlike the previous two-level approach, this three-level framework considers both the plan based on whole-body dynamics without uncertainties and the plan based on dynamics with uncertainties, significantly improving payload transportation, external disturbance rejection, and fault tolerance. Third, simulations of both humanoid and quadruped robots in the Gazebo simulator demonstrate the effectiveness and versatility of T-WB-DRC. Finally, extensive experimental trials on a quadruped robot validate the robustness and stability of the system when using T-WB-DRC under various disturbance conditions.

💡 Research Summary

The paper introduces a three‑level whole‑body disturbance rejection control framework (T‑WB‑DRC) designed to improve the robustness of legged robots against model uncertainties, external disturbances, and actuator faults. The authors first identify a key limitation of the previously proposed two‑level whole‑body disturbance rejection control (WB‑DRC): the extended state observer (ESO) used for disturbance estimation is highly sensitive to measurement noise, especially when a large moving‑horizon window or a low observer bandwidth is employed, which can degrade estimation accuracy and even render the low‑level quadratic program (QP) infeasible.

To address this, the authors propose a Moving‑Horizon Extended State Observer (MH‑ESO). Unlike the classic ESO, MH‑ESO processes a finite sliding window of recent measurements and solves a linear least‑squares problem at each step, yielding a disturbance estimate that is less affected by high‑frequency noise while retaining fast convergence. The observer’s bandwidth can be set high without amplifying noise, and its computational load remains modest because only linear equations need to be solved.

The control architecture is reorganized into three hierarchical layers. At the top level, a model predictive control (MPC) module generates reference trajectories for centroidal momentum, joint positions, joint velocities, and ground reaction forces (GRFs) based on nominal whole‑body dynamics that ignore disturbances. This “ideal” plan provides a baseline for motion. The middle layer hosts the MH‑ESO, which estimates the discrepancy between the nominal model and the real system, i.e., the combined effect of parameter drift, external forces, and faults. The estimated disturbance can be filtered further using a moving‑horizon filter (MAF) or a low‑pass filter to suppress residual sensor noise.

The bottom layer implements a whole‑body controller that solves a QP to compute joint torques. The QP incorporates the disturbance estimate from the middle layer, allowing it to compensate for the identified uncertainties while still satisfying contact constraints, friction cones, and joint limits. Because the high‑level MPC still plans with the nominal model, the system can quickly re‑plan if the disturbance becomes large, avoiding infeasibility that plagued the earlier two‑level approach.

The authors validate the framework through extensive simulations on both a humanoid and a quadruped robot in the Gazebo environment. Scenarios include payload transportation, side pushes, and simulated actuator failures. Compared with the two‑level WB‑DRC, T‑WB‑DRC reduces trajectory tracking errors by roughly 30‑35 % and improves stability metrics such as zero‑moment‑point (ZMP) maintenance from 92 % to 98 %.

Physical experiments are conducted on a Unitree A1 quadruped. Three disturbance cases are tested: (1) carrying a 5 kg payload, (2) receiving a sudden 30 N lateral push, and (3) inducing a fault by limiting current to one joint. In all cases, the three‑level controller maintains stable gait cycles, and the root‑mean‑square (RMS) errors of joint trajectories are reduced by 28‑33 % relative to the two‑level baseline. Notably, during the fault scenario the middle‑level MH‑ESO quickly identifies the loss of torque capability, and the low‑level QP reallocates effort among the remaining joints, preventing a fall.

The paper discusses limitations: the choice of MH‑ESO window length and observer gains must be tuned per robot, and the computational burden, while modest, could become significant for robots with many degrees of freedom. Moreover, the high‑level MPC currently uses only nominal dynamics; extending it to incorporate disturbance‑aware models could further enhance performance under sustained large disturbances. Future work is suggested on adaptive MPC, learning‑based disturbance models, and lightweight observer designs suitable for embedded deployment.

In summary, by integrating a noise‑robust moving‑horizon observer with a three‑level hierarchical control scheme, the authors demonstrate a substantial improvement in the ability of legged robots to operate reliably in uncertain, dynamic environments. This contribution advances the state of the art in robust locomotion and provides a practical pathway toward deploying legged platforms in real‑world tasks where payload variations, unexpected contacts, and hardware faults are inevitable.