Disturbance Estimation of Legged Robots: Predefined Convergence via Dynamic Gains

TL;DR

This paper tackles disturbance rejection in legged robots by developing a continuous-time online disturbance observer that leverages measurable variables and introduces dynamic gains coupled with comparison functions to achieve predefined convergence of the disturbance estimation error. The observer design yields an estimate $\hat d$ whose convergence behavior can be tailored via a $\mathcal{K}_F$-class gain function $\mu(t)$ and a comparison function $\gamma$, without requiring a priori bounds on $d(t)$ or $\dot d(t)$. A Lyapunov-based analysis establishes sufficient conditions on the gain and coupling functions to guarantee convergence types including ultimately uniformly bounded, asymptotic, and exponential, with explicit expressions for the constituent bounds. Simulation and real-robot experiments on a Unitree A1 quadruped confirm improved fault tolerance and robustness when the disturbance observer is active, underscoring practical applicability in legged locomotion and control. The work offers a flexible, computationally efficient disturbance estimation framework that can be tuned to desired convergence characteristics, advancing active disturbance rejection in legged robotics.

Abstract

In this study, we address the challenge of disturbance estimation in legged robots by introducing a novel continuous-time online feedback-based disturbance observer that leverages measurable variables. The distinct feature of our observer is the integration of dynamic gains and comparison functions, which guarantees predefined convergence of the disturbance estimation error, including ultimately uniformly bounded, asymptotic, and exponential convergence, among various types. The properties of dynamic gains and the sufficient conditions for comparison functions are detailed to guide engineers in designing desired convergence behaviors. Notably, the observer functions effectively without the need for upper bound information of the disturbance or its derivative, enhancing its engineering applicability. An experimental example corroborates the theoretical advancements achieved.

Figures (7)

• Figure 1: The Unitree A1 robot (left) and its model in the simulation environment with a 4.5 kg load (right).
• Figure 2: The height of the base link from the ground over time under the application of different external forces.
• Figure 3: The base link height of the robot with a 4.5 kg load, with and without the observer.
• Figure 4: The Unitree A1 robot as the experimental platform.
• Figure 5: The height of the base link when the output torque of the robot knee joint is reduced by 50%, with and without the observer.