TAG-K: Tail-Averaged Greedy Kaczmarz for Computationally Efficient and Performant Online Inertial Parameter Estimation

TL;DR

This work targets online inertial parameter estimation for real-time robotic control, addressing the limitations of traditional RLS and KF in abrupt parameter changes and computational cost. The authors introduce TAG-K, a Tail-Averaged Greedy Kaczmarz algorithm that uses greedy residual-driven row selection with adaptive thresholding and tail averaging to achieve fast adaptation and robust convergence, with per-iteration costs of $T\cdot O(mn)$. On simulated quadrotor tracking and embedded MCU benchmarks, TAG-K delivers $1.5$–$1.9\times$ faster solves on laptop-class CPUs and $4.8$–$20.7\times$ faster solves on microcontrollers, while also reducing estimation error by about 25% and nearly doubling end-to-end tracking performance. These results demonstrate TAG-K’s potential for real-time, resource-constrained robotic systems, enabling rapid and reliable updates to inertial models under payload changes and disturbances.

Abstract

Accurate online inertial parameter estimation is essential for adaptive robotic control, enabling real-time adjustment to payload changes, environmental interactions, and system wear. Traditional methods such as Recursive Least Squares (RLS) and the Kalman Filter (KF) often struggle to track abrupt parameter shifts or incur high computational costs, limiting their effectiveness in dynamic environments and for computationally constrained robotic systems. As such, we introduce TAG-K, a lightweight extension of the Kaczmarz method that combines greedy randomized row selection for rapid convergence with tail averaging for robustness under noise and inconsistency. This design enables fast, stable parameter adaptation while retaining the low per-iteration complexity inherent to the Kaczmarz framework. We evaluate TAG-K in synthetic benchmarks and quadrotor tracking tasks against RLS, KF, and other Kaczmarz variants. TAG-K achieves 1.5x-1.9x faster solve times on laptop-class CPUs and 4.8x-20.7x faster solve times on embedded microcontrollers. More importantly, these speedups are paired with improved resilience to measurement noise and a 25% reduction in estimation error, leading to nearly 2x better end-to-end tracking performance.

Figures (3)

• Figure 1: Closed-loop online estimation with fast control and slower parameter updates. A controller produces controls, $\mathbf{u}_k$, under a given set of model parameters, $\boldsymbol{\theta}_t$. These controls are inputs to a dynamics model (or real-world system) which outputs a new state, $\mathbf{x}_{k+1}$. An estimator updates $\boldsymbol{\theta}_t$ every $\kappa$ steps via \ref{['eq:ssm']} to improve controller performance. We add a physics check to safeguard the controller via \ref{['eq:safety-filter']}.
• Figure 2: Upper Left: Example single trial of a quadrotor tracking a figure-8 reference trajectory (dotted line) with unknown payload add/drop events (gray rings). Lower Left: Prediction error timeseries comparing TAG-K with baseline estimators averages over 2,000 trials per estimator. Grey shaded regions denote payload add/drop events, highlighting TAG-K’s rapid and consistent re-convergence after disturbances. Lower Right: Cumulative distribution function (CDF) of position tracking error over 2,000 trials per estimator, averaged across four different noise levels. TAG-K achieves the lowest overall error, demonstrating superior adaptation and end-to-end tracking performance.
• Figure 3: Ablation studies across algorithmic variants demonstrate the performance derived from our algorithmic design.