Learning robot inverse dynamics using sparse online Gaussian process with forgetting mechanism

TL;DR

This work tackles online learning of robot inverse dynamics under time-varying conditions by proposing a sparse online Gaussian process with forgetting (SOGP-FM). The approach combines a basis-vector maintenance scheme with a forgetting mechanism that balances short-term adaptability and long-term memory by adjusting a forgetting period $h$ while using a novelty measure $\gamma_{x_{t+1}}$ and a BV size $m$. The method is instantiated for a 7-DoF Panda robot, using an ESO to estimate velocities and accelerations, and is evaluated in both simulations and real experiments across task switches; results show that the forgetting-enabled SOGP outperforms pure PIS and OPS in modeling accuracy and tracking quality, with smoother predictions. This work advances real-time, data-efficient learning-based control by enabling robust online adaptation to changing tasks and disturbances without heavy computational demands, and it offers a pathway toward more resilient GP-based robot control under time-varying dynamics.

Abstract

Online Gaussian processes (GPs), typically used for learning models from time-series data, are more flexible and robust than offline GPs. Both local and sparse approximations of GPs can efficiently learn complex models online. Yet, these approaches assume that all signals are relatively accurate and that all data are available for learning without misleading data. Besides, the online learning capacity of GPs is limited for high-dimension problems and long-term tasks in practice. This paper proposes a sparse online GP (SOGP) with a forgetting mechanism to forget distant model information at a specific rate. The proposed approach combines two general data deletion schemes for the basis vector set of SOGP: The position information-based scheme and the oldest points-based scheme. We apply our approach to learn the inverse dynamics of a collaborative robot with 7 degrees of freedom under a two-segment trajectory tracking problem with task switching. Both simulations and experiments have shown that the proposed approach achieves better tracking accuracy and predictive smoothness compared with the two general data deletion schemes.

Figures (6)

• Figure 1: An online GP model that gradually forgets the oldest points at the forgetting period $h$ while retaining the more informative ones.
• Figure 2: A block diagram of robot control based on SOGP-FM that predicts the feedforward term $\bm{\tau}_\mathrm{ff}$ and is updated online by $(\bm{q}, \dot{\bm{q}}, \ddot{\bm{q}})$ and $\bm{\tau}$.
• Figure 3: Modeling accuracy as RMSE($\bm{e}_{m}$) by the three SOGP schemes in simulations, where Task 2 starts at $t=$ 40 s. Note that the proposed FS has the best modeling accuracy in both tasks.
• Figure 4: Position tracking accuracy as RMSE($\bm{e}$) by the three SOGP schemes in simulations, where Task 2 starts at $t=$ 40 s. Note that the proposed FS has the best tracking accuracy in both tasks.
• Figure 5: Position tracking accuracy as RMSE($\bm{e}$) by the three SOGP schemes in experiments, where Task 2 starts at $t=$ 124s. Note that the OPS has a larger tracking error in some areas of Task 1, and the proposed FS and the OPS outperform the PIS clearly in Task 2.