Model Learning with Local Gaussian Process Regression

Abstract

Precise models of the robot inverse dynamics allow the design of significantly more accurate, energy-efficient and more compliant robot control. However, in some cases the accuracy of rigidbody models does not suffice for sound control performance due to unmodeled nonlinearities arising from hydraulic cable dynamics, complex friction or actuator dynamics. In such cases, estimating the inverse dynamics model from measured data poses an interesting alternative. Nonparametric regression methods, such as Gaussian process regression (GPR) or locally weighted projection regression (LWPR), are not as restrictive as parametric models and, thus, offer a more flexible framework for approximating unknown nonlinearities. In this paper, we propose a local approximation to the standard GPR, called local GPR (LGP), for real-time model online-learning by combining the strengths of both regression methods, i.e., the high accuracy of GPR and the fast speed of LWPR.The approach is shown to have competitive learning performance for high-dimensional data while being sufficiently fast for real-time learning. The effectiveness of LGP is exhibited by a comparison with the state-of-the-art regression techniques, such as GPR, LWPR and ν-SVR. The applicability of the proposed LGP method is demonstrated by real-time online-learning of the inverse dynamics model for robot model-based control on a Barrett WAM robot arm.

Many regression algorithms, one unified model: A review

“…Such combination of ideas from both families are taken in Local Gaussian Process Regression (Nguyen-Tuong et al, 2009), see Sigaud et al (2011) for details, and more recently in (Meier et al, 2014).…”

“…• deriving a locally weighted regression variant of Support Vector Regression based on its specific Reference Algorithms compared (Atkeson and Schaal, 1995) lwr, mlffs (Schaal and Atkeson, 1997) rfwr, mlffs, ls (Vijayakumar and Schaal, 2000) lwpr, rfwr (Schwenker et al, 2001a) elm, BProp, svr (Williams and Rasmussen, 2006) lwpr, gpr, ls (Grollman and Jenkins, 2008) sogp, lwpr (Nguyen-Tuong et al, 2009) lgp, lwpr, svr, gpr (Cederborg et al, 2010) lgp, lwpr, gmr, svr, gpr (Lammert et al, 2010) lwr, mlffs (Huang et al, 2011) elm, BProp, svr (Gijsberts and Metta, 2012) gpr, lwpr, i-ssgpr (Droniou et al, 2012a) xcsf, lwpr, irfrls (Munzer et al, 2014) lwr, gmr, rbfn, irfrls Table 4: List of articles, and the algorithms between which they make empirical comparisons.…”

Learning to Control a Low-Cost Manipulator using Data-Efficient Reinforcement Learning

“…In recent years, GP dynamics models were more often used for learning robot dynamics [9,10,14]. However, they are usually not used for long-term planning and policy learning, but rather for myopic control and trajectory following.…”

“…However, they are usually not used for long-term planning and policy learning, but rather for myopic control and trajectory following. Typically, the training data for the GP dynamics models are obtained either by motor babbling [9] or by demonstrations [14]. For the purpose of data-efficient fully autonomous learning, these approaches are not suitable: Motor babbling is data-inefficient and does not guarantee good models along a good trajectory; demonstrations would contradict fully autonomous learning.…”

Estimating the non-linear dynamics of free-flying objects

“…3 Recent efforts at developing spare methods for alleviating this cost have produced promising results [52,53]. The computation remains however at best linear in the number of data points and there is no unique way to determine the subset of training points.…”