Local Gaussian Processes Regression for Real-time Model-based Robot Control

For human motor activities, internal models can play an important role [1] representing an input-output transformation of dynamical processes in the brain to the external world. Internal dynamics models can also be used for high performance and compliant robot control [2]. However, accurate dynamics models cannot be obtained analytically for sufficiently complex robot systems [3, 4]. In such cases, machine learning offers a promising alternative for approximating the robot dynamics using measured data. This approach offers a natural framework to incorporate unknown nonlinearities as well as to continually adapt online for changes in the robot dynamics. However, the most accurate regression methods, e.g., Gaussian processes regression (GPR) [5] and support vector regression (SVR) [6], suffer from exceptional high computational complexity which prevents their usage for large numbers of samples or online learning to date. Inspired by locally linear regression techniques, e.g., LWPR, we propose an approximation to the standard GPR using local Gaussian processes models inspired by [7, 8] combining the strength of local learning, e.g., fast computation, and global regression, e.g., high approximation performance. Due to reduced computational cost, local Gaussian processes (LGP) can be applied for larger sample-sizes and online learning. Comparisons with other nonparametric regressions, e.g. standard GPR, ν-SVR and locally weighted projection regression (LWPR) [7], show that LGP has higher accuracy than LWPR close to the performance of standard GPR and ν-SVR while being sufficiently fast for online learning. The proposed method is evaluated using real robot data generated on the Sarcos master arm and the Barrett WAM. Figure 1 shows the normalized mean squared error (nMSE) in percent of the evaluation on the test set for each of the two scenarios, i.e., the Barrett arm in (a) and the Sarcos arm in (b). Here, the normalized mean squared error is defined as: nMSE = Mean squared error/Variance of target. It can be seen that LGP generalizes well even when using only few local models for prediction. In all cases, LGP outpreforms LWPR while being close in learning accuracy to GPR and ν-SVR. Since only a small amount of local models in the vicinity of the query point are needed during prediction for LGP, the computation time is reduced significantly compared to GPR and ν-SVR. The comparison of prediction speed is shown in Figure 2. Here, we train LWPR, ν-SVR, GPR and LGP on 5 different data