Models are among the most essential tools in robotics, such as kinematics and dynamics models of the robot's own body and controllable external objects. It is widely believed that intelligent mammals also rely on internal models in order to generate their actions. However, while classical robotics relies on manually generated models that are based on human insights into physics, future autonomous, cognitive robots need to be able to automatically generate models that are based on information which is extracted from the data streams accessible to the robot. In this paper, we survey the progress in model learning with a strong focus on robot control on a kinematic as well as dynamical level. Here, a model describes essential information about the behavior of the environment and the influence of an agent on this environment. In the context of model-based learning control, we view the model from three different perspectives. First, we need to study the different possible model learning architectures for robotics. Second, we discuss what kind of problems these architecture and the domain of robotics imply for the applicable learning methods. From this discussion, we deduce future directions of real-time learning algorithms. Third, we show where these scenarios have been used successfully in several case studies.

Learning in real-time applications, e.g., online approximation of the inverse dynamics model for model-based robot control, requires fast online regression techniques. Inspired by local learning, we propose a method to speed up standard Gaussian process regression (GPR) with local GP models (LGP). The training data is partitioned in local regions, for each an individual GP model is trained. The prediction for a query point is performed by weighted estimation using nearby local models. Unlike other GP approximations, such as mixtures of experts, we use a distance based measure for partitioning of the data and weighted prediction. The proposed method achieves online learning and prediction in real-time. Comparisons with other non-parametric regression methods show that LGP has higher accuracy than LWPR and close to the performance of standard GPR and ν-SVR.

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.

Abstract-In recent years, learning models from data has become an increasingly interesting tool for robotics, as it allows straightforward and accurate model approximation. However, in most robot learning approaches, the model is learned from scratch disregarding all prior knowledge about the system. For many complex robot systems, available prior knowledge from advanced physics-based modeling techniques can entail valuable information for model learning that may result in faster learning speed, higher accuracy and better generalization. In this paper, we investigate how parametric physical models (e.g., obtained from rigid body dynamics) can be used to improve the learning performance, and, especially, how semiparametric regression methods can be applied in this context. We present two possible semiparametric regression approaches, where the knowledge of the physical model can either become part of the mean function or of the kernel in a nonparametric Gaussian process regression. We compare the learning performance of these methods first on sampled data and, subsequently, apply the obtained inverse dynamics models in tracking control on a real Barrett WAM. The results show that the semiparametric models learned with rigid body dynamics as prior outperform the standard rigid body dynamics models on real data while generalizing better for unknown parts of the state space.

Abstract-Computed torque control allows the design of considerably more precise, energy-efficient and compliant controls for robots. However, the major obstacle is the requirement of an accurate model for torque generation, which cannot be obtained in some cases using rigid-body formulations due to unmodeled nonlinearities, such as complex friction or actuator dynamics. In such cases, models approximated from robot data present an appealing alternative. In this paper, we compare two nonparametric regression methods for model approximation, i.e., locally weighted projection regression (LWPR) and Gaussian process regression (GPR). While locally weighted regression was employed for real-time model estimation in learning adaptive control, Gaussian process regression has not been used in control to-date due to high computational requirements. The comparison includes the assessment of model approximation for both regression methods using data originated from SARCOS robot arm, as well as an evaluation of the robot tracking performance in computed torque control employing the approximated models. Our results show that GPR can be applied for realtime control achieving higher accuracy. However, for the online learning LWPR is superior by reason of lower computational requirements.