The safe operation of physical systems typically relies on high-quality models. Since a continuous stream of data is generated during run-time, such models are often obtained through the application of Gaussian process regression because it provides guarantees on the prediction error. Due to its high computational complexity, Gaussian process regression must be used offline on batches of data, which prevents applications, where a fast adaptation through online learning is necessary to ensure safety. In order to overcome this issue, we propose the LoG-GP. It achieves a logarithmic update and prediction complexity in the number of training points through the aggregation of locally active Gaussian process models. Under weak assumptions on the aggregation scheme, it inherits safety guarantees from exact Gaussian process regression. These theoretical advantages are exemplarily exploited in the design of a safe and data-efficient, online-learning control policy. The efficiency and performance of the proposed real-time learning approach is demonstrated in a comparison to state-of-the-art methods.

Data-driven models are subject to model errors due to limited and noisy training data. Key to the application of such models in safety-critical domains is the quantification of their model error. Gaussian processes provide such a measure and uniform error bounds have been derived, which allow safe control based on these models. However, existing error bounds require restrictive assumptions. In this paper, we employ the Gaussian process distribution and continuity arguments to derive a novel uniform error bound under weaker assumptions. Furthermore, we demonstrate how this distribution can be used to derive probabilistic Lipschitz constants and analyze the asymptotic behavior of our bound. Finally, we derive safety conditions for the control of unknown dynamical systems based on Gaussian process models and evaluate them in simulations of a robotic manipulator.

A data-driven identification of dynamical systems requiring only minimal prior knowledge is promising whenever no analytically derived model structure is available, e.g., from first principles in physics. However, meta-knowledge on the system’s behavior is often given and should be exploited: Stability as fundamental property is essential when the model is used for controller design or movement generation. Therefore, this paper proposes a framework for learning stable stochastic systems from data. We focus on identifying a state-dependent coefficient form of the nonlinear stochastic model which is globally asymptotically stable according to probabilistic Lyapunov methods. We compare our approach to other state of the art methods on real-world datasets in terms of flexibility and stability.

Programming by Demonstration allows to transfer skills from human demonstrators to robotic systems by observation and reproduction. One aspect that is often overlooked is that humans show different trajectories over multiple demonstrations for the same task. Observed movements may be more precise in some phases and more diverse in others. It is well-known that the variability of the execution carries important information about the task. Therefore, we propose a Bayesian approach to model uncertainties from training data and to infer them in regions with sparse information. The approach is validated in simulation, where it shows higher precision than existing methods, and a robotic experiment with variance based impedance adaptation.

Dynamic Movement Primitives (DMPs) represent stable goal-directed or periodic movements, which are learned from observations or demonstrations. They rely on proper function approximators, which are sufficiently flexible to represent arbitrary movements but also ensure goal convergence in point-to-point motions. This work shows that Gaussian Processes (GPs) are suitable as a regressor for learning movements with DMPs ensuring stability. In addition, GPs provide a measure for the uncertainty about the current movement, which we exploit by proposing a new cooperation scheme for DMPs: For better reproduction of demonstrations, we follow the intuition, that individuals with more knowledge lead towards the goal, while others follow and focus on cooperation. Along with simulation results, we validate the presented methods in a robotic cooperative object manipulation task.

Cooperative manipulation, where several robots jointly manipulate an object from an initial configuration to a final configuration while preserving the robot formation, poses a great challenge in robotics. Here, we treat the problem of designing motion primitives for cooperative manipulation such that the robots move in formation and are robust with respect to external disturbances. Individual robot trajectories are generated by Dynamic Movement Primitives (DMPs) and coupled by a formation control approach enabling the DMP-trajectories to preserve a given formation while performing the manipulation. The proposed control scheme achieves an increased adaptability under external disturbances. The approach is evaluated in a full-scale experiment with two prototypical cooperative manipulation and synchronized motion tasks.