Probabilistic movement primitives

Movement Primitives (MP) are a well-established approach for representing modular and re-usable robot movement generators. Many state-of-the-art robot learning successes are based MPs, due to their compact representation of the inherently continuous and high dimensional robot movements. A major goal in robot learning is to combine multiple MPs as building blocks in a modular control architecture to solve complex tasks. To this effect, a MP representation has to allow for blending between motions, adapting to altered task variables, and co-activating multiple MPs in parallel. We present a probabilistic formulation of the MP concept that maintains a distribution over trajectories. Our probabilistic approach allows for the derivation of new operations which are essential for implementing all aforementioned properties in one framework. In order to use such a trajectory distribution for robot movement control, we analytically derive a stochastic feedback controller which reproduces the given trajectory distribution. We evaluate and compare our approach to existing methods on several simulated as well as real robot scenarios

Sample-based information-theoretic stochastic optimal control

Many Stochastic Optimal Control (SOC) approaches rely on samples to either obtain an estimate of the value function or a linearisation of the underlying system model. However, these approaches typically neglect the fact that the accuracy of the policy update depends on the closeness of the resulting trajectory distribution to these samples. The greedy operator does not consider such closeness constraint to the samples. Hence, the greedy operator can lead to oscillations or even instabilities in the policy updates. Such undesired behaviour is likely to result in an inferior performance of the estimated policy. We reuse inspiration from the reinforcement learning community and relax the greedy operator used in SOC with an information theoretic bound that limits the ‘distance’ of two subsequent trajectory distributions in a policy update. The introduced bound ensures a smooth and stable policy update. Our method is also well suited for model-based reinforcement learning, where we estimate the system dynamics model from data. As this model is likely to be inaccurate, it might be dangerous to exploit the model greedily. Instead, our bound ensures that we generate new data in the vicinity of the current data, such that we can improve our estimate of the system dynamics model. We show that our approach outperforms several state of the art approaches on challenging simulated robot control tasks

Model-free Probabilistic Movement Primitives for physical interaction

Physical interaction in robotics is a complex problem that requires not only accurate reproduction of the kinematic trajectories but also of the forces and torques exhibited during the movement. We base our approach on Movement Primitives (MP), as MPs provide a framework for modelling complex movements and introduce useful operations on the movements, such as generalization to novel situations, time scaling, and others. Usually, MPs are trained with imitation learning, where an expert demonstrates the trajectories. However, MPs used in physical interaction either require additional learning approaches, e.g., reinforcement learning, or are based on handcrafted solutions. Our goal is to learn and generate movements for physical interaction that are learned with imitation learning, from a small set of demonstrated trajectories. The Probabilistic Movement Primitives (ProMPs) framework is a recent MP approach that introduces beneficial properties, such as combination and blending of MPs, and represents the correlations present in the movement. The ProMPs provides a variable stiffness controller that reproduces the movement but it requires a dynamics model of the system. Learning such a model is not a trivial task, and, therefore, we introduce the model-free ProMPs, that are learning jointly the movement and the necessary actions from a few demonstrations. We derive a variable stiffness controller analytically. We further extent the ProMPs to include force and torque signals, necessary for physical interaction. We evaluate our approach in simulated and real robot tasks

Extracting low-dimensional control variables for movement primitives

Movement primitives (MPs) provide a powerful framework for data driven movement generation that has been successfully applied for learning from demonstrations and robot reinforcement learning. In robotics we often want to solve a multitude of different, but related tasks. As the parameters of the primitives are typically high dimensional, a common practice for the generalization of movement primitives to new tasks is to adapt only a small set of control variables, also called meta parameters, of the primitive. Yet, for most MP representations, the encoding of these control variables is pre-coded in the representation and can not be adapted to the considered tasks. In this paper, we want to learn the encoding of task-specific control variables also from data instead of relying on fixed meta-parameter representations. We use hierarchical Bayesian models (HBMs) to estimate a low dimensional latent variable model for probabilistic movement primitives (ProMPs), which is a recent movement primitive representation. We show on two real robot datasets that ProMPs based on HBMs outperform standard ProMPs in terms of generalization and learning from a small amount of data and also allows for an intuitive analysis of the movement. We also extend our HBM by a mixture model, such that we can model different movement types in the same dataset

A probabilistic approach to robot trajectory generation

Motor Primitives (MPs) are a promising approach for the data-driven acquisition as well as for the modular and re-usable generation of movements. However, a modular control architecture with MPs is only effective if the MPs support co-activation as well as continuously blending the activation from one MP to the next. In addition, we need efficient mechanisms to adapt a MP to the current situation. Common approaches to movement primitives lack such capabilities or their implementation is based on heuristics. We present a probabilistic movement primitive approach that overcomes the limitations of existing approaches. We encode a primitive as a probability distribution over trajectories. The representation as distribution has several beneficial properties. It allows encoding a time-varying variance profile. Most importantly, it allows performing new operations — a product of distributions for the co-activation of MPs conditioning for generalizing the MP to different desired targets. We derive a feedback controller that reproduces a given trajectory distribution in closed form. We compare our approach to the existing state-of-the art and present real robot results for learning from demonstration

Environmental influences on affect and cognition: A study of natural and commercial semi-public spaces

Research has consistently shown differences in affect and cognition after exposure to different physical environments. The time course of these differences emerging or fading during exploration of environments is less explored, as most studies measure dependent variables only before and after environmental exposure. In this within-subject study, we used repeated surveys to measure differences in thought content and affect throughout a 1-h environmental exploration of a nature conservatory and a large indoor mall. At each survey, participants reported on aspects of their most recent thoughts (e.g., thinking of the present moment vs. the future; thinking positively vs. negatively) and state affect. Using Bayesian multi-level models, we found that while visiting the conservatory, participants were more likely to report thoughts about the past, more positive and exciting thoughts, and higher feelings of positive affect and creativity. In the mall, participants were more likely to report thoughts about the future and higher feelings of impulsivity. Many of these differences in environments were present throughout the 1-h walk, however some differences were only evident at intermediary time points, indicating the importance of collecting data during exploration, as opposed to only before and after environmental exposures. We also measured cognitive performance with a dual n-back task. Results on 2-back trials replicated results from prior work that interacting with nature leads to improvements in working-memory performance. This study furthers our understanding of how thoughts and feelings are influenced by the surrounding physical environment and has implications for the design and use of public spaces