Programming by Demonstration on Riemannian Manifolds

This thesis presents a Riemannian approach to Programming by Demonstration (PbD). It generalizes an existing PbD method from Euclidean manifolds to Riemannian manifolds. In this abstract, we review the objectives, methods and contributions of the presented approach. OBJECTIVES PbD aims at providing a user-friendly method for skill transfer between human and robot. It enables a user to teach a robot new tasks using few demonstrations. In order to surpass simple record-and-replay, methods for PbD need to \u2018understand\u2019 what to imitate; they need to extract the functional goals of a task from the demonstration data. This is typically achieved through the application of statisticalmethods. The variety of data encountered in robotics is large. Typical manipulation tasks involve position, orientation, stiffness, force and torque data. These data are not solely Euclidean. Instead, they originate from a variety of manifolds, curved spaces that are only locally Euclidean. Elementary operations, such as summation, are not defined on manifolds. Consequently, standard statistical methods are not well suited to analyze demonstration data that originate fromnon-Euclidean manifolds. In order to effectively extract what-to-imitate, methods for PbD should take into account the underlying geometry of the demonstration manifold; they should be geometry-aware. Successful task execution does not solely depend on the control of individual task variables. By controlling variables individually, a task might fail when one is perturbed and the others do not respond. Task execution also relies on couplings among task variables. These couplings describe functional relations which are often called synergies. In order to understand what-to-imitate, PbDmethods should be able to extract and encode synergies; they should be synergetic. In unstructured environments, it is unlikely that tasks are found in the same scenario twice. The circumstances under which a task is executed\u2014the task context\u2014are more likely to differ each time it is executed. Task context does not only vary during task execution, it also varies while learning and recognizing tasks. To be effective, a robot should be able to learn, recognize and synthesize skills in a variety of familiar and unfamiliar contexts; this can be achieved when its skill representation is context-adaptive. THE RIEMANNIAN APPROACH In this thesis, we present a skill representation that is geometry-aware, synergetic and context-adaptive. The presented method is probabilistic; it assumes that demonstrations are samples from an unknown probability distribution. This distribution is approximated using a Riemannian GaussianMixtureModel (GMM). Instead of using the \u2018standard\u2019 Euclidean Gaussian, we rely on the Riemannian Gaussian\u2014 a distribution akin the Gaussian, but defined on a Riemannian manifold. A Riev mannian manifold is a manifold\u2014a curved space which is locally Euclidean\u2014that provides a notion of distance. This notion is essential for statistical methods as such methods rely on a distance measure. Examples of Riemannian manifolds in robotics are: the Euclidean spacewhich is used for spatial data, forces or torques; the spherical manifolds, which can be used for orientation data defined as unit quaternions; and Symmetric Positive Definite (SPD) manifolds, which can be used to represent stiffness and manipulability. The Riemannian Gaussian is intrinsically geometry-aware. Its definition is based on the geometry of the manifold, and therefore takes into account the manifold curvature. In robotics, the manifold structure is often known beforehand. In the case of PbD, it follows from the structure of the demonstration data. Like the Gaussian distribution, the Riemannian Gaussian is defined by a mean and covariance. The covariance describes the variance and correlation among the state variables. These can be interpreted as local functional couplings among state variables: synergies. This makes the Riemannian Gaussian synergetic. Furthermore, information encoded in multiple Riemannian Gaussians can be fused using the Riemannian product of Gaussians. This feature allows us to construct a probabilistic context-adaptive task representation. CONTRIBUTIONS In particular, this thesis presents a generalization of existing methods of PbD, namely GMM-GMR and TP-GMM. This generalization involves the definition ofMaximum Likelihood Estimate (MLE), Gaussian conditioning and Gaussian product for the Riemannian Gaussian, and the definition of ExpectationMaximization (EM) and GaussianMixture Regression (GMR) for the Riemannian GMM. In this generalization, we contributed by proposing to use parallel transport for Gaussian conditioning. Furthermore, we presented a unified approach to solve the aforementioned operations using aGauss-Newton algorithm. We demonstrated how synergies, encoded in a Riemannian Gaussian, can be transformed into synergetic control policies using standard methods for LinearQuadratic Regulator (LQR). This is achieved by formulating the LQR problem in a (Euclidean) tangent space of the Riemannian manifold. Finally, we demonstrated how the contextadaptive Task-Parameterized Gaussian Mixture Model (TP-GMM) can be used for context inference\u2014the ability to extract context from demonstration data of known tasks. Our approach is the first attempt of context inference in the light of TP-GMM. Although effective, we showed that it requires further improvements in terms of speed and reliability. The efficacy of the Riemannian approach is demonstrated in a variety of scenarios. In shared control, the Riemannian Gaussian is used to represent control intentions of a human operator and an assistive system. Doing so, the properties of the Gaussian can be employed to mix their control intentions. This yields shared-control systems that continuously re-evaluate and assign control authority based on input confidence. The context-adaptive TP-GMMis demonstrated in a Pick & Place task with changing pick and place locations, a box-taping task with changing box sizes, and a trajectory tracking task typically found in industr

Advancing Robot Autonomy for Long-Horizon Tasks

Autonomous robots have real-world applications in diverse fields, such as mobile manipulation and environmental exploration, and many such tasks benefit from a hands-off approach in terms of human user involvement over a long task horizon. However, the level of autonomy achievable by a deployment is limited in part by the problem definition or task specification required by the system. Task specifications often require technical, low-level information that is unintuitive to describe and may result in generic solutions, burdening the user technically both before and after task completion. In this thesis, we aim to advance task specification abstraction toward the goal of increasing robot autonomy in real-world scenarios. We do so by tackling problems that address several different angles of this goal. First, we develop a way for the automatic discovery of optimal transition points between subtasks in the context of constrained mobile manipulation, removing the need for the human to hand-specify these in the task specification. We further propose a way to automatically describe constraints on robot motion by using demonstrated data as opposed to manually-defined constraints. Then, within the context of environmental exploration, we propose a flexible task specification framework, requiring just a set of quantiles of interest from the user that allows the robot to directly suggest locations in the environment for the user to study. We next systematically study the effect of including a robot team in the task specification and show that multirobot teams have the ability to improve performance under certain specification conditions, including enabling inter-robot communication. Finally, we propose methods for a communication protocol that autonomously selects useful but limited information to share with the other robots.Comment: PhD dissertation. 160 page

Learning from Demonstration with Weakly Supervised Disentanglement

Robotic manipulation tasks, such as wiping with a soft sponge, require control from multiple rich sensory modalities. Human-robot interaction, aimed at teaching robots, is difficult in this setting as there is potential for mismatch between human and machine comprehension of the rich data streams. We treat the task of interpretable learning from demonstration as an optimisation problem over a probabilistic generative model. To account for the high-dimensionality of the data, a high-capacity neural network is chosen to represent the model. The latent variables in this model are explicitly aligned with high-level notions and concepts that are manifested in a set of demonstrations. We show that such alignment is best achieved through the use of labels from the end user, in an appropriately restricted vocabulary, in contrast to the conventional approach of the designer picking a prior over the latent variables. Our approach is evaluated in the context of two table-top robot manipulation tasks performed by a PR2 robot -- that of dabbing liquids with a sponge (forcefully pressing a sponge and moving it along a surface) and pouring between different containers. The robot provides visual information, arm joint positions and arm joint efforts. We have made videos of the tasks and data available - see supplementary materials at: https://sites.google.com/view/weak-label-lfd.Comment: 18 pages, 16 figures, accepted at the International Conference on Learning Representations (ICLR) 2021, supplementary website at https://sites.google.com/view/weak-label-lf

TimewarpVAE: Simultaneous Time-Warping and Representation Learning of Trajectories

Human demonstrations of trajectories are an important source of training data for many machine learning problems. However, the difficulty of collecting human demonstration data for complex tasks makes learning efficient representations of those trajectories challenging. For many problems, such as for handwriting or for quasistatic dexterous manipulation, the exact timings of the trajectories should be factored from their spatial path characteristics. In this work, we propose TimewarpVAE, a fully differentiable manifold-learning algorithm that incorporates Dynamic Time Warping (DTW) to simultaneously learn both timing variations and latent factors of spatial variation. We show how the TimewarpVAE algorithm learns appropriate time alignments and meaningful representations of spatial variations in small handwriting and fork manipulation datasets. Our results have lower spatial reconstruction test error than baseline approaches and the learned low-dimensional representations can be used to efficiently generate semantically meaningful novel trajectories.Comment: 17 pages, 12 figure

K-VIL: Keypoints-based Visual Imitation Learning

Visual imitation learning provides efficient and intuitive solutions for robotic systems to acquire novel manipulation skills. However, simultaneously learning geometric task constraints and control policies from visual inputs alone remains a challenging problem. In this paper, we propose an approach for keypoint-based visual imitation (K-VIL) that automatically extracts sparse, object-centric, and embodiment-independent task representations from a small number of human demonstration videos. The task representation is composed of keypoint-based geometric constraints on principal manifolds, their associated local frames, and the movement primitives that are then needed for the task execution. Our approach is capable of extracting such task representations from a single demonstration video, and of incrementally updating them when new demonstrations become available. To reproduce manipulation skills using the learned set of prioritized geometric constraints in novel scenes, we introduce a novel keypoint-based admittance controller. We evaluate our approach in several real-world applications, showcasing its ability to deal with cluttered scenes, new instances of categorical objects, and large object pose and shape variations, as well as its efficiency and robustness in both one-shot and few-shot imitation learning settings. Videos and source code are available at https://sites.google.com/view/k-vil