Riemannian geometry as a unifying theory for robot motion learning and control

Riemannian geometry is a mathematical field which has been the cornerstone of revolutionary scientific discoveries such as the theory of general relativity. Despite early uses in robot design and recent applications for exploiting data with specific geometries, it mostly remains overlooked in robotics. With this blue sky paper, we argue that Riemannian geometry provides the most suitable tools to analyze and generate well-coordinated, energy-efficient motions of robots with many degrees of freedom. Via preliminary solutions and novel research directions, we discuss how Riemannian geometry may be leveraged to design and combine physically-meaningful synergies for robotics, and how this theory also opens the door to coupling motion synergies with perceptual inputs.Comment: Published as a blue sky paper at ISRR'22. 8 pages, 2 figures. Video at https://youtu.be/XblzcKRRIT

Geometry-aware Manipulability Learning, Tracking and Transfer

Body posture influences human and robots performance in manipulation tasks, as appropriate poses facilitate motion or force exertion along different axes. In robotics, manipulability ellipsoids arise as a powerful descriptor to analyze, control and design the robot dexterity as a function of the articulatory joint configuration. This descriptor can be designed according to different task requirements, such as tracking a desired position or apply a specific force. In this context, this paper presents a novel \emph{manipulability transfer} framework, a method that allows robots to learn and reproduce manipulability ellipsoids from expert demonstrations. The proposed learning scheme is built on a tensor-based formulation of a Gaussian mixture model that takes into account that manipulability ellipsoids lie on the manifold of symmetric positive definite matrices. Learning is coupled with a geometry-aware tracking controller allowing robots to follow a desired profile of manipulability ellipsoids. Extensive evaluations in simulation with redundant manipulators, a robotic hand and humanoids agents, as well as an experiment with two real dual-arm systems validate the feasibility of the approach.Comment: Accepted for publication in the Intl. Journal of Robotics Research (IJRR). Website: https://sites.google.com/view/manipulability. Code: https://github.com/NoemieJaquier/Manipulability. 24 pages, 20 figures, 3 tables, 4 appendice

Analysis and Transfer of Human Movement Manipulability in Industry-like Activities

Humans exhibit outstanding learning, planning and adaptation capabilities while performing different types of industrial tasks. Given some knowledge about the task requirements, humans are able to plan their limbs motion in anticipation of the execution of specific skills. For example, when an operator needs to drill a hole on a surface, the posture of her limbs varies to guarantee a stable configuration that is compatible with the drilling task specifications, e.g. exerting a force orthogonal to the surface. Therefore, we are interested in analyzing the human arms motion patterns in industrial activities. To do so, we build our analysis on the so-called manipulability ellipsoid, which captures a posture-dependent ability to perform motion and exert forces along different task directions. Through thorough analysis of the human movement manipulability, we found that the ellipsoid shape is task dependent and often provides more information about the human motion than classical manipulability indices. Moreover, we show how manipulability patterns can be transferred to robots by learning a probabilistic model and employing a manipulability tracking controller that acts on the task planning and execution according to predefined control hierarchies.Comment: Accepted for publication in IROS'20. Website: https://sites.google.com/view/manipulability/home . Video: https://youtu.be/q0GZwvwW9A

On the Design of Region-Avoiding Metrics for Collision-Safe Motion Generation on Riemannian Manifolds

The generation of energy-efficient and dynamic-aware robot motions that satisfy constraints such as joint limits, self-collisions, and collisions with the environment remains a challenge. In this context, Riemannian geometry offers promising solutions by identifying robot motions with geodesics on the so-called configuration space manifold. While this manifold naturally considers the intrinsic robot dynamics, constraints such as joint limits, self-collisions, and collisions with the environment remain overlooked. In this paper, we propose a modification of the Riemannian metric of the configuration space manifold allowing for the generation of robot motions as geodesics that efficiently avoid given regions. We introduce a class of Riemannian metrics based on barrier functions that guarantee strict region avoidance by systematically generating accelerations away from no-go regions in joint and task space. We evaluate the proposed Riemannian metric to generate energy-efficient, dynamic-aware, and collision-free motions of a humanoid robot as geodesics and sequences thereof.Comment: Accepted for publication in IEEE/RSJ Intl. Conf. on Intelligent Robots and Systems (IROS) 2023. 8 pages, 7 figures, accompanying video at https://youtu.be/qT43XgYOlU

A Riemannian Take on Human Motion Analysis and Retargeting

Dynamic motions of humans and robots are widely driven by posture-dependent nonlinear interactions between their degrees of freedom. However, these dynamical effects remain mostly overlooked when studying the mechanisms of human movement generation. Inspired by recent works, we hypothesize that human motions are planned as sequences of geodesic synergies, and thus correspond to coordinated joint movements achieved with piecewise minimum energy. The underlying computational model is built on Riemannian geometry to account for the inertial characteristics of the body. Through the analysis of various human arm motions, we find that our model segments motions into geodesic synergies, and successfully predicts observed arm postures, hand trajectories, as well as their respective velocity profiles. Moreover, we show that our analysis can further be exploited to transfer arm motions to robots by reproducing individual human synergies as geodesic paths in the robot configuration space.Comment: Accepted for publication in IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) 202

Active Improvement of Control Policies with Bayesian Gaussian Mixture Model

Learning from demonstration (LfD) is an intuitive framework allowing non-expert users to easily (re-)program robots. However, the quality and quantity of demonstrations have a great influence on the generalization performances of LfD approaches. In this paper, we introduce a novel active learning framework in order to improve the generalization capabilities of control policies. The proposed approach is based on the epistemic uncertainties of Bayesian Gaussian mixture models (BGMMs). We determine the new query point location by optimizing a closed-form information-density cost based on the quadratic R\'enyi entropy. Furthermore, to better represent uncertain regions and to avoid local optima problem, we propose to approximate the active learning cost with a Gaussian mixture model (GMM). We demonstrate our active learning framework in the context of a reaching task in a cluttered environment with an illustrative toy example and a real experiment with a Panda robot.Comment: Accepted for publication in IROS'2

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