Learning Stable Robotic Skills on Riemannian Manifolds

In this paper, we propose an approach to learn stable dynamical systems evolving on Riemannian manifolds. The approach leverages a data-efficient procedure to learn a diffeomorphic transformation that maps simple stable dynamical systems onto complex robotic skills. By exploiting mathematical tools from differential geometry, the method ensures that the learned skills fulfill the geometric constraints imposed by the underlying manifolds, such as unit quaternion (UQ) for orientation and symmetric positive definite (SPD) matrices for impedance, while preserving the convergence to a given target. The proposed approach is firstly tested in simulation on a public benchmark, obtained by projecting Cartesian data into UQ and SPD manifolds, and compared with existing approaches. Apart from evaluating the approach on a public benchmark, several experiments were performed on a real robot performing bottle stacking in different conditions and a drilling task in cooperation with a human operator. The evaluation shows promising results in terms of learning accuracy and task adaptation capabilities.Comment: 16 pages, 10 figures, journa

Transverse Contraction Criteria for Existence, Stability, and Robustness of a Limit Cycle

This paper derives a differential contraction condition for the existence of an orbitally-stable limit cycle in an autonomous system. This transverse contraction condition can be represented as a pointwise linear matrix inequality (LMI), thus allowing convex optimization tools such as sum-of-squares programming to be used to search for certificates of the existence of a stable limit cycle. Many desirable properties of contracting dynamics are extended to this context, including preservation of contraction under a broad class of interconnections. In addition, by introducing the concepts of differential dissipativity and transverse differential dissipativity, contraction and transverse contraction can be established for large scale systems via LMI conditions on component subsystems.Comment: 6 pages, 1 figure. Conference submissio

Boosting Deep Open World Recognition by Clustering

While convolutional neural networks have brought significant advances in robot vision, their ability is often limited to closed world scenarios, where the number of semantic concepts to be recognized is determined by the available training set. Since it is practically impossible to capture all possible semantic concepts present in the real world in a single training set, we need to break the closed world assumption, equipping our robot with the capability to act in an open world. To provide such ability, a robot vision system should be able to (i) identify whether an instance does not belong to the set of known categories (i.e. open set recognition), and (ii) extend its knowledge to learn new classes over time (i.e. incremental learning). In this work, we show how we can boost the performance of deep open world recognition algorithms by means of a new loss formulation enforcing a global to local clustering of class-specific features. In particular, a first loss term, i.e. global clustering, forces the network to map samples closer to the class centroid they belong to while the second one, local clustering, shapes the representation space in such a way that samples of the same class get closer in the representation space while pushing away neighbours belonging to other classes. Moreover, we propose a strategy to learn class-specific rejection thresholds, instead of heuristically estimating a single global threshold, as in previous works. Experiments on RGB-D Object and Core50 datasets show the effectiveness of our approach.Comment: IROS/RAL 202

Dynamic Facial Expression Generation on Hilbert Hypersphere with Conditional Wasserstein Generative Adversarial Nets

In this work, we propose a novel approach for generating videos of the six basic facial expressions given a neutral face image. We propose to exploit the face geometry by modeling the facial landmarks motion as curves encoded as points on a hypersphere. By proposing a conditional version of manifold-valued Wasserstein generative adversarial network (GAN) for motion generation on the hypersphere, we learn the distribution of facial expression dynamics of different classes, from which we synthesize new facial expression motions. The resulting motions can be transformed to sequences of landmarks and then to images sequences by editing the texture information using another conditional Generative Adversarial Network. To the best of our knowledge, this is the first work that explores manifold-valued representations with GAN to address the problem of dynamic facial expression generation. We evaluate our proposed approach both quantitatively and qualitatively on two public datasets; Oulu-CASIA and MUG Facial Expression. Our experimental results demonstrate the effectiveness of our approach in generating realistic videos with continuous motion, realistic appearance and identity preservation. We also show the efficiency of our framework for dynamic facial expressions generation, dynamic facial expression transfer and data augmentation for training improved emotion recognition models