An Energy-based Approach to Ensure the Stability of Learned Dynamical Systems

Non-linear dynamical systems represent a compact, flexible, and robust tool for reactive motion generation. The effectiveness of dynamical systems relies on their ability to accurately represent stable motions. Several approaches have been proposed to learn stable and accurate motions from demonstration. Some approaches work by separating accuracy and stability into two learning problems, which increases the number of open parameters and the overall training time. Alternative solutions exploit single-step learning but restrict the applicability to one regression technique. This paper presents a single-step approach to learn stable and accurate motions that work with any regression technique. The approach makes energy considerations on the learned dynamics to stabilize the system at run-time while introducing small deviations from the demonstrated motion. Since the initial value of the energy injected into the system affects the reproduction accuracy, it is estimated from training data using an efficient procedure. Experiments on a real robot and a comparison on a public benchmark shows the effectiveness of the proposed approach.Comment: Accepted at the International Conference on Robotics and Automation 202

Antifragile Control Systems: The case of mobile robot trajectory tracking in the presence of uncertainty

Mobile robots are ubiquitous. Such vehicles benefit from well-designed and calibrated control algorithms ensuring their task execution under precise uncertainty bounds. Yet, in tasks involving humans in the loop, such as elderly or mobility impaired, the problem takes a new dimension. In such cases, the system needs not only to compensate for uncertainty and volatility in its operation but at the same time to anticipate and offer responses that go beyond robust. Such robots operate in cluttered, complex environments, akin to human residences, and need to face during their operation sensor and, even, actuator faults, and still operate. This is where our thesis comes into the foreground. We propose a new control design framework based on the principles of antifragility. Such a design is meant to offer a high uncertainty anticipation given previous exposure to failures and faults, and exploit this anticipation capacity to provide performance beyond robust. In the current instantiation of antifragile control applied to mobile robot trajectory tracking, we provide controller design steps, the analysis of performance under parametrizable uncertainty and faults, as well as an extended comparative evaluation against state-of-the-art controllers. We believe in the potential antifragile control has in achieving closed-loop performance in the face of uncertainty and volatility by using its exposures to uncertainty to increase its capacity to anticipate and compensate for such events

Learning Barrier Functions for Constrained Motion Planning with Dynamical Systems

Stable dynamical systems are a flexible tool to plan robotic motions in real-time. In the robotic literature, dynamical system motions are typically planned without considering possible limitations in the robot's workspace. This work presents a novel approach to learn workspace constraints from human demonstrations and to generate motion trajectories for the robot that lie in the constrained workspace. Training data are incrementally clustered into different linear subspaces and used to fit a low dimensional representation of each subspace. By considering the learned constraint subspaces as zeroing barrier functions, we are able to design a control input that keeps the system trajectory within the learned bounds. This control input is effectively combined with the original system dynamics preserving eventual asymptotic properties of the unconstrained system. Simulations and experiments on a real robot show the effectiveness of the proposed approach

Merging Position and Orientation Motion Primitives

In this paper, we focus on generating complex robotic trajectories by merging sequential motion primitives. A robotic trajectory is a time series of positions and orientations ending at a desired target. Hence, we first discuss the generation of converging pose trajectories via dynamical systems, providing a rigorous stability analysis. Then, we present approaches to merge motion primitives which represent both the position and the orientation part of the motion. Developed approaches preserve the shape of each learned movement and allow for continuous transitions among succeeding motion primitives. Presented methodologies are theoretically described and experimentally evaluated, showing that it is possible to generate a smooth pose trajectory out of multiple motion primitives

Learning Deep Robotic Skills on Riemannian manifolds

In this paper, we propose RiemannianFlow, a deep generative model that allows robots to learn complex and stable skills evolving on Riemannian manifolds. Examples of Riemannian data in robotics include stiffness (symmetric and positive definite matrix (SPD)) and orientation (unit quaternion (UQ)) trajectories. For Riemannian data, unlike Euclidean ones, different dimensions are interconnected by geometric constraints which have to be properly considered during the learning process. Using distance preserving mappings, our approach transfers the data between their original manifold and the tangent space, realizing the removing and re-fulfilling of the geometric constraints. This allows to extend existing frameworks to learn stable skills from Riemannian data while guaranteeing the stability of the learning results. The ability of RiemannianFlow to learn various data patterns and the stability of the learned models are experimentally shown on a dataset of manifold motions. Further, we analyze from different perspectives the robustness of the model with different hyperparameter combinations. It turns out that the model's stability is not affected by different hyperparameters, a proper combination of the hyperparameters leads to a significant improvement (up to 27.6%) of the model accuracy. Last, we show the effectiveness of RiemannianFlow in a real peg-in-hole (PiH) task where we need to generate stable and consistent position and orientation trajectories for the robot starting from different initial poses

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

Imitation Learning-based Visual Servoing for Tracking Moving Objects

In everyday life collaboration tasks between human operators and robots, the former necessitate simple ways for programming new skills, the latter have to show adaptive capabilities to cope with environmental changes. The joint use of visual servoing and imitation learning allows us to pursue the objective of realizing friendly robotic interfaces that (i) are able to adapt to the environment thanks to the use of visual perception and (ii) avoid explicit programming thanks to the emulation of previous demonstrations. This work aims to exploit imitation learning for the visual servoing paradigm to address the specific problem of tracking moving objects. In particular, we show that it is possible to infer from data the compensation term required for realizing the tracking controller, avoiding the explicit implementation of estimators or observers. The effectiveness of the proposed method has been validated through simulations with a robotic manipulator.Comment: International Workshop on Human-Friendly Robotics (HFR), 202