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

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 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

Control and Learning of Compliant Manipulation Skills

Humans demonstrate an impressive capability to manipulate fragile objects without damaging them, graciously controlling the force and position of hands or tools. Traditionally, robotics has favored position control over force control to produce fast, accurate and repeatable motion. For extending the applicability of robotic manipulators outside the strictly controlled environments of industrial work cells, position control is inadequate. Tasks that involve contact with objects whose positions are not known with perfect certainty require a controller that regulates the relationship between positional deviations and forces on the robot. This problem is formalized in the impedance control framework, which focuses the robot control problem on the interaction between the robot and its environment. By adjusting the impedance parameters, the behavior of the robot can be adapted to the need of the task. However, it is often difficult to specify formally how the impedance should vary for best performance. Furthermore, fast it can be shown that careless variation of the impedance can lead to unstable regulation or tracking even in free motion. In the first part of the thesis, the problem of how to define a varying impedance for a task is addressed. A haptic human-robot interface that allows a human supervisor to teach impedance variations by physically interacting with the robot during task execution is introduced. It is shown that the interface can be used to enhance the performance in several manipulation tasks. Then, the problem of stable control with varying impedance is addressed. Along with a theoretical discussion on this topic, a sufficient condition for stable varying stiffness and damping is provided. In the second part of the thesis, we explore more complex manipulation scenarios via online generation of the robot trajectory. This is done along two axes 1) learning how to react to contact forces in insertion tasks which are crucial for assembly operations and 2) autonomous Dynamical Systems (DS) for motion representation with the capability to encode a family of trajectories rather than a fixed, time-dependent reference. A novel framework for task representation using DS is introduced, termed Locally Modulated Dynamical Systems (LMDS). LMDS differs from existing DS estimation algorithms in that it supports non-parametric and incremental learning all the while guaranteeing that the resulting DS is globally stable at an attractor point. To combine the advantages of DS motion generation with impedance control, a novel controller for tasks described by first order DS is proposed. The controller is passive, and has the properties of an impedance controller with the added flexibility of a DS motion representation instead of a time-indexed trajectory

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

Learning Externally Modulated Dynamical Systems

Dynamical Systems (DS) are often used to represent motion, with the advantage of being easy to learn from demonstrations. We present a method to modulate DS depending on an external signal, extending our previous work on Locally Modulated DS (LMDS, Kronander 2017). We present two applications of our system, which would not have been possible to achieve without taking external sensing into account in the DS motion formulation. The first application is a task of localization and grasping of objects, using our previous work on compliant tactile exploration. We successfully localize and grasp objects whose position is unknown, using touch in a simulated environment. In the second application, we teach a robot how to react to collisions in order to navigate between obstacles while reaching