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

Motion Mappings for Continuous Bilateral Teleoperation

Mapping operator motions to a robot is a key problem in teleoperation. Due to differences between workspaces, such as object locations, it is particularly challenging to derive smooth motion mappings that fulfill different goals (e.g. picking objects with different poses on the two sides or passing through key points). Indeed, most state-of-the-art methods rely on mode switches, leading to a discontinuous, low-transparency experience. In this paper, we propose a unified formulation for position, orientation and velocity mappings based on the poses of objects of interest in the operator and robot workspaces. We apply it in the context of bilateral teleoperation. Two possible implementations to achieve the proposed mappings are studied: an iterative approach based on locally-weighted translations and rotations, and a neural network approach. Evaluations are conducted both in simulation and using two torque-controlled Franka Emika Panda robots. Our results show that, despite longer training times, the neural network approach provides faster mapping evaluations and lower interaction forces for the operator, which are crucial for continuous, real-time teleoperation.Comment: Accepted for publication at the IEEE Robotics and Automation Letters (RA-L

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

Fast diffeomorphic matching to learn globally asymptotically stable nonlinear dynamical systems

International audienceWe propose a new diffeomorphic matching algorithm and use it to learn nonlinear dynamical systems with the guarantee that the learned systems have global asymptotic stability. For a given set of demonstration trajectories, we compute a diffeomorphism that maps forward orbits of a reference stable time-invariant system onto the demonstrations, thereby deforming the whole reference system into one that reproduces the demonstrations, and is still stable

Compliant control of Uni/ Multi- robotic arms with dynamical systems

Accomplishment of many interactive tasks hinges on the compliance of humans. Humans demonstrate an impressive capability of complying their behavior and more particularly their motions with the environment in everyday life. In humans, compliance emerges from different facets. For example, many daily activities involve reaching for grabbing tasks, where compliance appears in a form of coordination. Humans comply their handsâ motions with each other and with that of the object not only to establish a stable contact and to control the impact force but also to overcome sensorimotor imprecisions. Even though compliance has been studied from different aspects in humans, it is primarily related to impedance control in robotics. In this thesis, we leverage the properties of autonomous dynamical systems (DS) for immediate re-planning and introduce active complaint motion generators for controlling robots in three different scenarios, where compliance does not necessarily mean impedance and hence it is not directly related to control in the force/velocity domain. In the first part of the thesis, we propose an active compliant strategy for catching objects in flight, which is less sensitive to the timely control of the interception. The soft catching strategy consists in having the robot following the object for a short period of time. This leaves more time for the fingers to close on the object at the interception and offers more robustness than a âhardâ catching method in which the hand waits for the object at the chosen interception point. We show theoretically that the resulting DS will intercept the object at the intercept point, at the right time with the desired velocity direction. Stability and convergence of the approach are assessed through Lyapunov stability theory. In the second part, we propose a unified compliant control architecture for coordinately reaching for grabbing a moving object by a multi-arm robotic system. Due to the complexity of the task and of the system, each arm complies not only with the objectâs motion but also with the motion of other arms, in both task and joint spaces. At the task-space level, we propose a unified dynamical system that endows the multi-arm system with both synchronous and asynchronous behaviors and with the capability of smoothly transitioning between the two modes. At the joint space level, the compliance between the arms is achieved by introducing a centralized inverse kinematics (IK) solver under self-collision avoidance constraints; formulated as a quadratic programming problem (QP) and solved in real-time. In the last part, we propose a compliant dynamical system for stably transitioning from free motions to contacts. In this part, by modulating the robot's velocity in three regions, we show theoretically and empirically that the robot can (I) stably touch the contact surface (II) at a desired location, and (III) leave the surface or stop on the surface at a desired point