Aude Billard - Learning for Adaptive and Reactive Robot Control: A Dynamical Systems Approach (Intelligent Robotics and Autonomous Agents series)

Intelligent Robotics and Autonomous Agents

Edited by Ronald C. Arkin

A complete list of the books in the Intelligent Robotics and Autonomous Agents series appears at the back of this book

Learning for Adaptive and Reactive Robot Control

A Dynamical Systems Approach

Aude Billard, Sina Mirrazavi, and Nadia Figueroa

The MIT Press

Cambridge, Massachusetts

London, England

2022 The Massachusetts Institute of Technology

This work is subject to a Creative Commons CC-BY-NC-SA license. Subject to such license, all rights are reserved.

The MIT Press would like to thank the anonymous peer reviewers who provided comments on drafts of this book. The generous work of academic experts is essential for establishing the authority and quality of our publications. We acknowledge with gratitude the contributions of these otherwise uncredited readers.

Library of Congress Cataloging-in-Publication Data

Names: Billard, Aude, author. | Mirrazavi, Sina, author. | Figueroa, Nadia, author.

Title: Learning for adaptive and reactive robot control: a dynamical systems approach / Aude Billard, Sina Mirrazavi, Nadia Figueroa.

Description: Cambridge, Massachusetts: The MIT Press, [2021] | Series: Intelligent robotics and autonomous agents series | Includes bibliographical references and index.

Identifiers: LCCN 2021005086 | ISBN 9780262046169 (hardcover)

Subjects: LCSH: Robots--Control systems--Mathematical models. | Machine learning. | Autonomous robots.

Classification: LCC TJ211.35.B55 2021 | DDC 629.8/92631--dc23

LC record available at https://lccn.loc.gov/2021005086

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List of Figures

Structure of the chapters in this book

A robot is tasked to grasp a static ball (left). There is an infinite number of paths, which change depending on the initial configuration (some of which are shown at right).

When the robot is subjected to a disturbance that sends it away from its planned trajectory, a new path must be computed. When the path is described through an explicit set of points in time, the time T to the target must also be recomputed along with the path, to prevent the robot from exceeding its speed limit. When the path is linear (left), computing the new time T is immediate. When the path is nonlinear (right), it is not easy to determine both the new path and the new time, as this depends on many factors, and new constraints may need to be taken into account in the optimization.

Different solutions to move a four-joint robot arm, both leading to a straight path in Cartesian space. When optimizing for minimal effort (minimal torque), the solution on the right, which moves the second joint, may be preferred over the solution on the left, which moves the first joint, as the second joint carries a lower mass than the first joint.

Representing the multiplicity of paths to the ball through a time-invariant DS that is asymptotically stable at the target, denoted with x*. Each line represents the temporal evolution of the DS from an initial state.

(Left) The robot is set to follow the dark gray path toward the ball located at x*, but the ball is moved before the robot reaches the ball. If the new location of the ball is the unique stable point of the DS, and if the DS is asymptotically stable at the balls location, there is a unique path that will lead the robot to the ball. This path is generated by following the vector field of the DS, as illustrated on the right side.

Snapshot of the humanoid robot iCub reaching for a ball rolling down a slope. The path of the ball is intersected as it hits an obstacle along the way. The robots arm adapts its path to the new balls trajectory. It speeds up and slows down as necessary to meet the ball on time and at the right location once the ball reaches the end of the table.

To be robust to changes in the orientation and location of an object, one can place the origin and frame of reference on the object.

Learning an estimate of the control law using machine learning techniques such as support vector regression (top) or neural networks (bottom) ensures a tight fit with the data, but it does not guarantee convergence at the attractor. Training data are illustrated in dark (red) lines. The learned flow is illustrated in grayscale. The pink trajectory illustrates the prediction of the model when starting from one of the training points. In both cases, the trajectory drifts once it reaches the attractor.

Examples of a system composed of two dynamical systems (DS) with two separate attractors. For each DS, a set of three sample trajectories is generated to train the model, delineated by the dark lines. The augmented SVM approach (see section 4.1) learns a partition of the two regions and the dynamics in each region. The local basin of attraction for each dynamics can be reconstructed by following the isolines of the learned energy function.

(top) Encoding of two DSs to catch an object at the neck or at the tail. (Middle and bottom) At run time, the robot switches across the two DSs to catch either the neck or the tail of the falling glass or bottle.

A modulation of a nominal linear DS allows for avoiding obstacles while preserving stability guarantees at the attractor [] (right) by learning a local rotation from data points provided in the orange region.

Coupling eye, arm, and hand movement through explicit dependency on each limbs DS simplifies the control and ensures that the eye, arm, and hand move in synch if the object suddenly moves, so as to close simultaneously on the object in its new location (a). It also allows to react rapidly to obstacles moving on the way (b).

To reach and follow the dynamics of the object, we combine two DSs. The first brings the arm toward the object while the other aligns the velocity vector with that of the object.

Robots working side by side with humans, as envisioned in a collaborative robotics paradigm, presents dangers to their human coworkers (a). To mitigate these dangers, one can render the robot compliant (b). A compliant robot would absorb the force resulting from undesired contact with humans (c), thereby mitigating the risk of injury.

Impedance control combined with DSs. The stiffness is controlled locally through an eigenvalue and eigenvector decomposition of the stiffness matrix. The first eigenvector aligns with the DS flow, whereas the second eigenvector and eigenvalue control for the compliance to external disturbances.

Force control can be achieved with DSs through decomposition of the flow with the normal component against the surface of the object generating the desired force []. Coupling two force-control DSs enables two robot arms to move in synch and balance the forces to lift and hold the box in the air (left figure), even with disturbances, such as when a human rotates the two robot arms (middle figure