In this work a Cartesian impedance controller for flexible joint robots was proposed. The control approach was based on the stability theory for cascaded systems. In the proposed controller an inner torque feedback loop decouples the torque dynamics from the rigid body dynamics. For the implementation of the impedance behaviour a control law well known from rigid body robotics is used in combination with the torque controller. It should also be mentioned that, apart from the considered impedance control problem, different rigid body controllers can be applied to the flexible joint model analogously to the procedure described herein. For the proof of the asymptotic stability of the closed-loop system one can take advantage of Theorem 2. Appendix In this appendix, a short lemma about uniform global boundedness of the solutions of time-varying differential equations is presented, which is used in Section 5.3 for the proof of uniform global asymptotic stability of the Cartesian impedance controller. Consider a time-varying system of the form (A.1) x = f ( x, t ) , with state x n . In order to show that the solutions of (A.1) are uniformly globally bounded (according to Definition A.1, which is taken from (Loria, 2001)), the following Lemma A.1 is usefull. This lemma can be proven easily based on the theorems presented in (Khalil, 2002).

By the dawn of the new millennium, robotics has undergone a major transf- mation in scope and dimensions. This expansion has been brought about by the maturity of the ?eld and the advances in its related technologies. From a largely dominant industrial focus, robotics has been rapidly expanding into the challenges of the human world. The new generation of robots is expected to safely and dependably co-habitat with humans in homes, workplaces, and c- munities, providing support in services, entertainment, education, healthcare, manufacturing, and assistance. Beyond its impact on physical robots, the body of knowledge robotics has produced is revealing a much wider rangeof applications reaching across diverse research areas and scienti?c disciplines, such as: biomechanics, haptics, n- rosciences, virtual simulation, animation, surgery, and sensor networks among others. In return, the challenges of the new emerging areas are proving an ab- dant source of stimulation and insights for the ?eld of robotics. It is indeed at the intersection of disciplines that the most striking advances happen. The goal of the series of Springer Tracts in Advanced Robotics (STAR) is to bring, in a timely fashion, the latest advances and developments in robotics on thebasisoftheirsigni?canceandquality.Itisourhopethatthewiderdissemi- tion of research developments will stimulate more exchanges and collaborations among the research community and contribute to further advancement of this rapidly growing ?eld.

Joint flexibility from harmonic or direct drives or flexible couplings limits the performance of robots. Performance can be improved by taking into account the fast dynamics that are introduced by joint flexibility. High gain acceleration feedback from the link angles simplifies the robot dynamics, but is limited by joint flexibility. One solution is to use joint torque feedback to stabilize the fast dynamics. In light of this, drive systems that incorporate joint torque sensors are being developed. Flexible Joint Robots is the first book to consider the myriad problems and potential solutions that affect flexible joint robot design. The book covers fundamental concepts, including joint torque feedback control laws, acceleration feedback, and adaptive control laws. It presents a dynamic model of a flexible joint robot in several coordinate systems and includes an analysis of the fast dynamics.

This book introduces an unified function approximation approach to the control of uncertain robot manipulators containing general uncertainties. It works for free space tracking control as well as compliant motion control. It is applicable to the rigid robot and the flexible joint robot. Even with actuator dynamics, the unified approach is still feasible. All these features make the book stand out from other existing publications.

Scientific Study from the year 2020 in the subject Engineering - Robotics, University of Baghdad (University of Baghdad, Department of Aeronautical Engineering, Baghdad, Iraq), language: English, abstract: This paper is concerned with summarizing the categories of impedance control showing the feature and the limitations of each category. Much attention is paid to variable impedance control considering the possible control schemes, performance, the stability, the integration of constant/variable compliant elements with the host robots, etc. For a long time, the robotics community concentrated on improving the performance of the robotic systems in free space. The advanced control strategies for position control could not be sufficient to stabilize the motion of robots in constrained spaces. In general, there are two categories of force control schemes with miscellaneous subdivisions: hybrid position-force control and impedance control. The former is well suitable for well-known interaction environment, however, it does not consider the dynamic interaction between robot end-effector and the environment. In contrast, impedance control includes regulation and stabilization of robot motion via creating a mathematical relationship between the interaction forces and the reference trajectories. In general, a mass-spring-damper impedance filter is used for stabilization purposes. Tuning the parameters of the impedance filter is not trivial and may lead to unstable contact if an unsuitable strategy is used. The human, however, has amazing control systems with advanced biological actuators. He/she can manipulate the muscles stiffness to softly comply to the interaction forces. Accordingly, the parameters of the impedance filter should be time-varying rather than value-constant in order to meet the human behavior during interaction tasks.

This book introduces novel thinking and techniques to the control of robotic manipulation. In particular, the concept of teleimpedance control as an alternative method to bilateral force-reflecting teleoperation control for robotic manipulation is introduced. In teleimpedance control, a compound reference command is sent to the slave robot including both the desired motion trajectory and impedance profile, which are then realized by the remote controller. This concept forms a basis for the development of the controllers for a robotic arm, a dual-arm setup, a synergy-driven robotic hand, and a compliant exoskeleton for improved interaction performance.

The second edition of this handbook provides a state-of-the-art overview on the various aspects in the rapidly developing field of robotics. Reaching for the human frontier, robotics is vigorously engaged in the growing challenges of new emerging domains. Interacting, exploring, and working with humans, the new generation of robots will increasingly touch people and their lives. The credible prospect of practical robots among humans is the result of the scientific endeavour of a half a century of robotic developments that established robotics as a modern scientific discipline. The ongoing vibrant expansion and strong growth of the field during the last decade has fueled this second edition of the Springer Handbook of Robotics. The first edition of the handbook soon became a landmark in robotics publishing and won the American Association of Publishers PROSE Award for Excellence in Physical Sciences & Mathematics as well as the organization’s Award for Engineering & Technology. The second edition of the handbook, edited by two internationally renowned scientists with the support of an outstanding team of seven part editors and more than 200 authors, continues to be an authoritative reference for robotics researchers, newcomers to the field, and scholars from related disciplines. The contents have been restructured to achieve four main objectives: the enlargement of foundational topics for robotics, the enlightenment of design of various types of robotic systems, the extension of the treatment on robots moving in the environment, and the enrichment of advanced robotics applications. Further to an extensive update, fifteen new chapters have been introduced on emerging topics, and a new generation of authors have joined the handbook’s team. A novel addition to the second edition is a comprehensive collection of multimedia references to more than 700 videos, which bring valuable insight into the contents. The videos can be viewed directly augmented into the text with a smartphone or tablet using a unique and specially designed app. Springer Handbook of Robotics Multimedia Extension Portal: http://handbookofrobotics.org/

This book introduces an unified function approximation approach to the control of uncertain robot manipulators containing general uncertainties. It works for free space tracking control as well as compliant motion control. It is applicable to the rigid robot and the flexible joint robot. Even with actuator dynamics, the unified approach is still feasible. All these features make the book stand out from other existing publications.