A simple PD controller for robots with elastic joints

doi:10.1109/9.90238

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A simple PD controller for robots with elastic joints

Journal Article•DOI•

A simple PD controller for robots with elastic joints

01 Oct 1991-IEEE Transactions on Automatic Control (IEEE)-Vol. 36, Iss: 10, pp 1208-1213

TL;DR: In this paper, the point-to-point control of a manipulator with three revolute elastic joints is considered and it is shown that a simple PD controller, similar to that used for rigid robots, suffices to globally stabilize the elastic joint robots about a reference position.

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Abstract: The point-to-point control of manipulators having elastic joints is considered. It is shown that a simple PD (proportional plus derivative) controller, similar to that used for rigid robots, suffices to globally stabilize the elastic joint robots about a reference position. A robustness analysis is also given with respect to uncertainties on the robot parameters. The results of numerical simulation tests of a manipulator with three revolute elastic joints are presented. >

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Journal Article•DOI•

Dynamic analysis of flexible manipulators, a literature review

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Santosha K. Dwivedy¹, Peter Eberhard²•Institutions (2)

Indian Institute of Technology Guwahati¹, University of Stuttgart²

01 Jul 2006-Mechanism and Machine Theory

TL;DR: A survey of the literature related to dynamic analyses of flexible robotic manipulators has been carried out in this article, where both link and joint flexibility are considered in this work and an effort has been made to critically examine the methods used in these analyses, their advantages and shortcomings and possible extension of these methods to be applied to a general class of problems.

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791 citations

Cites methods from "A simple PD controller for robots w..."

...Tomei [354] studied robots with elastic joints using a simple PD controller....
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...[354] P....
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Journal Article•DOI•

A Unified Passivity-based Control Framework for Position, Torque and Impedance Control of Flexible Joint Robots

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Alin Albu-Schaffer¹, Christian Ott¹, Gerd Hirzinger¹•Institutions (1)

German Aerospace Center¹

01 Jan 2007-The International Journal of Robotics Research

TL;DR: In this article, a general passivity-based framework for the control of flexible joint robots is described, and the relations between the individual contributions are highlighted, and an overview of several applications are given in which the controllers have been applied.

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Abstract: This paper describes a general passivity-based framework for the control of flexible joint robots. Recent results on torque, position, as well as impedance control of flexible joint robots are summarized, and the relations between the individual contributions are highlighted. It is shown that an inner torque feedback loop can be incorporated into a passivity-based analysis by interpreting torque feedback in terms of shaping of the motor inertia. This result, which implicitly was already included in earlier work on torque and position control, can also be used for the design of impedance controllers. For impedance control, furthermore, potential energy shaping is of special interest. It is shown how, based only on the motor angles, a potential function can be designed which simultaneously incorporates gravity compensation and a desired Cartesian stiffness relation for the link angles. All the presented controllers were experimentally evaluated on DLR lightweight robots and their performance and robustness shown with respect to uncertain model parameters. Experimental results with position controllers as well as an impact experiment are presented briefly, and an overview of several applications is given in which the controllers have been applied.

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685 citations

Cites background or methods from "A simple PD controller for robots w..."

...The well known stability analysis for PD control and gravity compensation of flexible joint robots (Tomei 1991) directly applies also to the case of the controller given by (6), (10)....
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...The error θ̃ = θ − θ d is computed using a desired value θ d = qd + K−1g(qd), (5) This constitutes an extension of the PD controller from Tomei (1991) to a full state feedback....
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...The 8. θ 0 and q0 stand for the equilibrium values of θ and q . usual solution adopted in Tomei (1991), Albu-Achäffer et al. (2001), Zollo et al. (2005), Ott et al. (2004), Albu-Schäffer et al. (2004b) in order to ensure the passivity in {q̇ , −τ a} is to chose u as a function of θ and its…...
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...The position control problem for flexible joint robots has been treated extensively in the robot control literature (Spong 1987; Tomei 1991; Brogliato et al. 1995; De Luca 2000; Lin and Goldenberg 1995)....
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...The work most closely related to this paper can be traced back to Takegaki and Arimoto (1981) for the rigid robot case and contains, among others (Tomei 1991; Kelly 1997; Kelly and Santibanez 1998; Ortega et al. 1995; Lozano et al. 2000; Zollo et al. 2005)....
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Journal Article•DOI•

On the Passivity-Based Impedance Control of Flexible Joint Robots

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Christian Ott, Alin Albu-Schaffer, Andreas Kugi¹, Gerd Hirzinger•Institutions (1)

University of Vienna¹

01 Apr 2008-IEEE Transactions on Robotics

TL;DR: A novel type of impedance controllers for flexible joint robots with physical interpretation as a scaling of the motor inertia and the physical interpretation of torque feedback allows a proof of the asymptotic stability of the closed-loop system based on the passivity properties of the system.

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Abstract: In this paper, a novel type of impedance controllers for flexible joint robots is proposed. As a target impedance, a desired stiffness and damping are considered without inertia shaping. For this problem, two controllers of different complexity are proposed. Both have a cascaded structure with an inner torque feedback loop and an outer impedance controller. For the torque feedback, a physical interpretation as a scaling of the motor inertia is given, which allows to incorporate the torque feedback into a passivity-based analysis. The outer impedance control law is then designed differently for the two controllers. In the first approach, the stiffness and damping terms and the gravity compensation term are designed separately. This outer control loop uses only the motor position and velocity, but no noncollocated feedback of the joint torques or link side positions. In combination with the physical interpretation of torque feedback, this allows us to give a proof of the asymptotic stability of the closed-loop system based on the passivity properties of the system. The second control law is a refinement of this approach, in which the gravity compensation and the stiffness implementation are designed in a combined way. Thereby, a desired static stiffness relationship is obtained exactly. Additionally, some extensions of the controller to viscoelastic joints and to Cartesian impedance control are given. Finally, some experiments with the German Aerospace Center (DLR) lightweight robots verify the developed controllers and show the efficiency of the proposed control approach.

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356 citations

Cites background or methods from "A simple PD controller for robots w..."

...In [10] it has been shown that for a motor position based PD-controller a feedforward term of the gravity torques in the desired steady state qd can be used in order to achieve asymptotic stability....
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...Furthermore, in [10], [15] a gravity compensation term base d on the desired configuration was used....
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...In [15], [16] a controller with a complete static state feedb ack (position and torque as well as their first derivatives) was i ntroduced, for which (analogously to [10]) asymptotic stabi lity was shown based on the passivity properties of the controlle r....
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Journal Article•DOI•

PD control with on-line gravity compensation for robots with elastic joints: Theory and experiments

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Alessandro De Luca¹, Bruno Siciliano, Loredana Zollo²•Institutions (2)

Sapienza University of Rome¹, Sant'Anna School of Advanced Studies²

01 Oct 2005-Automatica

TL;DR: A proportional-derivative control with on-line gravity compensation is proposed for regulation tasks of robot manipulators with elastic joints and it is proved via a Lyapunov argument that the control law globally asymptotically stabilizes the desired robot configuration.

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232 citations

Cites background or methods from "A simple PD controller for robots w..."

...The robot dynamic model can be written as follows (Tomei, 1991): B(q)q̈c + C(qc, q̇c)q̇c + e(q) + Keqc = m, (1) whereqc=[qT T]T is the(2n×1) vector of configuration variables, beingq and the(n×1) vectors of link positions and motor positions (reflected through the gears), respectively....
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...Following a similar analysis as in (Tomei, 1991), it can be shown that the closed-loop equilibrium configuration(q, ) = (q∗, ∗) satisfying g(q) + K(q − ) = 0 K( − q) = KP(̂d − ) + ĝ(̂), with ̂d = qd + K̂−1ĝ(qd) and ̂ = − K̂−1ĝ(qd), is still unique and globally asymptotically stable under the…...
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...The PD control withconstantgravity compensation in (Tomei, 1991) is expressed as u = KP( d − ) − KḊ + g(qd), (7) whereKP>0 andKD >0 are both symmetric (and typically diagonal) matrices, and d = qd + K−1g(qd)....
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...The sufficient condition (9) is the same as in (Tomei, 1991)....
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...For regulation tasks, instead,Tomei (1991)has proved that a simple proportional-derivative (PD) controller suffices to globally stabilize a robot with elastic joints about any desired configuration....
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Journal Article•DOI•

A Review of Algorithms for Compliant Control of Stiff and Fixed-Compliance Robots

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Andrea Calanca¹, Riccardo Muradore¹, Paolo Fiorini¹•Institutions (1)

University of Verona¹

01 Apr 2016-IEEE-ASME Transactions on Mechatronics

TL;DR: This survey presents the state of the art of basic compliant control algorithms in a unified view of past and present literature with an expansion of taxonomy to account for recent research.

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Abstract: This survey presents the state of the art of basic compliant control algorithms in a unified view of past and present literature. Compliant control is fundamental when dealing with unstructured environments, as in the case of human–robot interaction. This is because it implicitly controls the energy transfer to the environment, providing a safe interaction. In this review, we analyze solutions from traditional robotics, usually involving stiff joints, and recent literature to find common control concepts and differences. To this aim, we bring back every schemas and relative mathematics formulation to a common and simplified scenario. Then, for each schema, we explain its intuitive meaning and report issues raised in the literature. We also propose an expansion of taxonomy to account for recent research.

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222 citations

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References

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Journal Article•DOI•

On the adaptive control of robot manipulators

[...]

Jean-Jacques E. Slotine¹, W. Li¹•Institutions (1)

Massachusetts Institute of Technology¹

01 Sep 1987-The International Journal of Robotics Research

TL;DR: In this paper, an adaptive robot control algorithm is derived, which consists of a PD feedback part and a full dynamics feed for the compensation part, with the unknown manipulator and payload parameters being estimated online.

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Abstract: A new adaptive robot control algorithm is derived, which consists of a PD feedback part and a full dynamics feedfor ward compensation part, with the unknown manipulator and payload parameters being estimated online. The algorithm is computationally simple, because of an effective exploitation of the structure of manipulator dynamics. In particular, it requires neither feedback of joint accelerations nor inversion of the estimated inertia matrix. The algorithm can also be applied directly in Cartesian space.

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2,117 citations

Journal Article•DOI•

Modeling and Control of Elastic Joint Robots

[...]

Mark W. Spong¹•Institutions (1)

University of Illinois at Urbana–Champaign¹

01 Dec 1987-Journal of Dynamic Systems Measurement and Control-transactions of The Asme

1,542 citations

Journal Article•DOI•

Fast Nonlinear Control with Arbitrary Pole-Placement for Industrial Robots and Manipulators

[...]

E. Freund¹•Institutions (1)

FernUniversität Hagen¹

01 Mar 1982-The International Journal of Robotics Research

TL;DR: In this paper, three nonlinear methods are presented, two of which are direct design procedures for industrial robots, based on a suitable partition of the dynamic equation of the industrial robot and provide directly applicable, explicit control laws for each drive.

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Abstract: Models of industrial robots are characterized by highly nonlinear equations with nonlinear couplings between the variables of motion. In this paper, three nonlinear methods are presented, two of which are direct design procedures for industrial robots. These direct nonlinear methods are based on a suitable partition of the dynamic equation of the industrial robot and provide directly applicable, explicit control laws for each drive. The design procedures presented greatly simplify the derivation of the algorithm for computer-controlled industrial robots. The methods are applied to two different types of industrial robots.

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470 citations

Journal Article•DOI•

An integral manifold approach to the feedback control of flexible joint robots

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Mark W. Spong¹, Khashayar Khorasani², Petar V. Kokotovic¹•Institutions (2)

University of Illinois at Urbana–Champaign¹, University of Michigan²

01 Aug 1987

TL;DR: The control problem for robot manipulators with flexible joints is considered and it is shown how to approximate the feedback linearizing control to any order in µ, an approximate feedback linearization which linearizes the system for all practical purposes.

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Abstract: The control problem for robot manipulators with flexible joints is considered. The results are based on a recently developed singular perturbation formulation of the manipulator equations of motion where the singular perturbation parameter µ is the inverse of the joint stiffness. For this class of systems it is known that the reduced-order model corresponding to the mechanical system under the assumption of perfect rigidity is globally linearizable via nonlinear static-state feedback, but that the full-order flexible system is not, in general, linearizable in this manner. The concept of integral manifold is utilized to represent the dynamics of the slow subsystem. The slow subsystem reduces to the rigid model as the perturbation parameter µ tends to zero. It is shown that linearizability of the rigid model implies linearizability of the flexible system restricted to the integral manifold. Based on a power series expansion of the integral manifold around µ = 0, it is shown how to approximate the feedback linearizing control to any order in µ. The result is then an approximate feedback linearization which, assuming stability of the fast variables, linearizes the system for all practical purposes.

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444 citations

Journal Article•DOI•

Dynamic Models for Control System Design of Integrated Robot and Drive Systems

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Malcolm Good¹, L. M. Sweet¹, K. L. Strobel¹•Institutions (1)

General Electric¹

01 Mar 1985-Journal of Dynamic Systems Measurement and Control-transactions of The Asme

TL;DR: In this article, the authors present analytical models and experimental data to show that interactions between electromechanical drives coupled with compliant linkages to arm link drive points are of fundamental importance to robot control system design.

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Abstract: The design of high performance motion controls for industrial robots is based on accurate models for the robot arm and drive systems. This paper presents analytical models and experimental data to show that interactions between electromechanical drives coupled with compliant linkages to arm link drive points are of fundamental importance to robot control system design. Flexibility in harmonic drives produces resonances in the 5 Hz to 8 Hz range. Flexibility in the robot linkages and joints connecting essentially rigid arm members produces higher frequency modes at 14 Hz and 40 Hz. The nonlinear characteristics of the drive system are modeled, and compared to experimental data. The models presented have been validated over the frequency range 0 to 50 Hz. The paper concludes with a brief discussion of the influence of model characteristics on motion control design.

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307 citations