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TECHNICAL PAPERS

Accuracy/Robustness Dilemma in Impedance Control

[+] Author and Article Information
Tomer Valency, Miriam Zacksenhouse

Sensory Motor Integration Laboratory, Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa, Israel1

J. Dyn. Sys., Meas., Control 125(3), 310-319 (Sep 18, 2003) (10 pages) doi:10.1115/1.1590685 History: Received October 29, 2001; Revised January 23, 2003; Online September 18, 2003
Copyright © 2003 by ASME
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References

Figures

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Block diagram of the instantaneous model impedance control (IM-IC). See text for notation. The external state feedback, which uses the current state to compute the desired trajectory, is unique to the IM-IC.
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Planar robotic task: The planar robot (bold line) should follow the desired/virtual path (dashed line), which includes contact with a rigid wall. The rigid wall is modeled as an ideal spring with constant stiffness (Ke), so the contact force is proportional to the extent the robot is behind (to the right of) the wall times the stiffness. When the robot is in front (to the left of) the wall it loses contact with the wall and there is no interaction force.
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Model trajectory: the model trajectory (dashed line) traced by a robot that responds according to the desired impedance model and follows the virtual trajectory (solid line) specified by the task of Fig. 4.
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The IM-IC adequately controls the robot to perform the task of Fig. 4 with a double than estimated load. The trajectory of the robot with a double than estimated load under the IM-IC (marked with x) slightly deviates from the model trajectory (marked with circles) upon hitting the wall, and the robot maintains contact.
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The DB-IC inadequately controls the robot to perform the task of Fig. 4 with a double than estimated load. The trajectory of the robot with a double than estimated load under the DB-IC (marked with x) significantly deviates from the model trajectory (marked with circles) upon hitting the wall, and the robot temporarily loses contact.
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The IM-IC adequately controls the robot to perform the task of Fig. 4 with double than estimated environment stiffness. The trajectory of the robot under the IM-IC (marked with solid circles) slightly deviates from the model trajectory (dashed line) upon hitting the double-than estimated stiff wall, and the robot maintains contact.
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The PB-IC evokes contact instability when controlling the robot to perform the task of Fig. 4 with a double than estimated environment stiffness. The trajectory of the robot under the PB-IC (dashed-point line) significantly deviates from the model trajectory (dashed line) upon hitting the double than estimated stiff wall, and depicts contact instability.
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Eigenvalue analysis: The effect of an error in estimating the plant damping parameter on the location of the eigenvalues of the closed-loop system, for the DB-IC, PB-IC, and IM-IC. The nominal eigenvalues are marked by squares. The relative error is varied between [−0.8,+0.8] of the real value.
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One-dimensional model of a manipulator plant. The manipulator is located at xp and characterized by mass Mp, damping Bp and stiffness Kp, as seen from the environment. The virtual position of the manipulator xo,p reflects the position of the manipulator when the spring is free. The manipulator is subjected to the interaction force Fint and the controller force Ucontroller.

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