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Volume 27 Issue 6 - Publication Date: 1 June 2008
 
Operational Space Control: A Theoretical and Empirical Comparison
 
Jun Nakanishi ICORP, Computational Brain Project, Japan Science and Technology Agency, Saitama 332-0012, Japan and ATR Computational Neuroscience Laboratories, Department of Humanoid Robotics and Computational Neuroscience, Kyoto 619-0288, Japan, Rick Cory Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA, Michael Mistry, Jan Peters Computer Science & Neuroscience, University of Southern California, Los Angeles, CA 90089-2520, USA and Stefan Schaal ATR Computational Neuroscience Laboratories, Department of Humanoid Robotics and Computational Neuroscience, Kyoto 619-0288, Japan and Computer Science & Neuroscience, University of Southern California, Los Angeles, CA 90089-2520, USA
 
Dexterous manipulation with a highly redundant movement system is one of the hallmarks of human motor skills. From numerous behavioral studies, there is strong evidence that humans employ compliant task space control, i.e. they focus control only on task variables while keeping redundant degrees-of-freedom as compliant as possible. This strategy is robust towards unknown disturbances and simultaneously safe for the operator and the environment. The theory of operational space control in robotics aims to achieve similar performance properties. However, despite various compelling theoretical lines of research, advanced operational space control is hardly found in actual robotics implementations, in particular new kinds of robots like humanoids and service robots, which would strongly profit from compliant dexterous manipulation. To analyze the pros and cons of different approaches to operational space control, this paper focuses on a theoretical and empirical evaluation of different methods that have been suggested in the literature, but also some new variants of operational space controllers. We address formulations at the velocity, acceleration, and force levels. First, we formulate all controllers in a common notational framework, including quaternion-based orientation control, and discuss some of their theoretical properties. Second, we present experimental comparisons of these approaches on a seven-degree-of-freedom anthropomorphic robot arm with several benchmark tasks. As an aside, we also introduce a novel parameter estimation algorithm for rigid body dynamics, which ensures physical consistency, as this issue was crucial for our successful robot implementations. Our extensive empirical results demonstrate that one of the simplified acceleration-based approaches can be advantageous in terms of task performance, ease of parameter tuning, and general robustness and compliance in the face of inevitable modeling errors.
 
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Example 1: Experiment (1) (“figure 8” movement at slow speed) with the controller 5. (2.2 MB) mp4

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Example 2: Experiment (2) (“figure 8” movement at fast speed) with the controller 5. (2.6 MB) mp4
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Example 3: Experiment (4) (star-like pattern at fast speed with high task space gain) with the controller 5. (2.2 MB) mp4
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Example 4: Experiment (7) (“figure 8” movement with orientation control at slow speed) with the controller 5. A cup containing water is placed on the end-effector to demonstrate the effectiveness of orientation control. (4.8 MB) mp4
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Example 5: Manually applying perturbations to the robot during the motion to show the level of compliance and robustness of the control using the controller 5). (3.9 MB) mp4
 
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