## A unifying methodology for the control of robotic systems (2005)

Venue: | in IEEE International Conference on Intelligent Robots and Systems |

Citations: | 24 - 13 self |

### BibTeX

@INPROCEEDINGS{Peters05aunifying,

author = {Jan Peters and Michael Mistry and Firdaus Udwadia and Jun Nakanishi and Stefan Schaal},

title = {A unifying methodology for the control of robotic systems},

booktitle = {in IEEE International Conference on Intelligent Robots and Systems},

year = {2005}

}

### Years of Citing Articles

### OpenURL

### Abstract

Abstract — Recently, [1] suggested to derive tracking controllers for mechanical systems using a generalization of Gauss’ principle of least constraint. This method allows us to reformulate control problems as a special class of optimal control. We take this line of reasoning one step further and demonstrate that well-known and also several novel nonlinear robot control laws can be derived from this generic methodology. We show experimental verifications on a Sarcos Master Arm robot for some of the the derived controllers. We believe that the suggested approach offers a promising unification and simplification of nonlinear control law design for robots obeying rigid body dynamics equations, both with or without external constraints, with over-actuation or underactuation, as well as open-chain and closed-chain kinematics. Index Terms — Non-linear control, robot control, tracking control.

### Citations

294 |
A unified approach for motion and force control of robot manipulators: The operational space formulation
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- 1987
(Show Context)
Citation Context ...F = J T � JM −1 J T �−1 (¨xd + KD ( ˙xd − ˙x) + KP (xd − x) − ˙J(q) ˙q + JM −1 (C + G)) + M(I − M −1 J T � JM −1 J T �−1 −1 J)M u1. It turns out that this is another well-known control law suggest in =-=[13]-=- with an additional null-space term. This controllaw is used in [1] and is especially interesting as it has a clear physical interpretation [1], [6], [7]: the metric used is consistent with principle ... |

210 |
Applied Optimal Control
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(Show Context)
Citation Context ...a closed-form solution usually does not exist and numerical solutions for high-dimensional systems are often prohibitively expensive in terms of computations due to the ‘Curse of Dimensionality’ [4], =-=[5]-=-. Recently, a novel way of thinking about tracking control of mechanical systems was suggested in [1] inspired by results from analytical dynamics with constrained motion. The major insight in [1] is ... |

88 |
Foundations of Robotics. Analysis and Control
- Yoshikawa
- 1990
(Show Context)
Citation Context ...from the control law and that the chosen metric N is not relevant – the derived solution is unique and general. It turns out that this a well-known control law, i.e., the Inverse Dynamics Control Law =-=[2]-=-, [3]. 2 An open topic of interest is to handle underactuated robot arm control. This will be part of future work. 2) Overactuated Robots : Overactuated robot arms as they can be found in biological s... |

58 |
Analytical Dynamics: A New Approach
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- 2008
(Show Context)
Citation Context ...otion. The major insight in [1] is that tracking control can be reformulated in terms of constraints, which in turn allows the application of a generalization of Gauss’ principle of least constraint1 =-=[6]-=- in order to derive a controller. As it is outlined already in [1], this insight leads to a specialized 1 Gauss’ principle of least constraint [6] is a general axiom on the mechanics of constrained mo... |

37 | Dynamic Programming and Modern Control Theory - Bellman, Kalaba - 1965 |

26 |
Dynamic control of Redundant Manipulators
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(Show Context)
Citation Context ...e obtain the control law u = MJ + (¨xd + KD ( ˙xd − ˙x)+KP (xd − x) − ˙J˙q) (31) + M(I − J + J)M −1 u0 + C + G. This control law is the combination of a resolvedacceleration kinematic controller [2], =-=[8]-=- with a modelbased controller and an additional null-space term. Similar controllers have been introduced in [9]–[12]. The null-space term can be eliminated by setting u0 = 0; however,this can result ... |

21 | Gauss’ principle and the dynamics of redundant and constrained manipulators
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(Show Context)
Citation Context ... see how the choice of N results in several different controllers. Note that this framework has been suggested in general in [1], [6], and the special case with a metric N = M−1 has been presented in =-=[7]-=- with respect to robot control. C. Stability Analysis Up to this point, this framework has been introduced in an idealized fashion neglecting the possibility of imperfect initial conditions and measur... |

15 |
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(Show Context)
Citation Context ... control law is the combination of a resolvedacceleration kinematic controller [2], [8] with a modelbased controller and an additional null-space term. Similar controllers have been introduced in [9]–=-=[12]-=-. The null-space term can be eliminated by setting u0 = 0; however,this can result in instabilities if there are redundant degrees of freedom. This controller will be evaluated in Section IV. 2) Dynam... |

9 |
A New Perspective on the Tracking Control of Nonlinear Structural and Mechanical Systems
- Udwadia
(Show Context)
Citation Context ...ogy Agency, Kyoto, 619-0288, Japan ‡ ATR Computational Neuroscience Laboratories, Kyoto, 619-0288, Japan {jrpeters, mmistry, fudwdia,}@usc.edu, {cory, jun}@atr.jp, sschaal@usc.edu Abstract— Recently, =-=[1]-=- suggested to derive tracking controllers for mechanical systems using a generalization of Gauss’ principle of least constraint. This method allows us to reformulate control problems as a special clas... |

4 |
Theory of robot control. SpringerVerlag Telos
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(Show Context)
Citation Context ...ined. To date, robot controllers are often derived from insights such as the reduction of the controlled system onto a linear system by linearization or by inversion of the dynamics of the robot [2], =-=[3]-=-. While this approach is viable for many problems, it is in a sense limiting because it ignores potentially useful properties of the inherent nonlinearities. Only few statements can be made about the ... |

4 |
Characterization of instability of dynamic control for kinematically redundant manipulators
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- 2002
(Show Context)
Citation Context ...This control law is the combination of a resolvedacceleration kinematic controller [2], [8] with a modelbased controller and an additional null-space term. Similar controllers have been introduced in =-=[9]-=-–[12]. The null-space term can be eliminated by setting u0 = 0; however,this can result in instabilities if there are redundant degrees of freedom. This controller will be evaluated in Section IV. 2) ... |

3 | Null torque based dynamic control for kinematically redundant manipulators - Chung, Chung, et al. - 1993 |