L1 Robustness of Computed Torque Method for Robot Manipulators

Jung Hoon Kim1, Sung-Moon Hur2, Yonghwan Oh2

  • 1Korea Institute of Science and Technology
  • 2Korea Institute of Science & Technology (KIST)

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Interactive Session

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10:30 - 13:00 | Tue 22 May | podF | TuA@F

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Abstract

This paper revisits computed torque method for robot manipulators and aims at developing its new framework based on the $L_1$ robustness, in which the $L_infty$ norm together with its induced norm is employed to characterize model uncertainties and a performance measure. More precisely, we consider the $L_1$ robust stability and performance for a given robot manipulator with a computed torque controller. We first show that the modelling errors in the computed torque method can be divided into an exogenous disturbance and a multiplicative model uncertainty, which are bounded in terms of the $L_infty$ norm and its induced norm, respectively. It is next shown that the robot manipulator with the computed torque controller can be equivalently represented by an interconnection of a continuous-time linear time-invariant (LTI) nominal plant and a stabilizing controller together with the $L_infty$-induced norm bounded model uncertainty. Based on the interconnected representation, the $L_1$ robust stability condition and an upper bound of the $L_1$ performance against the exogenous disturbance with respect to all model uncertainties in a class of a bounded $L_infty$-induced norm are dealt with by using the small-gain theorem. Finally, the effectiveness of the theoretical results is demonstrated through some experiment results.

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Summary

Interconnection of nominal plant, controller and model uncertainty

  • Robustness on computed torque method in terms of the time-domain
  • Bounded persistent external disturbances
  • L-infinity-induced norm bounded model uncertainty
  • Interconnected representation by nominal plant, controller and model uncertainty