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Design of a momentum-based disturbance observer for rigid and flexible joint robots

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Abstract

Disturbance observer (DOB) is widely used in many practical applications due to its simple structure and high performance. However, the DOB cannot be directly applied to the robotic systems because of the nonlinearities/couplings in the inertia matrix (by means of coupling, we mean off-diagonal terms of the inertia matrix). This paper proposes a momentum-based DOB for general rigid joint robotic systems. By introducing the generalized momentum, it is possible to utilize full nonlinearities and couplings of the inertia matrix in the DOB design. Moreover, the momentum-based DOB design for the rigid joint robots can be easily extended to the flexible joint robot applications by applying it to the link-side dynamics and motor-side dynamics, respectively. As a result, we can estimate the external torque acting on the link-side and can compensate the disturbance occurring in the motor-side at the same time. Uniformly ultimated boundedness of the closed-loop dynamics can be shown through the Lyapunov-like approaches. The proposed scheme is verified using the numerical simulations.

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Notes

  1. \(Q(s)\) should be designed to make \(Q(s)G_{n}(s)^{-1}\) proper. In the implementation, one has to implement \(Q(s)\) and \(Q(s)G_{n}(s)^{-1}\).

    Fig. 1
    figure 1

    Structure of the standard DOB. The resulting transfer function from input \(u\) to \(y\) is \(G_{n}\) in low-frequency region if \(Q\) is designed as a low-pass filter

    Full size image

  2. Here, although \(L\) is a matrix, it is treated like a scalar value for simplicity of writing. However, no confusion occurs because \(L\) is a diagonal matrix.

  3. It should be noted that the definition of \(A_{ss}\), \(B_{ss}\), and the state \(x\) may differ depending on the controller. For example, if a PID tracking control is of interest, \(x\) will be defined by \(x=[\int e \;\; e \;\; \dot{e}]\), where \(e \triangleq q_{d} - q\) with properly redefined \(A_{ss}\) and \(B_{ss}\). Nevertheless, the proposed momentum-based DOB can be applied seamlessly.

  4. As a matter of fact, in this case, we can assume \(\dot{\tau }_{d}=0\). In this case, we can always prove the asymptotic stability (\(x\) and \(\tau _{d}-\widehat{\tau }_{d}\) converge to zero).

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Acknowledgments

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2011-0030075).

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Authors and Affiliations

  1. Robotics Laboratory, Department of Mechanical Engineering, Pohang University of Science and Technology (POSTECH), Pohang, Korea

    Min Jun Kim & Wan Kyun Chung

  2. Samsung Advanced Institute of Technology, Samsung Electronics Co., Ltd, Suwon, Korea

    Young Jin Park

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  1. Min Jun Kim
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  2. Young Jin Park
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  3. Wan Kyun Chung
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Correspondence to Wan Kyun Chung.

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Kim, M.J., Park, Y.J. & Chung, W.K. Design of a momentum-based disturbance observer for rigid and flexible joint robots. Intel Serv Robotics 8, 57–65 (2015). https://doi.org/10.1007/s11370-014-0163-9

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