Visual Servo Control of Slender Manipulators Using an Approximate Jacobian Operator

근사 자코비안 연산자를 이용한 경량 매니퓰레이터의 시각 서보 제어

  • Published : 2000.12.01

Abstract

To realize a visual servo control of slender manipulators, two problems to be solved are analysed. The stability problem on so-called noncolocation control and the infinite order problem of the real Jacobian matrix caused by the elastic deformation are discussed. By considering the dynamic relations between rigid and elastic modes, a Jacobian operator is derived and the physical meaning is also explained. Then, for practical control, a simple control scheme using an approximate Jacobian is proposed and its stable conditions are proven by means of the $L_$2$ stability theory. The scheme is structurally similar to the conventional PD control laws, but external sensors(e. g. visual sensor) are used for positioning and internal sensors for damping. A good performance is obtained via control experiments of a slender two link manipulator.

Keywords

References

  1. M. Takegaki. and S Arimoto. 'A new feedback method for dynamic control of manipulators', Trans. ASME. J. of DSMC, vol. 103, pp. 119-125, 1981
  2. H. G. Lee, H. Kanoh, S. Kawamura, F. Miyazaki, and S. Arimoto: 'Distributed parameter systems: Modeling and simulation', Elsevier Science Publishers B.V., pp. 345-352, 1989
  3. H. G. Lee, F. Miyazaki, and S. Arimoto: 'PDS control of flexible Multi-Link manipulators', SICE, vol. 33, pp. 479-486, 1989
  4. S. M. Joshi: 'Robustness properties of collocated controllers for flexible spacecraft', J. of Guidance, vol. 9, no. 1, pp. 85-91, 1986
  5. F. Matsuno: 'Mechanical softness: Link flexibility' J. of Robotics Society of Japan, vol. 17, no. 6, pp. 778-781, 1999
  6. T. Yoshikawa, Hosota: 'A modeling of flexible arms using virtual rigid links and unactuated joints', SICE, vol. 27, no. 12, pp. 1389-1395, 1991
  7. H. B. Hablani: 'Constrained and unconstrained model: Some modeling aspect of flexible space craft,' J. of Guidance and Control, vol. 5, no. 2, 1982
  8. M. Vidyasagar: Input and Output Analysis of Large-Scale Interconnected Systems, Springer-Verlag, 1981
  9. Meirovich: Analytical Method in Vibrations, The Macmillan Company, 3'rd printing, 1971