Unconstrained and constrained motion control of a planar two-link structurally flexible robotic manipulator. (English) Zbl 0811.70019
From the summary: Unconstrained and constrained motion control of a planar two-link structurally-flexible robotic manipulator are considered. The dynamic model is obtained by using the extended Hamilton’s principle and the Galerkin criterion. A method is presented to obtain the linearized equations of motion in Cartesian space for use in designing the control system. The approach to solving the control problem is to use feedforward and feedback control torques. The feedforward torques maneuver the flexible manipulator along a nominal trajectory and the feedback torques minimize any deviations from the nominal trajectory. The feedforward and feedback torques are obtained by solving the inverse dynamics problem for the rigid manipulator and designing linear quadratic Gaussian with loop transfer recovery compensators, respectively.
MSC:
| 70Q05 | Control of mechanical systems |
| 70B15 | Kinematics of mechanisms and robots |
| 70K50 | Bifurcations and instability for nonlinear problems in mechanics |
Keywords:
extended Hamilton’s principle; Galerkin criterion; linearized equations of motion; feedforward torques; feedback torques; inverse dynamics problem; linear quadratic Gaussian with loop transfer recovery compensatorsReferences:
| [1] | J. A. Maples, ”Force control of robotic manipulators with structural flexibility,” Ph.D. Dissertation, Stanford University, Stanford, CA, 1985. |
| [2] | J. A. Maples and J. J. Becker, ”Experiments in force control of robotic manipulators,” Proc. of the IEEE Int. Conf. on Robotics and Automation, 1986, pp. 695-702. |
| [3] | Whitney, Historical perspective and state of the art in robot force control,, Int. J. of Robotics Research 6 pp 3– (1987) |
| [4] | An, The role of dynamic models in Cartesian force control of manipulators,, Int. J. of Robotics Research 8 pp 51– (1989) |
| [5] | S. W. Tilley and R. H. Cannon, Jr., ”Experiments on end-point position and force control of a flexible arm with a fast wrist,” Proc. of the AIAA Guidance, Navigation and Control Conf., 1986, pp. 41-49. |
| [6] | Tilley, Robotics: Theory and Application 3 pp 1– (1986) |
| [7] | G.-W. Fan and I. A. Castelazo, ”Force control in flexible manipulators,” Proc. of the USA-Japan Symposium on Flexible Automation, 1988, pp. 361-368. |
| [8] | F. Matsuno, Y. Sakawa and T. Asano, ”Quasi-static hybrid position/force control of a flexible manipulator,” Proc. of the IEEE Int. Conf. on Robotics and Automation, 1991, pp. 2838-2843. |
| [9] | B. C. Chiou and M. Shahinpoor, ”The effects of joint and link flexibilities on the dynamic stability of force-controlled manipulators,” Proc. of the IEEE Int. Conf. on Robotics and Automation, 1989, pp. 398-403. |
| [10] | Chiou, Dynamic stability analysis of a two-link force-controlled flexible manipulator,, ASME J. of Dynamic Systems, Measurement and, Control 112 pp 661– (1990) |
| [11] | J. K. Salisbury, ”Active stiffness control of a manipulator in Cartesian coordinates,” Proc. of the IEEE Conf. on the Decision and Control, 1980, pp. 383-388. |
| [12] | D. E. Whitney, ”Force feedback control of manipulator fine motions,” ASME J. of Dynamic Systems, Measurement, and Control, 91-98, 1977. |
| [13] | Raibert, Hybrid position/force control of manipulators,, ASME J. of Dynamic Systems, Measurement, and Control 102 pp 126– (1981) |
| [14] | B. C. Chiou and M. Shahinpoor, ”Experimental and theoretical observations on the dynamic stability of a one-link force-controlled flexible manipulator,” Proc. of the IEEE Int. Conf. on Robotics and Automation, 1991, pp. 1208-1213. |
| [15] | S. D. Eppinger and W. P. Seering, ”On dynamic models of robot force control,” Proc. of the IEEE Int. Conf. on Robotics and Automation, 1986, pp. 29-34. |
| [16] | F. G. Pfeiffer, ”Path and force control of elastic manipulators,” Proc. of the IEEE Conf. on Decision and Control, 1990, pp. 514-519. |
| [17] | K. Richter and F. G. Pfeiffer, ”A flexible link manipulator as a force measuring and controlling unit,” Proc. of the IEEE Int. Conf. on Robotics and Automation, 1991, pp. 1214-1219. |
| [18] | R. P. Paul and B. Shimano, ”Compliance and control,” Proc. of the Joint Automatic Control Conf., 1976, pp. 694-699. |
| [19] | Hogan, Impedance control: An approach to manipulation: Part I-III,, ASME J. of Dynamic Systems, Measurement, and Control 107 pp 1– (1985) · Zbl 0566.93025 |
| [20] | Anderson, Hybrid impedance control of robotic manipulators,, IEEE J. of Robotics and Automation 4 pp 549– (1988) |
| [21] | T. J. Tarn, A. K. Bejczy, and X. Yun, ”Robot arm force control through system linearization by nonlinear feedback,” Proc. of the IEEE Int. Conf. on Robotics and Automation, 1988, pp. 1618-1625. |
| [22] | DeSchutter, Compliant robot motion II: A control approach based on external control loops,, Int. J. of Robotics Research 7 pp 18– (1988) |
| [23] | Stein, The LQG/LTR procedure for multivariable feedback control design,, IEEE Trans. on Automatic Control AC-32 pp 105– (1987) · Zbl 0628.93038 |
| [24] | M. Athans, ”A tutorial on the LQG/LTR method,” Proc. of American Control Conf., 1986, pp. 1289-1296. |
| [25] | W. H. Pfeil, M. Athans, and H. A. Spang, III, ”Multi-variable control of the GE T700 engine using the LQG/LTR design methodology,” Proc. of American Control Conf., 1986, pp. 1297-1312. |
| [26] | A. A. Rodriguez and M. Athans, ”Multivariable control of a twin lift helicopter system using the LQG/LTR design methodology,” Proc. of American Control Conf., 1986, pp. 1325-1332. |
| [27] | Athans, Linear-quadratic Gaussian with loop-transfer recovery methodology for the F-100 engine,, J. of Guidance 9 pp 45– (1986) · Zbl 0606.93048 |
| [28] | S. Garg, ”Turbofan engine control system design using the LQG/LTR methodology,” Proc. of American Control Conf., 1989, pp. 134-141. |
| [29] | Ridgely, Linear-quadratic Gaussian with loop-transfer recovery methodology for an unmanned aircraft,, J. of Guidance 10 pp 82– (1987) |
| [30] | R. J. Martin, L. Valavani, and M. Athans, ”Multivariable control of a submersible using the LQG/LTR design methodology,” Proc. of American Control Conf., 1986, pp. 1313-1324. |
| [31] | Choi, Flexible robotic manipulators for contact tasks: Modeling issues,, Mathematical Modelling and Scientific Computing 2 pp 1002– (1993) · Zbl 0800.93918 |
| [32] | L. S. Ward, ”Dynamics and control of a nonlinear flexible manipulator,” M.S. Thesis, MIT, Cambridge, MA, 1986. |
| [33] | Zheng, Mathematical modeling of a robot collision with its environment,, J. of Robotic Systems 2 pp 289– (1985) |
| [34] | R. Volpe and P. Khosla, ”Experimental verification of a strategy for impact control,” Proc. of the IEEE Int. Conf. on Robotics and Automation, 1991, pp. 1854-1860. |
| [35] | B. V. Chapnik, G. R. Heppler, and J. D. Aplevich, ”Controlling the impact response of a one-link flexible robotic arm,” Proc. of the IEEE Int. Conf. on Robotics and Automation, 1990, pp. 1444-1449. |
| [36] | Kane, Dynamics of a cantilever beam attached to a moving base,, J. of Guidance, Control, and Dynamics 10 pp 139– (1987) |
| [37] | Doyle, Multivariable feedback design: Concepts for a classical/modern synthesis,, IEEE Trans. on Automatic Control AC-26 pp 4– (1981) · Zbl 0462.93027 |
| [38] | E. Bayo, ”Computed torque for the position control of open-chain flexible robots,” Proc. of the IEEE Int. Conf. on Robotics and Automation, 1988, pp. 346-351. |
| [39] | G. G. Hastings and W. J. Book, ”Experiments in optimal control of a flexible arm,” Proc. of American Control Conference, 1985, pp. 728-729. |
| [40] | D. Nemir, A. J. Koivo, and R. L. Kashyap, ”Control of gripper position of a complaint link using strain gauge measurements,” Proc. of the IEEE Conf. on Decision and Control, 1986, pp. 1140-1144. |
| [41] | Yim, Sensors and Controls for Manufacturing 33 pp 163– (1988) |
| [42] | A. De Luca et al. ”Control experiments on a two-link robot with a flexible forearm,” Proc. of the IEEE Conf. on Decision and Control, 1990, pp. 520-527. |
| [43] | Chalhoub, Modeling and Control of Robotic Manipulators and Manufacturing Processes 6 pp 287– (1987) |
| [44] | Wang, Experiments on the position control of a one-link flexible robot arm,, IEEE Trans. on Robotics and Automation 5 pp 373– (1989) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
