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Research Papers

A Hybrid Robust Lyapunov Controller for Dynamic Catch, Grasp and Carry Maneuvers

[+] Author and Article Information
Kerim Yunt

Mem. ASME
General Control Design Inc.,
am Holbrig 4,
Zürich 8049, Switzerland
e-mail: kerimyunt@web.de

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received October 7, 2014; final manuscript received March 23, 2015; published online May 26, 2015. Assoc. Editor: Jingang Yi.

J. Dyn. Sys., Meas., Control 137(8), 081012 (Aug 01, 2015) (11 pages) Paper No: DS-14-1404; doi: 10.1115/1.4030285 History: Received October 07, 2014; Revised March 23, 2015; Online May 26, 2015

A hybrid Lyapunov based controller for dynamic catch, grasp, and carry tasks of grippers is developed. The Lyapunov controller unifies the trajectory planning and tracking tasks in one, and neither a separate trajectory planning algorithm is needed to run offline nor any type of learning process. The robustness of the controller is demonstrated, through simulations with inertial parametric uncertainties. The concept is presented with the simulations of six degrees-of-freedom (DOF) double revolute (RR) planar manipulator with a 4DOF gripper and a 8DOF triple revolute (RRR) manipulator with a 5DOF gripper.

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References

Powell, M. J., Zhao, H., and Ames, A. D., 2012, “Motion Primitives for Human-Inspired Bipedal Robotic Locomotion: Walking and Stair Climbing,” 2012 IEEE International Conference on Robotics and Automation (ICRA), IEEE, Piscataway, NJ, pp. 543–549.
Kallmann, M., Bargmann, R., and Mataric, M., 2004, “Planning the Sequencing of Movement Primitives,” Proceedings of the International Conference on Simulation of Adaptive Behavior (SAB), pp. 193–200.
Michelman, P., and Allen, P., 1994, “Forming Complex Dextrous Manipulations From Task Primitives,” 1994 IEEE International Conference on Robotics and Automation, IEEE, Piscataway, NJ, pp. 3383–3388.
Kazemi, M., Valois, J.-S., Bagnell, J. A., and Pollard, N., 2012, “Robust Object Grasping Using Force Compliant Motion Primitives,” Proceedings of Robotics: Science and Systems.
Cohen, B. J., Chitta, S., and Likhachev, M., 2010, “Search-Based Planning for Manipulation With Motion Primitives,” 2010 IEEE International Conference on Robotics and Automation (ICRA), IEEE, Piscataway, NJ, pp. 2902–2908.
Stulp, F., Theodorou, E., Kalakrishnan, M., Pastor, P., Righetti, L., and Schaal, S., 2011, “Learning Motion Primitive Goals for Robust Manipulation,” 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), IEEE, Piscataway, NJ, pp. 325–331.
Napier, J. R., and Tuttle, R., 1993, Hands, Princeton University Press, Princeton, NJ.
Cutkosky, M. R., and Howe, R. D., 1990, “Human Grasp Choice and Robotic Grasp Analysis,” Dextrous Robot Hands, Springer, New York, pp. 5–31.
Gutman, S., and Leitmann, G., 1976, “Stabilizing Control for Linear Systems With Bounded Parameter and Input Uncertainty,” Optimization Techniques Modeling and Optimization in the Service of Man Part 2 (Lecture Notes in Computer Science), Vol. 41, J.Cea, ed., Springer, Berlin, pp. 729–755.
Gutman, S., 1979, “Uncertain Dynamical Systems–A Lyapunov Min-Max Approach,” IEEE Trans. Autom. Control, 24(3), pp. 437–443. [CrossRef]
Khatib, O., 1986, “Real-Time Obstacle Avoidance for Manipulators and Mobile Robots,” Int. J. Rob. Res., 5(1), pp. 90–98. [CrossRef]
Khansari-Zadeh, S. M., and Billard, A., 2012, “A Dynamical System Approach to Realtime Obstacle Avoidance,” Auton. Rob., 32(4), pp. 433–454. [CrossRef]
Branicky, M. S., 1998, “Multiple Lyapunov Functions and Other Analysis Tools for Switched and Hybrid Systems,” IEEE Trans. Autom. Control, 43(4), pp. 475–482. [CrossRef]
Ames, A. D., and Powell, M., 2013, “Towards the Unification of Locomotion and Manipulation Through Control Lyapunov Functions and Quadratic Programs,” Control of Cyber-Physical Systems, Springer, Switzerland, pp. 219–240. [CrossRef]
Ames, A. D., Galloway, K., Sreenath, K., and Grizzle, J. W., 2014, “Rapidly Exponentially Stabilizing Control Lyapunov Functions and Hybrid Zero Dynamics,” IEEE Trans. Autom. Control, 59(4), pp. 876–891. [CrossRef]
Aghili, F., 2013, “Pre- and Post-Grasping Robot Motion Planning to Capture and Stabilize a Tumbling/Drifting Free-Floater With Uncertain Dynamics,” 2013 IEEE International Conference on Robotics and Automation (ICRA), pp. 5461–5468.
Kim, S., Shukla, A., and Billard, A., 2014, “Catching Objects in Flight,” IEEE Trans. Rob., 30(5), pp. 1049–1065. [CrossRef]
Lampariello, R., Nguyen-Tuong, D., Castellini, C., Hirzinger, G., and Peters, J., 2011, “Trajectory Planning for Optimal Robot Catching in Real-Time,” 2011 IEEE International Conference on Robotics and Automation (ICRA), IEEE, Piscataway, NJ, pp. 3719–3726.
Horowitz, M. B., and Burdick, J. W., 2012, “Combined Grasp and Manipulation Planning as a Trajectory Optimization Problem,” 2012 IEEE International Conference on Robotics and Automation (ICRA), IEEE, Piscataway, NJ, pp. 584–591.
Berenson, D., Kuffner, J., and Choset, H., 2008, “An Optimization Approach to Planning for Mobile Manipulation,” IEEE International Conference on Robotics and Automation (ICRA 2008), IEEE, Piscataway, NJ, pp. 1187–1192.
Ko, C.-H., Lin, S.-H., and Chen, J.-K., 2013, “Motion Planning of Multifingered Hand-Arm System With Optimal Grasping Force,” 2013 IEEE International Symposium on Next-Generation Electronics (ISNE), IEEE, Piscataway, NJ, pp. 262–265.
Bauml, B., Wimbock, T., and Hirzinger, G., 2010, “Kinematically Optimal Catching a Flying Ball With a Hand-Arm-System,” 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 2592–2599.
Moreau, J. J., 1988, “Bounded Variation in Time,” Topics in Nonsmooth Mechanics, J. J.Moreau, P. D.Panagiotopoulos, and G.Strang, eds., Birkhäuser, Basel, Switzerland, pp. 1–74.
Moreau, J. J., 1988, “Unilateral Contact and Dry Friction in Finite Freedom Dynamics,” Nonsmooth Mechanics and Applications (CISM Courses and Lectures), Vol. 302, J. J.Moreau, and P. D.Panagiotopoulos, eds., Springer, New York, pp. 1–82.
Yunt, K., 2014, “On the Relation of the Principle of Maximum Dissipation to the Principles of Jourdain and Gauss for Rigid Body Systems,” ASME J. Comput. Nonlinear Dyn., 9(3), p. 031017. [CrossRef]
Glocker, C., 2001, Set-Valued Force Laws—Dynamics of Non-Smooth Systems (Lecture Notes in Applied Mechanics), Vol. 1, Springer, Berlin.
Yunt, K., 2011, “An Augmented Lagrangian Based Shooting Method for the Optimal Trajectory Generation of Switching Lagrangian Systems,” Dyn. Contin. Discrete Impulsive Syst., Ser. B, 18(5), pp. 615–645.
Utkin, V. I., Guldner, J., and Shi, J., 1999, Sliding Mode Control in Electromechanical Systems, Vol. 9, CRC Press, Boca Raton.
Edwards, C., and Spurgeon, S. K., 1998, Sliding Mode Control: Theory and Applications, Vol. 7, CRC Press, Boca Raton.
Sabanovic, A., Fridman, L., and Spurgeon, S. K., 2004, Variable Structure Systems: From Principles to Implementation, Vol. 66, IET, Stevenage, UK.
Venkataraman, S., and Gulati, S., 1993, “Control of Nonlinear Systems Using Terminal Sliding Modes,” ASME J. Dyn. Syst., Meas., Control, 115(3), pp. 554–560. [CrossRef]
Itkis, U., 1976, Control Systems of Variable Structure, Wiley, New York.
Draženović, B., 1969, “The Invariance Conditions in Variable Structure Systems,” Automatica, 5(3), pp. 287–295. [CrossRef]
Paden, B., and Sastry, S., 1987, “A Calculus for Computing Filippov's Differential Inclusion With Application to the Variable Structure Control of Robot Manipulators,” IEEE Trans. Circuits Syst., 34(1), pp. 73–82. [CrossRef]

Figures

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Fig. 1

The configuration of the 6DOF gripper

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Fig. 2

Workspace of the 6DOF planar gripper

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Fig. 3

Spatial rigid body contact between two rigid bodies

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Fig. 4

Contact forces and contact surfaces

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Fig. 5

Workspace of the 8DOF gripper

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Fig. 6

The configuration of the 8DOF manipulator

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Fig. 7

Finite state machine of the 6DOF gripper

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Fig. 8

Maneuver A: tasks one and two

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Fig. 9

Maneuver A: task three

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Fig. 10

Maneuver A: the control input history

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Fig. 11

Maneuver A: the change of Φ with the distance

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Fig. 12

Maneuver A: the Lyapunov function over all trajectories

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Fig. 13

Maneuver A: the normal contact forces

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Fig. 14

Maneuver A: the relative contact distances

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Fig. 15

Maneuver B: the control input history

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Fig. 16

Maneuver B: tasks one and two

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Fig. 17

Maneuver B: task three

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Fig. 18

Maneuver B: the change of Φ with the distance to the target

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Fig. 19

Maneuver C: tasks one and two

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Fig. 20

Maneuver C: task three

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Fig. 21

Maneuver C: phase plots of the maneuver in T3

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