Feedback Control of a 3-DOF Planar Underactuated Manipulator

Hirohiko Arai, Kazuo Tanie and Naoji Shiroma

Proceedings of 1997 IEEE International Conference on Robotics and Automation (ICRA'97), pp.703-709, Albuquerque, New Mexico, April 1997.

[Abstract]

Feedback control of a manipulator with a passive joint which has neither an actuator nor a holding brake is investigated. The manipulator has three degrees of freedom in a horizontal plane, with the third joint being passive. The dynamic constraint on the free link is 2nd-order nonholonomic. A trajectory for positioning is composed of simple translational and rotational trajectory segments. The trajectory segments are stabilized by nonlinear feedback, considering the motion of the center of percussion of the free link. Simulation results show the effectiveness of the feedback control.

[Keywords]

Manipulator, Dynamics, Passive Joint, Underactuated Mechanism, Nonholonomic Constraint, Nonlinear Feedback Control, Exact Linearization

[Contributions and Applications]

This paper presents feedback control of a 3-DOF manipulator with a passive joint. The free link is under a 2nd-order nonholonomic constraint, which is represented as a non-integrable differential equation including the accelerations. There have been few studies on feedback control of such mechanical systems. Based on Brockett's theorem, this system cannot be asymptotically stabilized to an equilibrium point by any smooth state feedback. This paper proposes a nonlinear feedback control law which stabilizes the system to desired trajectories. This method allows the control of more joints than actuators, and reduces the weight, energy consumption, and cost of the manipulator. It will be also effective in fault-tolerant control of a manipulator. The same dynamics are found in pushing manipulation of a object, a hovercraft, and an omnidirectional tractor connected to a ball-caster trailer. The proposed control law can also be applied to these systems.