Time-scaling Control of an Underactuated Manipulator

Hirohiko Arai, Kazuo Tanie and Naoji Shiroma

Proceedings of 1998 IEEE International Conference on Robotics and Automation (ICRA'98), pp.2619-2626, Leuven, Belgium, May 1998.


Position control of an underactuated manipulator that has one passive joint is investigated. The dynamic constraint caused by the passive joint is second-order nonholonomic. Time-scaling of the active joint trajectory and bi-directional motion planning from the initial and the desired configurations provide an exact solution of the positioning trajectory. The active and passive joints can be positioned to the desired angles simultaneously by swinging the active joints only twice. Feedback control constrains the manipulator along the planned path in the configuration space. Simulation and experimental results show the validity of the proposed methods.


Underactuated Manipulator, Passive Joint, Nonholonomic Constraint, Time-scaling

[Contributions and Applications]

This paper presents a motion planning and feedback control method for positioning of an underactuated manipulator. The underactuated manipulator has a second-order nonholonomic constraint, which is represented as a non-integrable differential equation including the accelerations. Because of the drift term in the state equation, control methods for typical nonholonomic systems such as wheeled vehicles and space robots cannot be directly applied. There have been several previous studies on control of such manipulators. However, those methods take a long time for positioning or depend on the specific dynamics of the individual mechanisms. The method proposed in this paper allows a much faster positioning and can be generally applied to the underactuated manipulators which have one passive joint with no gravity applied. 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.