A condition on the trajectories of planar torque-unit manipulator for controlling all state variables

Torque-unit Manipulator(TUM) is a design concept of (space) manipulator and a Multibody system with nonholonomic constraints. Each joint of TUM is free and a device which is called “torque unit” is attached on each link. The “torque unit” can be made easily of a rotary actuator and a disc. Position-controllability of the links of TUM has been shown with conventional control laws for manipulators. However a problem arises that the discs in torque units usually have residual angular velocities when the links approach desired positions. The reason of the problem is that TUM is a kind of nonholonomic system, hence the angular velocity of each disc at each time depends on the motion history of the links. Controllability of the angular velocities of the discs to desired values has been considered by planning motion trajectories of links. Then, a control scheme for the TUM from zero-velocity initial state to zero-velocity final state has been given. However the trajectories of the links were not smooth enough. Then, a condition is made clear for the trajectories of the links to satisfy for bringing the angular velocity of a disc to zero in this paper. Also trajectories of the links are planned which is smooth enough as an example of application of the condition.