Conditions in trajectory generation for controlling all state variables of Torque-unit Manipulator

Torque-unit Manipulator (TUM) is a design concept of space manipulator. A device which is called ‘‘torque unit’’ is equipped on each link of a kinematic chain whose joints are free. The ‘‘torque unit’’ can be made easily of a rotary actuator and a disc. TUM is a kind of nonholonomic system and the angular velocity of each disc at each time depends on the trajectories of the links. Controllability has been considered to control the position of each link to desired position and the angular velocity of each disc to desired constant value, by planning the trajectories of the links for 2-dimensional N d.o.f. TUM. It consequently has been shown that it is impossible to control the angular velocity of each disc to desired constant value since TUM has a first integral. However the first integral allows us to control the angular velocities of the all discs to a constant value of zero. Then, a control strategy is considered and described based on the results of the consideration. The control strategy consists of two phases: 1) controlling the positions of the links to desired positions, 2) controlling the residual angular velocities of the discs to zero by planning trajectory of the links. This paper presents the conditions of the trajectory in phase 2) and simulation results of the control strategy described above.