【正文】 aint function in every interval[qinit, qknot], the equation (27) is the pontes of two segmentsof the trajectory at the key knot.According to the constraint conditions presented inequation (26), the authors define a quintic polynomial togenerate a sequence q at time interval t = [t0, t1,...,tn].Simulation StudyIn section V, the authors addressed the method to plan aspiral ascending trajectory in Cartesian space and Jointspace respectively, and map into joint space using intervalalgorithm. In this section, we utilize an illustrativeexample to demonstrate that this trajectory can berealized in real space manipulator, the space robot systemhas a six DOF manipulator and all joints are rotationaljoints. Moreover, the geometric structure is the same asPUMA robot in order to make the inverse kinematicssolution easy. Here, we assume that each link ofmanipulator is cylindric. The radius of link r = . Thetable I shows the dynamics parameters of the spacemanipulator system. In the simulation study, the authors use the trigonometricspline function to plan the desired tracking trajectory inCartesian space, then choosing the key knot points in thistrajectory as the interval reference point using intervalalgorithm, they calculate and select the inverse kinematicsolutions. Finally, they use the five order polynomialfunction to generate the trajectory in Joint to desired angular value, angular velocityfrom joint trajectory generator, the authors use theDynamic model of space manipulator as the controlobject design PD controller to control the joint. Here, theauthors define the attitude control system of space robotis off in order to simplify the control. The goal of simulation is to verify that the spiralascending trajectory can be realized in Joint space. Theauthors also measure the coupling force and torquebetween the manipulator and space base in order toconfirm whether the attitude and orbit control system canpensate the orientation and position disturbance ofthe space base. shows the desired spiral ascendingtrajectory in Cartesian space. and show theposition and orientation disturbance of the space basebecause of the motion of the space manipulator. Theresults always keep in a small bound so that thesedisturbances can be pensated by the attitude andorbit control system. Moreover, the orientation andposition of the space base keep the formula shows the joint angular degree after inversekinematics during operation. shows the torque ofthe manipulator joint because of the motion of spacemanipulator. All simulation results can be used to verifythat the tracking trajectory of space manipulator is easy torealize in fact.Table I: Parameters of space robot system:空間基地空間機(jī)械手鏈接1鏈接2鏈接3鏈接4鏈接5鏈接6質(zhì)量300長(zhǎng)度Ixx50Iyy50Izz50Fig. 3. Spiral ascending trajectory in Cartesian spaceFig. 4. Position disturbance of space baseFig. 5. Orientation disturbance of space baseFig. 6. Joint angular degree after inverse kinematicsFig. 7. Joint torque of the space manipulator4. Conclusion This paper plans a spiral ascending trajectory of spacemanipulator for tracking and approaching the USS. Oneadvantage of proposed trajectory is to change the relativemotion mission to the fixture objective capture when theendeffector tracks the USS. The simulation study verifiesthat the proposed trajectory can be realized formengineering point of view. Approaching and catching the uncontrolled satellite hasbee an important class of future space robotic this paper, the authors present the proposed trackingtrajectory and preliminary work. 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