Reactionless Path Planning Strategies for Capture of Tumbling Objects in Space Using a Dual-Arm Robotic System

Transcription

1 Reactionless Path Planning Strategies for Capture of Tumbling Objects in Space Using a Dual-Arm Robotic System Suril V. Shah Robotics Research Center, IIIT Hyeraba, Anhra Praesh, 53, Inia surilshah@iiit.ac.in an Inna Sharf an Arun K. Misra 3 Mechanical Engineering Department, McGill University, Montreal, QCH3A C3, Canaa inna.sharf@mcgill.ca, 3 arun.misra@mcgill.ca This paper presents strategies for point-to-point reactionless manipulation of a satellite mounte ual-arm robotic system for capture of tumbling orbiting objects, such as out-ofcommission satellites an space ebris. Use of the ual-arm robot coul be more effective than the single arm when there is no provision for a grapple fixture or the object is tumbling. The ual arms can also provie exterous manipulation. As the main objective in capture of orbital objects is to move the en-effector from initial position to the grapple point with esire velocity, the task-level reactionless constraints in terms of en-effector velocities are erive. The trajectory planne using these constraints, however, results in several singular points within the robot s workspace. In orer to overcome this shortcoming, three point-to-point path planning strategies are presente, which improve the reactionless operation of the ual-arm robot. The strategies are illustrate by carrying out simulations for a 6-egree-of-freeom (DOF) ual-arm robotic system mounte on a satellite. corresponing author

2 I. Introuction Autonomous on-orbit services, such as capture of orbiting objects, an refueling, repair an refurbishment of isable satellites, using a robot mounte on a service satellite will be one of the important space operations in the future [-3]. Particularly, active ebris removal [3] has gaine a lot of attention in the recent years ue to the increase in the number of ebris. While performing these on-orbit services, it is esirable that the fuel consumption to overcome any attitue isturbance of the base satellite is negligible, as limite fuel is mainly reserve for orbital transfer maneuvers. The main motivation behin capturing space ebris is to avoi their possible collision with a working satellite in the same orbit. Some research efforts have been irecte towars achieving capture of a satellite with zero attitue isturbances to the base. This is also commonly referre to as reactionless manipulation. Such reactionless manipulation of a robot mounte on a satellite can translate into fuel savings an increase the operating life of the servicing system. In this regar, an optimization technique was propose in [4] for minimization of the base reactions, which i not lea to a satisfactory result on reactionless manipulation. The concept of isturbance map was propose in [5], which provie the minimum attitue isturbance paths leaing to lower fuel consumption. Later, a more effective extene isturbance map was also propose in [6]. These maps inee help in reucing attitue isturbance, but may not lea to nil attitue isturbance. A unique esign of manipulator was provie in [7] that le to reactionless manipulation. However, the major isavantage of such a esign is that it makes the robot architecture very complex. A reaction null space (RNS) base path planning was introuce in [8] for reactionless manipulation of a robot with flexible base. Later, in [9] the RNS base approach was use for control of space robots. It was shown in [8-9] that the joint velocities, obtaine using the RNS formulation, result in zero reaction moments on the satellite-base. Subsequently, the flight valiation with ETS-VII space robot an its extension to a kinematically reunant arm, for the zero reaction maneuvers, were presente in []. It was shown in [] that the constraints for reactionless manipulation, in terms of joint velocities, can be augmente with the task-level constraints in orer to obtain esire motion of the en-effector. The RNS-base concept was also use in [] for capture of a tumbling satellite. Moreover, the RNS-base approach with backwar integration was attempte in [] for trajectory planning of -link robot in the approach phase. Reactionless motion of a space robot when capturing an unknown tumbling target was also presente in [3] base on the momentum conservation equation an the recursive least squares metho.

3 In the above mentione stuies, the focus was mainly on completing the task with a singlearm robot. However, when the orbiting object oes not have provision for grapple or is tumbling, the interception may be very ifficult. In such cases, interception using a ual-arm robotic system can be appealing as this will increase the probability of grasp in comparison to a single-arm robot. Use of a ual-arm robot was escribe in [4], where one arm trace a given path while the secon arm worke both to control the base attitue an to optimize the total operational torque of the system. The path planning of a planar ual-arm free-floating manipulator was also presente in [5]. In both [4] an [5], the secon arm was only involve in attitue control of the base satellite rather than capture of the object. An autonomous approach for berthing of a moving satellite with two robots using a flexible wrist mechanism an impeance control was propose in [6]. Capture of a spinning object by two flexible manipulators using hybri position/force control an vibration suppression control was also presente in [7]. A harware-in-the-loop simulation of the spatial ual-arm space robot was presente in [8]. In [6-8], the robot arms were manipulate without paying any attention to the base attitue. More recently, in [9], the coorinate motion planning of a spatial ual-arm space robot for target capture was presente. In that work also, capture of the target with both arms was carrie out without regar to the base attitue. It is worth noting that in the above cite works, either the ual arms capture the orbiting object regarless of the attitue of the base satellite or the one arm captures the object while the secon arm is specifically use to control the attitue of the satellite. Thus, the reactionless capture using a ual-arm robotic system is least explore in the literature. The reactionless trajectories have to be esigne such that the two arms start from ifferent initial configurations an intercept the esignate points on the object. It is also essential that both en-effectors capture the tumbling object with velocity equal to that of the contact points in orer to avoi any significant impact. Hence, the major challenge in capture of a tumbling object is point-to-point reactionless manipulation of the robot arms with esire en-effector velocities at the capture instant. This is a complex problem as the reactionless constraints are nonholonomic an the resulting path has many singular points within the robot s workspace []. In comparison to the single-arm manipulation, the case of ual-arm manipulation requires that the paths have to be planne such that both arms stay away from singular configurations, which themselves are path epenents. Motivate by these facts, the reactionless point-to-point path planning strategies are propose in this work for ual-arm robotic systems for capture of a tumbling object. In the

4 present work, the two arms are move so as to prouce zero net reaction moment in orer to capture the tumbling target. Compare to the single-arm scenario, reactionless manipulation of the ual-arm may bring forth some interesting aspects of path planning. The point-to-point motion is achieve by eriving the task-level reactionless constraints for ual-arm robotic system by projecting the joint-level reactionless constraints [8] using the Generalize Jacobian Matrix []. As the resulting equations are highly constraine an have many singular points within the robot s workspace, three point-to-point path planning strategies are also presente. Extension of reactionless path planning to a ual-arm robotic system an strategies to avoi singular configurations are the main contributions of this work. Numerical illustrations are provie using a 6-DOF ual-arm robotic system. The rest of the paper is organize as follows: Some mathematical preliminaries are provie in Section II. The reactionless manipulation of the ual-arm robotic system is presente in Section III, whereas several point-to-point reactionless path planning strategies are evelope in Section IV. Finally, conclusions are given in Section V. II. Preliminaries an Notation In this section the equations of motion for ual-arm robotic systems an constraints for reactionless manipulation are erive as an extension of those given in [] for a single-arm robotic system. A. Equations of motion The equations of motion for an n-dof robot mounte on a floating-base can be written similarly to those in [] as: T Hb Hbm && xb cb Fb J b T + = + T F Hbm Hm φ&& cm τm Jm h () where H b R 6 6 an H m R n n are the inertia matrices of the base an manipulator, respectively, H bm R 6 n is the coupling inertia matrix, x&& b R 6 is the vector of linear an angular accelerations of the base, φ&& R n is the vector of joint accelerations, c b R 6 an c m R n are the velocity epenent nonlinear terms of the base an manipulator, F b an F h R 6 are the vectors of force an moment exerte on the centroi of the base an en-effector, respectively, τ m R n is the manipulator joint torque, J b R 6 6 an J m R 6 n are the Jacobian

5 matrices for the base an manipulator. For the ual-arm robotic system, H bm, H m, φ&, c m, τ m, J b, J m an F h can be written as follows: H O φ&& c H [ H H ] H φ&& c τm Jb Jm O Fh τm =, Jb =, J m = an Fh = τm Jb O Jm Fh m m m bm = bm bm, m =, =, m =, O H m φ&& m cm (a) where the subscripts an represent arm- an arm-, respectively. The floating-base moule of the Recursive Dynamics Simulator (ReDySim) [], evelope base on (-), is use for the simulations carrie out in this paper. B. Constraints for reactionless manipulation The matrices H b an H bm, of (), may also be expresse as T Hb _ v H b _ c Hbm _ v H b = an Hbm = Hb _ c Hb _ ω Hbm _ ω (3a) Now, the constraints for reactionless manipulation can be written using those in [] as H % φ & = where H % = H H H H (3b) - bm bm bm _ ω b_ v b_ c bm _ v Equation (3b) represents the nonholonomic constraints, where φ& belongs to the subspace of reactionless motion of the robot. The above equation forms the constraint leaing to zero reaction moments but non-zero reaction forces. It is assume that the satellite has reaction jets or thrusters to take care of the base reaction forces. As in the previous literature, hereafter, the term reactionless manipulation will imply manipulation with zero base moments only. For the ual-arm robotic system, (3b) can also be expresse as φ& m H% bm H % bm = or H% bmφ& m+ H% bmφ& m = φ& m (4) It can be seen from (4) that for the ual-arm robot the sum of the coupling angular momenta of both arms, not of the iniviual, has to be zero. Solution of (4) for φ& man φ& m can be obtaine using the pseuo inverse approach [8]. It is note that (3b-4) represent the constraints as a function of joint velocities, an will be referre to as joint-level reactionless constraints.

6 III. Reactionless Manipulation of Dual-Arm Robot In this section, the task-level constraints for reactionless manipulation are obtaine first, followe by a numerical example an iscussion on singularity. A. Task-level constraints for reactionless manipulation Since (4) is represente in terms of joint velocities, it cannot reaily provie a solution for the reactionless motion of the en-effectors in the Cartesian space. In such cases, one may use the constraint augmentation technique propose in [] for a single-arm robotic system. In the present work the point-to-point path planning for the en-effectors of the ual-arm robot is carrie out using task-level reactionless constraints. These constraints are obtaine by projecting the constraints in (4) using the Generalize Jacobian Matrix (GJM) []. For the ual-arm robot, the en-effectors velocities are relate to joint velocities by x& = J φ& + J φ &, where J = J J H H an J = J H H (5) - - h g m g m g m b b bm g b b bm x& = J φ& + J φ &, where J = J J H H an J = J H H - - h g m g m g m b b bm g b b bm (6) where J g an J g are the Generalize Jacobian matrices of the iniviual arms an, respectively, an J g an J g are the coupling Jacobians. The task-level constraints are obtaine by substituting expressions for φ && m an φ&& m from (5-6) into (4) as: x& h H% bh H % bh = or H% bhx& h+ H% bhx& h= x& h (7) In the above, J g J g H% bh H% bh = H% bm H% bm J g an J g = (8) J g J g where J g may be interprete as GJM of the ual-arm system. We assume that J g is invertible; a pseuo inverse can be use otherwise. Equation (7) represents the task-level reactionless constraints an will be use for point-topoint reactionless manipulation of the ual-arm robot. The egree-of-reunancy (DOR), f r, associate with (7) is given by the ifference in the number of columns an rows % %. Solution of (7) belongs to the f r -imensional subspace of R n. In other wors, of H bh H bh f r en-effectors velocities, out of x& h an x& h, can be controlle or prescribe inepenently. Solution of (7) can be obtaine using the pseuo inverse approach as:

7 + x& = ( E H % H % ) ξ & (9) h bh bh T T T where x& h =[ x& h x& h], H % bh = [ H % bh H % bh ], ( + E H% ) bhh % bh is the null-space projector an ξ & is an arbitrary velocity vector mappe into the null space. Alternatively, one may use coorinate partitioning as: i x h H% bh H% & bh = i x& h () where i x& h an x& h are the inepenent or free an epenent velocities. In (), the number of inepenent velocities is equal to f r, whereas the epenent velocities are obtaine as x& = H% H% x& () i i h bh bh h Equations (-) are preferre over (9), as the former allow one to irectly prescribe f r en-effector velocities inepenently. For example, for the 6-link planar ual-arm robot, shown in Fig., the linear an angular velocities of the en-effectors of arm-, i.e., (v Ex, v Ey, ω E ), an arm-, i.e., (v Ex, v Ey, ω E ), are the six variables in the task-space. The DOR associate with (7) is five, an hence, any five out of the above six can be chosen inepenently. On the other han, solution of () can be obtaine, provie Otherwise, () will lea to a singularity as illustrate in section III-C. H % is invertible. bh.5.5 φ 3 Arm- (,.5) Y (m).5 Satellite (Base) φ φ (.3,.) Orbiting object (,.5) Grapple points φ 4 φ 5 φ 6 (.7, -.9) Arm X (m) Figure. A ual-arm robotic system mounte on a satellite

8 B. A numerical example In orer to illustrate the use of (-), a planar ual-arm robotic system mounte on a satellite, as shown in Fig., is consiere. Each arm is comprise of three rigi links an 3- DOF. The centers-of-mass of the satellite an orbiting object lie at ( m, m), an ( m, m), respectively. The ual arms are initially in a non-symmetric configuration, as in practice it is not possible to achieve perfect symmetry. The points to be grapple on the object are also shown in Fig.. For this particular example, the object is assume to be stationary relative to satellite. The geometric an inertia properties of the ual arms an satellite are given in Table I. TABLE I. MODEL PARAMETERS OF THE DUAL-ARM AND SATELLITE Satellite Arm Arm Orbital () object Mass (Kg) 5 - Length (m) m ia. I zz (Kg.m ) Equations (-) are use to obtain the reactionless motion in the Cartesian space. As the ual-arm robot has DOR equal to five, the five velocities, v Ex, v Ey, v Ex, v Ey an ω E, are i chosen as free or inepenent, i.e., x&, while ω E is chosen as the epenent velocity, i.e., h The inepenent velocities are esigne using a fourth orer interpolating polynomial as follows: 3 4 t t t x& ( t) = a+ b + 4c + 5 () T T T where a= x&, b= e (6x& + 4 x& ), c= 5 e+ (8x& + 7 x& ), = 6 e (3x& + 3 x& ), an I I F I F I F e =[ x x ]/ T. Moreover, (x I an x F ) an ( x& an x& ) are the initial an final positions an F I I velocities, respectively. Equation () ensures zero initial an final acceleration. The initial an final positions are summarize in Table II, while the initial velocities of the en-effectors are assume to be zero. In orer to avoi high impact forces, the final velocities are set to match those of the grapple points, which are zeros in this particular example. With the above, the epenent velocity leaing to reactionless manipulation is obtaine using (). F x& h. TABLE II. INITIAL AND FINAL CONFIGURATIONS OF THE DUAL-ARM p Ex (m) p Ey (m) p Ex(m) p Ey (m) φ E (ra) t = s T = s Note: Initial orientation of the en-effector was taken as taken as.47 ra

9 Simulation of the ual-arm robotic system moving to the grapple points on the orbiting object was carrie out for the time perio of sec. The torque inputs following Proportional an Derivative (PD) control law given by (3) were use for carrying out the ynamic simulations: τ = K ( φ φ ) + K ( φ& φ & ), =, (3) mk p k ak k ak k In (3), K p an K are the iagonal matrices of proportional an erivative gains, an φ& k vector an φ& are the vectors of esire an actual joint rates, respectively, of the k th arm. The ak φ& k is obtaine using (5-6) from alreay esigne en-effectors velocities in (-). The iagonal elements of K p an K are obtaine empirically an are assume here to be 49 an 6, respectively. The inverse ynamics control for contacting robot, as propose in [- 3], can also be use, however, (3) is use here as ual-arm in approach phase is not subjecte to any external constraints. The paths travelle by the en-effectors are shown in Fig. by the otte curves. Figure also shows the final configuration of the ual-arm where the final positions of the eneffectors match with those provie in Table II. The angular velocity of the base, as epicte in Fig. 3, is of O( -6 ), proving reactionless manipulation of the ual-arm. Moreover, the final velocities of both en-effectors are zero as shown in Fig. 4. To provie partial valiation of the results obtaine using the ReDySim, the linear an angular momenta are also plotte in Fig. 5. The change in linear an angular momenta is of O( -7 ), confirming conservation of momenta by the ynamics simulator. x -6 Y (m) ω z - - X (m) Figure. Motion in X-Y plane -4 5 Figure 3. Angular velocity of base

10 Linear velocity (m/s).. v Ex v Ey v Ex v Ey 5 5 x -3 ω E ω E 5 (a) Linear velocity (b) Angular velocity Figure 4. Velocity of the en-effectors of the ual-arm Angular velocity (ra/s) 5 L x L y L z P x P y P z x -7 x -7 5 L (Nm.s) P (Nm) (a) Angular momentum (b) Linear momentum Figure 5. Angular an linear momenta C. Illustration of singularity Equation () is highly constraine an the resulting path can have many singular points within the robot s workspace. It is worth noting that these singular points are in general ifferent from those associate with ynamic singularities [4] an occur when the configuration epenent matrix H %, employe in (), becomes non-invertible. Therefore, it bh is important to etect this singularity so that appropriate corrective action can be taken. It is interesting to observe that the point-to-point path planne using (-) can be nonsingular for one set of esire final velocities an singular for another set. This is ue to the nonholonomic nature of the path planner. We illustrate this by attempting to fin a solution for the same example as consiere before, but with the object now spinning at constant angular rate of. ra/s, resulting in the velocities of the two grapple points of -. an. m/s in the X-irection. In this scenario, the path planner an simulation faile at t=6. sec, because of the singularity associate with singularity efine as: H %. Figure 6 plots the commonly use measure of matrix bh

11 T S= et( H% bhh % bh ) (4) while Fig. 7 shows that the torque at joint 3 is increasing rapily as the singularity is nearing. Given that it is not possible to ensure a non-singular path with the planner efine by (), we next propose alternative point-to-point strategies which can avoi such singular configurations while capturing a tumbling object. Singularity inex (S) Joint torques (Nm) 5-5 τ τ τ Time(s) Figure 6. Singularity inex 4 6 Time(s) Figure 7. Joint torques of arm- IV. Point-to-Point Reactionless Path Planning Strategies In this section three strategies are presente to alleviate the singularity problem in achieving reactionless manipulation of the ual-arm robotic system for capture of the tumbling object. A. Reactionless manipulation through choice of inepenent variables For the example consiere in III-C, the number of inepenent variables use in the path planner was chosen equal to DOR, i.e., 5. As objective in point-to-point path planning is mainly to capture the tumbling object at grapple points with esire velocity, one may alternatively choose only the translational task-level velocities v Ex, v Ey, v Ex an v Ey as the inepenent variables, leaving ω E an ω E to be the epenent variables. The compromise on the trajectory of ω E makes () reunant an provies enhance workspace. This is acceptable if the orientation of the en-effectors falls within the allowable limit at the time of capture. Therefore, the epenent velocities are calculate as: + i i + x& = H % H % x& + ( E H % H % ) ξ & (5) h bh bh h bh bh The example consiere in III-C is now simulate by computing the epenent velocities accoring to (5) with ξ& =. The resulting plots are illustrate in Figs. 8 an 9 an show that the en-effectors are able to reach the points on the spinning object with the require

12 velocities. The angular velocity of base is also shown in Fig., which is of O( -6 ) confirming reactionless manipulation of the ual-arm. However, the path travelle by arm- traverses the object as shown in Fig., which in a real setting woul result in collision. In such situations, one may chose alternative value of ξ &. Another possible solution is to move the ual-arm to an intermeiate point before it captures the object, as escribe in the following section..3 v Ex v Ey v Ex v Ey Y (m) Velocity (m/s).. - X (m) Figure 8. Motion in X-Y plane -. 5 Figure 9. En-effector s velocity 6 x -6 ω z 4 Y (m) 5 Figure. Angular velocity of base - - X (m) Figure.Snapshots of arm- B. Reactionless manipulation through intermeiate points In this approach, the intermeiate points between initial an final points are consiere when the en-effectors are not able to reach the grapple points accoring to (5) ue to either singular configuration or collision. Then, we propose that the motion is planne as follows: + i i + x& hj = H% bh H% bhx& hj + ( E H% bh H% bh ) ξ & j, j=,..., p+ (6) where x& hj an i x& hj are the epenent an esire inepenent velocities from (j-) th to j th point, an p is total number of intermeiate points. It may be note that i x& hj are esigne using (), which allows one to prescribe initial an final velocities for each intermeiate segment.

13 Equation (6) enables moving from the initial to intermeiate point an intermeiate to next point in a reactionless manner. The proceure for the propose piecewise path planner is illustrate by simulating the example of IV-A, however, with the en effectors of arm- an - commane to travel via intermeiate points (.,.8) an (.5, -.3), respectively. Moreover, the en-effector velocities of the two arms in the X-irection are graually increase through values of -.8m/s an.8 m/s at the intermeiate points. Figures an 3 show the simulation results, which epict that the en-effectors are able to reach the points on the spinning object with the require velocity. The ual-arm is able to move in a reactionless manner as the change in angular velocity of base is of O( -5 ) as shown in Fig. 4. The upper arm (arm-) is also able to avoi a collision, as epicte in Fig.5. For collision avoiance a metho base on repulsion potential fiel [5] can also be applie, which however is beyon the scope of the paper. v Ex v Ey v Ex v Ey.3 Y (m) Velocity (m/s).. - X (m) Figure. Motion in X-Y plane -. 5 Figure 3. En-effector s velocity x -5 ω z - Y (m) Figure 4. Angular velocity of base - - X (m) Figure 5. Snapshots of arm- It can be observe from Fig. 5 that the joint angle φ (efine in Fig. ) of arm-traverses through a value φ =8, which correspons to a ynamic singularity. Aitional insight is

14 gleane by consiering, singularity inices for H % an J bh g (the GJM of arm-) plotte in Figs. 6 an 7, respectively. It is seen that the peaks in Fig. 6 correspon to singular points in Fig. 7. Such situations are not esirable as they can result in high joint torque requirements. Even though for the problem uner stuy, the joint torques shown in Fig. 8 remaine in a reasonable range, high joint torques were observe when ifferent intermeiate points were chosen. The concept of hybri manipulation is propose next, which is foun to be more avantageous when such ynamic singularities are unavoiable. τ τ τ 3 Singularity inex (S) Singularity inex (S) Joint torques (Nm) Time(s) Time(s) Time(s) Figure 6. Singularity inex S( H% bh ) Figure 7. Singularity inex S(J g ) Figure 8.Joint torques for arm- C. Hybri reactionless manipulation In this approach, the path planning is carrie out using both joint- an task-level constraints for reactionless manipulation, erive in (4) an (7), respectively. The joint-level constraints are mainly use to cross the singular configurations, whereas the task-level constraints are use to reach the esire points. Equation (5) is use for the task-level path planning, an the joint-level path planning is carrie out similarly to (5) as In (7), + i i + φ& = H % H % φ& + ( E H % H % ) ξ & (7) h bm bm h bm bm H % bm is not function of the GJM, an hence, (7) is unaffecte by ynamic singularity. The concept of hybri reactionless manipulation is illustrate using the example solve in IV-B, however, with the motion of the ual arm robot ivie into three stages. In stage, the en-effectors travel form initial points to the intermeiate points, illustrate in Table III, using the task-level planner of Eq. (5) The intermeiate points are selecte closer to the object such that that φ or 8. Note that the angle φ was -.47 ra in the beginning an ra at the en of stage. In stage, the angle φ is brought from to.533 ra using joint-level planner of Eq. (7). In the thir an final stage, the eneffectors travel from current to final position using task-level planner.

15 TABLE III. INITIAL AND FINAL CONFIGURATOIN FOR THE VARIOUS STAGES IN HYBRID MANIPULATION p Ex (m) p Ey (m) p Ex(m) p Ey (m) Stage t= t= φ (ra) φ 4 (ra) φ 4 (ra) φ 5 (ra) φ 6 (ra) Stage t= t= p Ex (m) p Ey (m) p Ex(m) p Ey (m) Stage 3 t= T=.5.5 Note:. Joint angles correspon to the en-effector s position at the en of stage. En-effector s position correspon to the joint angles at the en of stage Figure 9 shows that the en-effectors are able to reach the points on the spinning object. The en-effectors are also able to match the velocities of grapple points as epicte in Fig.. Figure epicts that the angular velocity of the base is of O( -5 ), which ensure reactionless manipulation of the ual-arm. The singularity inex for stages -3 is plotte in Fig., which illustrate that H % is non-singular in stages an 3, whereas bh This shows the effectiveness of the hybri reactionless manipulation. H % is non-singular in stage. bm.4 v Ex v Ey v Ex v Ey Y (m) Velocity (m/s). - X (m) Figure 9. Motion in X-Y plane 5 Figure. En-effector s velocity ω z (ra/s) x Figure. Angular velocity of base Singularity inex (S) 8 6 Stage Stage Stage3 S( H % ) bh S( H % ) bm 5 Time(s) Figure. Singularity inex

16 V. Conclusions The point-to-point reactionless path planning for interception of the orbiting object using a ual-arm robotic system has been presente. It is shown that the reactionless paths contain singular points in the transformation between inepenent an epenent task velocities. To remey this problem, three strategies, namely, through a choice of fewer than maximum inepenent variables, reactionless manipulation through intermeiate points an hybri reactionless manipulation, have been presente. By changing a subset of inepenent variables one can exploit the reunancy in the ual-arm robot to enhance the reactionless manipulation. On the other han, reactionless manipulation through intermeiate points allows one to obtain an alternative non-singular or collision-free path, whereas the hybri reactionless manipulation helps in overcoming the ynamic singularity, which cannot be completely avoie using the former two approaches. The above three path planning strategies are simple yet effective for capturing the tumbling target using a ual-arm system in a reactionless manner. Even though the above methos allow to move the ual-arm in a reactionless manner, the following issues nee to be aresse: ) evelopment of a systematic approach for selection of the number of intermeiate points an their locations, ) calculation of optimum path out of the multiple reactionless paths resulting out of the point-to-point strategies, e.g., the path giving favourable orientation of the en-effector or minimum energy consumption, 3) use of inverse ynamics control for trajectory planning. These will be carrie out as future work. References [] F. Sellmaier, T. Boge, J. Spurmann, S. Gully, T. Rupp an F. Huber, On-Orbit Servicing Missions: Challenges an Solutions for Spacecraft Operations, AIAA SpaceOps Conference,, pp [] On-Orbit Satellite Servicing Stuy, NASA Project Report, ( [3] J. Liou, An active ebris removal parametric stuy for LEO environment remeiation, Avances in Space Research, 47(), ,. [4] C. L. Chung, S. Desa, an C. W. esilva, Base reaction optimization of reunant manipulators for space applications, The Robotic Institute CMU-RI-TR, pp. 88-7, 988.

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