ISME Journal of Mechanics and DesignVol.2, No. 1, 2018, pp. 9–25

Overlaid Orthogonal Force Oscillations for Robot AssistedLocalization and Assembly

Arun Dayal Udai1∗, Subir Kumar Saha2 and Ashutosh Dayal3

1Department of Mechanical Engineering, Birla Institute of Technology,Mesra, Ranchi, India

2Department of Mechanical Engineering, Indian Institute of Technology Delhi,Hauz Khas New Delhi, India.

3Manan Vidya, Dumardaga, Ranchi, India.

*Corresponding author: arun_udai@bitmesra.ac.in

Abstract

In this paper an intuitive and anthropomorphic approach for robot assisted assembly usinga joint-torque controlled robots is presented. Overlaid orthogonal force oscillations were utilizedto precisely locate a hole, and perform an automated assembly. The work was extended furtherto a serial-chain standard industrial robot with a 6 Revolute-Spherical-Spherical (RSS) Stewartplatform with current limited soft-servo actuators as an add-on wrist. The serial-parallel hybridrobot system was used to perform localization and assembly using current limited soft-servodrives. The reported experiments conducted were consistently successful and motivated usingsuch a strategy for higher order industrial assemblies involving complicated shapes.

Keywords: Robotic Assembly; Serial-Parallel Hybrid Robot; Overlaid Force Oscillation

1. IntroductionIndustrial assembly is a major challenge in the industry which has been attempted by variousresearchers in the past using serial-chain industrial robots. Most of these are limited eitherby the time it requires for the overall assembly process, high failure rates for very small cham-fer dimensions or fillet radii of the peg and the hole, or it fails to address the situation whenthere exists a tight tolerance between the peg and the hole. With the evolution of robot designand cutting-edge technology available today, industrial robots are known to have a high po-sitional accuracy and repeatability even at a higher speed. These robots also demonstrate ahigh positional stiffness at its end-effector. A precise robotic assembly requires a robot to per-form assemblies in which the tolerance is better than the robot’s repeatability [1]. However,due to various uncertainties in the robot environment like, inaccurate gripping, imprecisetool calibration, sensor noise, industrial floor vibration, and the loosely modeled fixtures ofan automated assembly system, pure position based localization and assembly turn up to beinadequate. It is often desirable to attach an add-on device like, remote center compliance(RCC) [2], a wrist Force/Torque (F/T) sensor [3], 6 Degrees-of-Freedom Stewart platform [4],compliant micro-gripper [5], passive springs, etc.Alternatively, using a soft servo is proven to be more advantageous over pure force-controlbased approaches by various researchers in recent past as in [1, 6–9]. With the advent ofindustrial robots having joint-torque control capability, like KUKA LBR iiwa, Sawyer, Baxter,ABB YuMi, P2, etc., using soft servo to perform assembly task became quite favorable as

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these robots delivers out of the box support for Cartesian impedance controller with super-posed force oscillations [10]. This can be used to generate standard search paths like spiralor Lissajous on the surface of the hole while maintaining a constant contact with the surfaceusing a normal-force overlay. However, such robots are inordinately expensive and also havea smaller operational workspace and payload capacity as compared to a standard positioncontrolled industrial robots.Use of precise positioner on top of an industrial robot as an add-on wrist or a gripper for finemotions has been attempted in the past to overcome the limitation in precision of an industrialrobot as in [4]. The work presented in [4] demonstrated the use of 6 Degrees-of-Freedom (DoF)Stewart platform as a fine positioning device that can be applied for assembly task. However,any position or orientation error during assembly may result in jamming or wedging of themating parts and may damage the robot [11]. A compliant ionic polymer metal composite(IPMC) based micro gripper was used by [5] with a SCARA robot which demonstrated addingof compliance along with micro motion capabilities. This assisted in achieving a better as-sembly of a smaller sized peg-in-hole operation.Most of the industrial assembly task can be broken down to permutations of a widely re-searched benchmark problem, i.e., a peg-in-hole task [12]. The proposed research takes upthe challenge outside a state-of-the-art lab demesne on to a more challenging and demandingindustrial environment. A joint-torque controlled robot, namely KUKA LBR iiwa was used inthis work as a reference platform to demonstrate a peg-in-hole assembly operation using theproposed overlaid orthogonal force oscillation based technique. The proposed research workfurther used a 6-RSS Stewart platform as an add-on positioner to a standard position con-trolled industrial robot, KUKA KR5 Arc. The actuators used for the design of Stewart platformproposed in this work supported torque control and limiting its maximum value. This capa-bility enabled controlling the maximum end-effector force, i.e., by the top platform that holdsthe peg. Having such an arrangement allowed the end-effector to have a precise micro-motioncapability for a larger search workspace, along with the compliance which is a requisite forany assembly task with a tight tolerance.The strategy for peg-in-hole proposed in this paper requires the hole to lie within themaximumspiral search path envelope. While the peg moves in the spiral-search path, any interactionbetween the hole and the peg edges will produce an interaction force due to positional con-straints. As the peg can apply only a limited force in any direction due to current/torquelimits applied on the actuators, the peg follows a trajectory with no positional constraintsand automatically brings the peg closer to the hole.This method is quite intuitive and is inspired by the way a human does operations like blindlyinserting a key into the hole of a lock. The only pre-requisite for a successful peg-in-hole op-eration is to create a spiral sufficiently bigger to include the hole within the spiral boundary.This ensures path corrections from all directions and finally follow a position constrainedpath for the final assembly. The serial-robot just lands the peg sufficiently nearer to the holethrough a pre-programmed motion. Any uncertainty in the hole position is taken care of bythe spiral search path executed by the added parallel robot with maximum end-effector forcelimits.The remainder of this paper is organized as follows: Section 2 discusses the reference joint-torque controlled robot and the outcome of the peg-in-hole task that was performed usingthe proposed overlaid orthogonal force oscillation technique. Section 3 describes the pro-posed serial-parallel hybrid robot setup with a standard industrial robot to perform a robotassisted assembly task. This section also discusses the design and control of passive compli-ant 6-RSS Stewart platform, and the results of peg-in-hole assembly task using this proposedserial-parallel hybrid robot setup. Finally, Section 5 concludes the paper with a discussionon the outcome of the proposed research.

2. Assembly using a joint-torque controlled robotIn this section we discuss a peg-in-hole assembly operation that was performed using a 7-DoF joint-torque controlled robot, namely KUKA LBR iiwa. Figure 1 shows the completesetup that was rigged in order to perform the experiment. With this robot it is possible tohave a programmable stiffness at the joints or at the end-effector. The end-effector Cartesianmotion can be controlled entirely by joint-torque control through the impedance controller asin [13]. An intuitive assembly technique was proposed in this section that used a superposed

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orthogonal force oscillations [10] imposed at the end-effector through joint-torque pulsations.This is trivially done using τ s = JTwe, where we ≡ [n f ]T is a 6 × 1 wrench available at theend-effector and J is the 6 × 7 matrix for robot’s Jacobian. The components fx and fy offorce f ≡ [fx fy fz] comprises of the sinusoidal orthogonal force oscillation desired at theend-effector and the moment n was kept as zero. The resulting pulsating joint-torques τ s ≡[τ1 τ2 τ3 τ4 τ5 τ6 τ7]T corresponding to the desired forces f is applied to the joints of a gravitycompensated robot with impedance controller. In order to maintain a constant contact withthe hole surface a force overlay of fz was used which was normal to the spiral search pathgenerated due to the oscillating orthogonal forces.

Cylindrical Pellets

Hole on flat surface

Gripper

KUKA LBR iiwa robot

Z Y

X

Figure 1: Experimental setup for peg-in-hole using KUKA LBR iiwa robot

In order to do so, the end-effector stiffness Kp was defined in two orthogonal directions on the‘hole’ plane where search path is to be made with robot end-effector holding the ‘peg’. Thusthe two sinusoidal forces of equal amplitude acting in orthogonal directions (phase shiftedby π/2) would cause a circular end-effector path. The amplitude of the force was graduallyincreased to a maximum value and then brought back to zero within the given time T for thesearch path. Thus the total time gets equally divided into diverging and converging motionof spiral trajectory which is given by (1). The pitch p of the spiral depends on the total timeT , amplitude of force oscillation A N , stiffness (0 ≤ Kp ≤ 5000N/m) and the frequency ofsinusoidal force oscillation (0 ≤ f ≤ 15Hz for KUKA LBR iiwa robot). The total time getsequally divided into diverging and converging motion of spiral trajectory which is given by

Number of spiral turns n = TfMaximum deflection ∆x = A/Ks

Pitch of the spiral path p = 2∆x/n(1)

The Cartesian extents of the spiral ∆x and the pitch would decrease due to friction if the end-effector rubs against the hole-surface. The size of the pitch would also decrease if the forceapplied to maintain a constant contact with the hole-surface during the search process isincreased (as it leads to an increase in frictional force). Finally, when the peg finds the hole itbecomes a self guided assembly as the external forces due to the hole surface/edges becomesdominant over the orthogonal sinusoidal forces, and the normal contact force pushes the peg

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into the hole.Such orthogonal forces are helpful to generate different search patterns like, spiral pathswhen finding the hole which is equally probable in all directions, e.g. for a blind search, or aLissajous search pattern which is more suited for any rectangular workspace.

2.1. Generation of spiral search trajectory by overlaid force oscillationsIn order to test the proposed force-oscillation based search technique using KUKA LBR iiwarobot, the controller was set with stiffnesses along two orthogonal directions X and Y , shownin Fig. 1 on the search planeXY as 1000N/m, frequency of sinusoidal forces as 1Hz, maximumsearch time as 30s, and amplitude of force as 30N . With these parameters set, the end-effectorwas allowed to make spiral in air without making contact with the surface in order to check theactual behavior of the force oscillation on the Cartesian path of the end-effector. The numberof spiral turns observed was 15 and the maximum displacement was 11.6mm as shown inFig. 2. The observed displacement was slightly less than 15mm, which is expected with the

-475 -470 -465 -460 -455 -450 -445

X (mm)

774

776

778

780

782

784

786

788

790

792

X: -459.9Y: 776.8Z: 216.3

X: -459.8Y: 790.2Z: 215.2

X: -448.1Y: 783.9Z: 215.9

X: -471.3Y: 783.8Z: 215.1

Figure 2: End-effector trajectory due to orthogonal force oscillations

set parameters. This may be due to inaccurately identified robot model parameters taken forthe controller design by the manufacturer.A constant normal force along Z shown in Fig. 1, of 15N was superposed along with theorthogonal planar forces in order to establish contact with the flat surface without a holein order to study the behavior of trajectory due to the effect of friction. The material of thesurface was same as that of the surface with the hole and the contact was made with thepeg. Figure 3 shows the end-effector trajectory under the effect of friction.It may be observed that the extents of spiral gets reduced from 23.2mm to 21.2mm along X and13.4mm to 12.7mm along Y due to friction. The difference in extents along both the directionsmay be attributed to the poor surface finish, inaccurate controller implementation, etc.The oscillating forces along both the orthogonal directions in the XY plane that created thediverging and converging spiral search path is shown in Fig. 4.

2.2. Results of peg-in-hole assembly using joint-torque controlled robotThe peg of 19mm diameter was now interacted with a surface having a hole at (X : −759.65mm,Y :783.7mm) with a diametrical clearance between the hole and the peg of 0.01mm. Figure 5 showsthe trajectory of peg during hole search and insertion using orthogonal force oscillations. Thepeg makes contact with the hole surface at 139.5mm and during insertion it moves by 0.5mmtowards the hole while lowering the peg by 2.4mm. The recorded movement of the peg withinthe hole during insertion was more than the diametrical clearance between the hole and thepeg, as the end-effector makes the fixture (gripper and hole surface) move due to inherent

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X (mm)

776

778

780

782

784

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mm

)

X: -459.9Y: 777.6Z: 206.7

X: -460Y: 790.3Z: 206.7

X: -448.9Y: 784Z: 206.7

X: -470.1Y: 784Z: 206.8

Figure 3: End-effector trajectory on the flat surface due to orthogonal force oscillations

0 5 10 15 20 25 30Time (Seconds)

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0

5

10

15

20

Forc

eal

ong

Xan

dY

(N)

Force XForce Y

Force Y

Force X

Figure 4: Forces along orthogonal directions creating spiral search path

system compliance. It may be observed that, any positional constraints caused due to interac-tion between the peg and hole edges modified the commanded spiral trajectory and forced thepeg to move towards the hole center until it finally gets inserted into the hole due to normalcontact force. The insertion was completed within 6 seconds with 99% success rate against20 seconds with 95% success rate using the depth-profile based insertion technique reportedin [6]. This was also faster than soft servo spiral search used by [1] where the insertion timewas reported to be dependent on the position offset and normal force oscillation was used toprevent binding/sticking. This makes the force oscillation based localization and assemblyfaster as compared to a position-based technique for automated assembly, even with impre-cise robot controller that was observed during experiments. However, force-oscillation basedtechnique is limited to the robots with joint-torque control only.

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782.8 783 783.2 783.4 783.6 783.8 784

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137

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mm

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X: -458.9Y: 783.7Z: 139.5

X: -460.1Y: 783.9Z: 137.4X: -460.1

Y: 783.4Z: 137.1

(a) Trajectory of peg during insertion

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X(mm)

782.6

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m)

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X: -460.1Y: 783.4Z: 137.1

(b) Trajectory of peg during insertion

Figure 5: Peg interaction with the hole at (X : −759.65mm,Y : 783.7mm) during spiral-searchwith maximum-force limits.

3. Assembly using a Serial-Parallel Hybrid Robot SystemThis section introduces a novel approach that uses a soft-servo parallel Stewart platform ontop of a standard industrial robot. Figure 6 shows the proposed experimental setup where aStewart platform was mounted at the end-effector of a KUKA KR5 Arc industrial robot. Anall rotary 6-RSS Stewart platform was chosen among other architectures of parallel robotsas it is more agile as compared to more commonly referred Gough-Stewart platform with sixlinear actuators. Due to the presence of rotary actuators it is easy to have a back-drivablesystem which is responsive to any external force. A 6-Axis ATI-Schunk R© Gamma, Type: NetSI-32-2.5, Force/Torque (F/T) Sensor was also attached at the parallel robot base in orderto acquire the dynamic forces during search and insertion phase of the peg into the hole.It may be noted that the F/T sensor was used only to analyze the data during search andinsertion phase of the assembly and was not used for implementing the proposed algorithm.A 6-RSS Stewart platform was specially designed so as to have the features of a joint-torque

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X

YZ

Hole on flat surface

Cylindrical Pellet

KUKA KR5 Arc robot

Stewart Platform

F/T Sensor

Figure 6: Experimental setup for serial-parallel hybrid robot system

actuated robot and hence can be run with soft-servo. Parallel robot has an inherent advantageof structural rigidity and faster cycle time. Whereas, a serial robot is preferred for most ofthe existing industrial application due to its large workspace and ease to access constrainedspaces. Overall, the proposed system is an inexpensive and rugged alternative for a joint-torque controlled robot, which exploits the advantages offered by both serial and parallelrobots. It may be noted that existing joint-torque controlled robots are state-of-the-art andare also limited by reduced load carrying capacity and ruggedness necessary to handle thecurrent scenario of industrial robot environment prevailing in the industry. Various aspectsof the design of 6-RSS Stewart platform used in this work is discussed next.

Design of 6-RSS Stewart platformActuators: All the six active joints were actuated by Robotis Dynamixel MX-64T motors. Thesemotors are equipped with on-board 32-bit ARM Cortex M3 processor that operates the closedloop Proportional-Integral-Derivative (PID) for position, velocity, and torque control (via cur-rent sensing). A 360◦ position control with 0.088◦ resolution is achieved without any dead zonevia contactless absolute encoder. The actuator encloses high performance Maxon motors withmetal gears and ball bearings which enhances the precision and performance. With the max-imum possible speed of the actuator along with the associated dynamics at torque limitingmode a maximum Cartesian speed of 0.5m/s was obtained.Communication: The actuators were connected in series using three wired daisy-chain thatcommunicates bidirectional data using half-duplex asynchronous serial communication (with8-data bits, 1-stop bit and, no parity). It allows a high baud-rate of 4.5Mbps for communica-tion to/from the desktop computer (PC).Power Supply: The actuators were powered by 12V, 25A DC regulated supply via one of thewires of the serial daisy-chain.Mechanical Design: The standard top platform of fixed rotary Stewart platform as reported byvarious researchers earlier was modified. The top platform was made as a ‘Y’ shape to makeit lighter and to allow the rod-end bearings to be fitted at the new location, as shown in theFig. 7 i.e., along the sides of the Y-beams instead of fitting it at the outward facing sides (oldlocation in Fig. 7). With this new attachment technique the maximum misalignment angleof the rod-end bearings allowed more end-to-end linear displacement, roll and pitch anglesof the top platform. A thorough discussion on inverse kinematics of 6-RSS Stewart platformwith rotary actuators is covered in Section 4. This was used to obtain the joint trajectoriesfor a given end-effector motion trajectory, which is a diverging and converging spiral in the

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Rod-end bearings

Top platform - 'Y'

Actuators MX-64T

Modified Location

OldLocation

Base platform

Link 1

Link 2

Axis of Motor

Figure 7: Rendered CAD model of the modified 6-RSS Stewart platform

proposed work. With the above sets of actuator configuration and the mechanical design, theplatform comprised of a minimal set of complex wiring and circuitry, that made the platformvery simple and reliable. For any desired motion trajectory of the peg attached to the topplatform of the Stewart platform the inverse kinematics and joint trajectory calculation wasperformed in the central computer that communicates to both, the serial robot KUKA KR5 Arcand, the parallel Stewart platform. The actuators were made to run at a reduced-current or intorque-limiting mode. This made the joint motion soft and responsive to any undesired forcesdeveloped due to the interaction of the peg with the hole-edges and sliding motion during thesearch phase, or due to the contact force of the hole-surface with the peg while lowering ofthe peg.

4. Inverse Kinematics of 6-RSS Stewart platformFollowing are the symbols used to represent different components of the kinematic structureof 6-RSS Stewart platform as shown in Fig. 8. It shows a representative shape of the topplatform using a convex polygon formed by the joint locations.a1, a2 : Length of links 1 and 2O, Op : Origin of Base and Moving top platformBi : Frame (Xbi , Ybi , Zbi) attached to the ith actuatorPi : Frame attached to the ith joint of the top platformpi : Position vector of Pi with respect to Op

bi : Position vector of ith actuator frame Bi

qi : Position vector of actuator frame Pi

t : Position vector of actuator frame Op

1, · · · , 6 : Actuator numbers, iθi : Joint angle of ith actuatorli, li : Vector joining Bi and Pi, and its magnitude ‖li‖The precise locations of the actuator frames Bi and top platform frames Pi were obtainedthrough CAD software and later through external measurements using FARO R© Arm Coordi-nate Measuring Machine (CMM). The position vector of the ith joint on the top platform withrespect to the ith actuator frame is given by

li = t +P RO · pi − bi (2)

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Figure 8: Kinematic diagram with symbols used for 6-RSS Stewart platform

where PRO is the combined rotation matrix of the top frame with respect to the Stewart baseframe O(X,Y, Z).

PRO = Rz(φ) ·Ry(θ) ·Rx(ψ), where (3)

PRO =

cosφ cos θ − sinφ cosψ + cosφ sin θ sinψ sinφ sinψ + cosφ sin θ cosψsinφ cos θ cosφ cosψ + sinφ sin θ sinψ − cosφ sinψ + sinφ sin θ cosψ− sin θ cos θ sinψ cos θ cosψ

Rz(φ) is the rotation matrix corresponding to the yaw angle φ about Z axis, similarlyRy(θ) andRx(ψ) are rotation matrices corresponding to the roll and pitch angles θ and ψ respectively.The vector li was expressed in actuator frame Bi in order to obtain the joint angle of the ithactuator using

l̃i = [li]Bi= Rz(γi) · li (4)

where γi’s are the angles of the actuator axis Xbi of the frame Bi with respect to X of the baseframe as shown in Fig. 9, and Rz(γi) is the corresponding rotation matrix for rotation aboutZ axis. The frames were placed as shown in Fig. 8 to ensure a positive acute angle solutionfor the ith joint actuator, i.e., −π/2 ≤ θi ≤ π/2 for any given pose of the moving platform withinthe workspace of the Stewart platform. This was required due to actuator angle limitationsin case of servo motors.Table 1 shows the numerical values of γi used in this paper. Also, the edges B1B6, B2B3 andB4B5 form an equilateral triangle when extended.

Table 1: Axes angles for actuators on base.i 1 2 3 4 5 6

γi −150◦ 150◦ −30◦ −90◦ 90◦ 30◦

Knowing the pose of the top platform and corresponding locations of Pi, the problem of in-verse kinematics reduces to finding the solution of remaining 3 DoF arm with one active andtwo passive joints. The rotation of second link about its own longitudinal axis do not affectthe arm kinematics and is redundant. Figure 10 shows the kinematic structure of each leg ofthe Stewart platform comprising of two links connected with one active revolute joint drivenby the actuator and a passive spherical joint at the end of first link.Additional symbols used in Fig. 10 are:

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Figure 9: Axis frames for actuators on Stewart base

θ1 : Angle of rotation of the first link measured about Xbi at Bi in ZY plane from Ybiθ2 : Angle subtended by the second link with respect to the first link measured in ZY planeθ3 : Angle subtended by the second link measured in the plane perpendicular

to the plane ZY and passing through QiP′i (shown in grey color)

Bi : Start of the first link having an actuated joint with 1 DoFQi : End of the first link having a free joint with 2 DoFP̃i : Pi ≡ (xi, yi, zi) expressed in frame Bi, and end of the second linkl̃i : li expressed in frame Bi

P ′i (0, yi, zi) : Projection of P̃i on ZY planea′2 : Projected length of a2 on ZY plane

Figure 10: Kinematic diagram of an isolated 3-R manipulator.

Once l̃i ≡ [xi yi zi] is evaluated by (4) the algebraic solution for joint angles were performed.

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From Fig. 10xi = a2 sin θ3

which gives,θ3 = sin−1

xia2

and a′2 = a2 cos θ3 (5)

Also,yi = a1 cos θ1 + a′2 cos(θ1 + θ2)zi = a1 sin θ1 + a′2 sin(θ1 + θ2)

(6)

Squaring and adding yi and zi in (6) gives:

y2i + z2i = a21 + a′22 + 2a1a′2 cos θ2

Or,

θ2 = cos−1[y2i + z2i − (a21 + a′22 )

2a1a′2

](7)

Expanding yi in (6) gives:

yi = a1 cos θ1 + a′2 cos θ1 cos θ2 − a′2 sin θ1 sin θ2

On rearranging it gives,

yi = (a1 + a′2 cos θ2) cos θ1 − a′2 sin θ2 sin θ1 (8)

Assuming, (a1 + a′2 cos θ2) = A cosϕ and a′2 sin θ2 = A sinϕ, which on squaring and adding leadsto:

A =√

(a1 + a′2 cos θ2)2 + (a′2 sin θ2)2 (9a)

ϕ = tan−1(

a′2 sin θ2a1 + a′2 cos θ2

)(9b)

Using (8) and (9), yi can now be written as:

yi = A[cosϕ cos θ1 − sinϕ sin θ1]= A cos(θ1 + ϕ)

Which reduces to,θ1 = cos−1

(yiA− ϕ

)(10)

Using equation (10) the final solution for joint angle of the ith actuator was obtained. Onsuccessive evaluations of the top frame locations Pi for any given pose of the moving platformand base frame locations Bi, the joint angles of all the active joint actuators for i =1, 2, 3, 4,5, and 6 were obtained.

4.1. Controller for Passive Compliant Stewart PlatformThe modified Stewart platform was run purely in position control mode with limited currentflowing through its actuators. This results the end-effector to become compliant (passivelylike a spring) if encountered by any obstruction on its way. The maximum force that the end-effector can apply is also limited as in [14]. The current limits were just sufficient to executethe spiral search path while rubbing against the surface with a normal contact force. Anyobstruction due to the edge-interaction would constrain the path and the peg follows the holeedge until fully constrained and gets inserted due to the surface normal force into the hole.The overall control system that was used to execute the end-effector motion of the Stewartplatform can be depicted using Fig. 11. The input Cartesian pose trajectory pd was fed toinverse kinematics block (I. Kin) where the corresponding joint trajectory θd was evaluated.The internal Proportional-Integral-Derivative (PID) controller of the actuator handles the jointtrajectory tracking based on the difference between the actual joint angles θa and the desiredangles θd, which in turn feeds current to the actuators. In parallel, the actuators are alsoconstrained by current limits imposed by the inbuilt programmable torque controller. Thejoint torque limits τmax were estimated by the amount of end-effector force that was intendedat any given position as discussed in Section 2 for serial joint torque controlled robots. Theoutput joint angles θ from the actuators were affected by the external positional constraints(and finally the joint angle constraints θc) and it finally delivers the joint angle θa. The end-effector pose pa was obtained by the resulting joint angles θa.

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I. Kin+

−PID Actuators

Current/Torque Limiter

+

−Robot

pd θd ∆θ I

θτmax

θ

θc

θa pa

Figure 11: Controller scheme for passive compliant Stewart platform

4.2. System IntegrationThe hardware devices like KUKA KR5 Arc robot, F/T Sensor, and Dynamixel servo motorswere interfaced through an independent node which in turn communicates to the centralcore program written in Python programming language. The central program also checks forthe errors like, joint limits overshoot, workspace singularity, device input/output error, etc.which is also recorded in the common log node. The nodes for trajectory planning, performinginverse kinematics, and managing Dynamixel actuators were supervised by a central programthat can execute any motion profile for the Stewart platform.Independent node for KUKA KR5 Arc robot communicates to the KUKA robot controller (KRC4) via Ethernet using optional software support package Robot Sensory Interface provided bythe robot manufacturer [15]. It allows PC based control of the robot motion, getting feedbackfrom various inputs and changing the output status via Ethernet communication.The Force/Torque sensor program node continuously acquires the raw 16−bit data from thesensor at 7kHz over Ethernet. The protocol for the data packets was governed by the Appli-cation Programming Interface (API) as in [16] provided by the manufacturer.Finally, the node for Dynamixel servo motor control was developed in Python using a modi-fied version of API available as a standard program in public domain [17]. With the modifiedversion it was possible to control the position, velocity, current and torque delivered by anyMX − 64T servo motor.

4.3. Generation of search trajectory in reduced current modeIn order to generate a small spiral search path (of maximum diameter 2.1cm) the force oscilla-tions required very small joint-torque oscillations. Due to high gearing and inaccurate torquereproduction of the actuator, it was commanded to trace a spiral trajectory in position controlmode with a limited maximum current. This created a precise spiral search path and also al-lowed a maximum normal interaction force of 35N . Effectively, limiting joints torque produceda spring-like stiffness effect at the end-effector. This effectively created similar results to thatof an overlaid orthogonal force oscillations to create a spiral search path. The resultant spiralsearch path was measured using a FARO R© laser tracker having the end-effector fitted with aSpherically Mounted Retro-reflector (SMR) as shown in Fig. 12.Figure 13 shows the commanded and the measured end-effector test spiral trajectory. Amaximum error of 6mm was observed for a test spiral trajectory of maximum diameter of50mm. This may be attributed to the inaccurate components like the links, rod-end bearings,modeling errors, and reduced currents in the actuators. However, this order of error does notcause any harm to the search process. The algorithm for implementation of diverging andconverging spiral search trajectory adapted is given in Algorithm 4.1.

4.4. Results of peg-in-hole assembly using serial-parallel hybrid robotThe same set of peg and hole as was used earlier in Section 2.2, i.e., the peg of 19mm diameterand the hole with diametrical clearance of 0.01mm was used. A diverging-converging positioncontrolled spiral search with current limits was used. The pitch was commanded as 0.7 mmwith total number of 30 turns for the entire cycle of 6.5s. The peg was successfully insertedwithin 2s with 98% success rate with an offset of 4− 5mm from the hole center out of 50 trials.

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SMR

Top Platform

(a) End-effector mounted with SMR for motion tracking (b) A FARO R© laser tracker

Figure 12: Experimental setup for measuring the spatial spiral trajectory.

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-50

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50

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m)

CommandedMeasured Commanded

Measured

Figure 13: Commanded and measured spiral trajectory

The forces were also recorded using wrist force/torque sensor during the assembly process.Figure 14 shows the planar forces along XY plane which is similar to Fig. 4. The noise inthe readings was mainly due to rubbing over the surface. It also shows a noticeable jitterduring the insertion between 1.5 − 2.0s. The overall spiral motion lasted around 6.2s. Due toparallel mechanism and light platform, search patterns can be executed at higher frequencyas compared to that of joint torque controlled robot.Figure 15 shows the normal force measured along Z direction (as in Fig. 6) during the completeassembly process. The initial measured force during lowering was 0 N (after compensatingfor gravitational force) for the platform holding the peg. The contact was established at 3.5s

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Algorithm 4.1: SpiralSearch(N, p, n, Op)

comment: N : Steps, p: Pitch, n: Turns, Op ≡ [ox, oy, oz]: Initial position, fz: Contact force

START: Peg over the holex[ ]← 01×(N+1)

y[ ]← 01×(N+1) :Variables initializationfinitial ← fcurrent :Store initial contact force along Zr ← 0t← 0 :Intermediate parameter 0 ≤ t ≤ 1rmax ← (p× n)/2 :Maximum radiuscount← 1while t < 1

do

if t < 0.5then r ← p× n× telse r ← rmax − p× n× (t− 0.5)

x[count]← ox + r cos(2πnt)y[count]← oy + r sin(2πnt)z[count]← ozif fcurrent < finitial − 5 :Check for hole detection by normal force change

then exit whilet← t+ 1/Ncount← count+ 1

z ← zinitial − 10 :Insert the pegEND: Return array: x[ ]1×(N+1) and y[ ]1×(N+1)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5Time (Seconds)

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

Forc

eal

ong

Xan

dY

(N)

Force XForce X Force Y

Force Y

Figure 14: Forces along orthogonal directions during spiral search

when the steep rise in force up to 35N can be observed and the spiral search process wasstarted. The force oscillations continues for next 6.5s within which the peg gets into the holeat 5.5s, i.e., 2.0s after establishing contact when the force reduces back to normal and keepsoscillating due to orthogonal forces. On observing this the peg was pushed further into thehole to complete the assembly process.The variation can only be observed along X and Y axes due to the positional constrains

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imposed by the hole surfaces and the spiral motion commands in XY plane. However, thereis only slight variation of force due to wall friction along Z-axis, as the peg is free to movealong Z direction. A contact force of around 37N can be seen, in Fig. 15 while the contact isestablished till the peg is inserted.

0 1 2 3 4 5 6 7 8 9 10

Time (Seconds)

-50

-40

-30

-20

-10

0

10

20

For

ce a

long

Z (

N)

Figure 15: Normal force along Z during spiral search

Table 2 shows the localization time for some of the recorded data. The overall time of insertion

Table 2: Localization time with different positional offsets.Position Offset (cx, cy) Timea

Serial No. Offset X (mm) Offset Y (mm) (Seconds)

1 0 2 1.62 0 4 1.83 0 6 1.94 2 0 1.75 4 0 1.86 6 0 2.07 -4 0 1.98 -6 0 2.19 0 -4 1.810 0 -6 2.0

aLocalization time: Contact establishment to hole detection.

can be split in three phases which comprises of the time required to establish the contactwhile lowering the peg in force control mode (in reduced current) from the taught location tothe surface of the hole, localization time, i.e., the time of contact establishment till the holedetection, and the time required to finally push the peg into the hole. The peg was brought30mm above the surface of the hole by moving KUKA KR5 Arc robot with a trial offset (cx, cy)from the hole center and was lowered further by the Stewart platform in reduced currentmode till the F/T sensor detects the normal force when the contact was established. TheStewart platform then executes the search trajectory and checks for any change in verticalpeg position (along Z direction) due to hole detection, after the contact was established. Thepeg was finally pushed gradually further into the hole while it keeps oscillating in reducedcurrent mode in order to avoid jamming. The time required to establish contact was higher,i.e. 3.5s, and can be reduced substantially by starting from the taught position which is verynear to the surface of the hole.

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5. ConclusionIn this paper an approach for robot assisted assembly using overlaid orthogonal forces is pro-posed. In the first case a joint-torque controlled robot was used that showed an improved per-formance over any pure position controlled assembly technique reported earlier. This methodtakes care of any localization and alignment error automatically due to inherent nature ofimpedance controlled end-effector pose.This work was further extended and proposes a hybrid robot system comprising of serial-chain standard industrial robot mounted with an 6-RSS Stewart platform that holds the peg.In this case soft-servo drives by limiting actuator current were used to drive the Stewartplatform that limited the maximum interaction force. The measured forces during assemblyshow similar force variations as that of a joint-torque controlled robot. A diverging-convergingspiral search analogous to that used for joint-torque robot was used for assembly process.The recorded assembly time for a peg-in-hole process was found to be faster with same suc-cess rate as compared to the joint-torque controlled robot. This was possible due to the lightweight parallel structure of the end-effector that enabled orthogonal oscillations at higherfrequencies and hence the search path execution. The hybrid system exploits the advantagesof serial robots of its larger maneuverable workspace and parallel robots of its faster manip-ulation capabilities. The proposed hybrid system is inexpensive and easy to implement withthe existing robots present in the industry. The process eliminates wrist F/T sensor and theconstraints posed due to the inclusion of the sensor itself. However, the payload capacity nowwould depend on the capacity of the Stewart platform which in this case was limited to 3Kg.The video for the work presented in this paper can viewed at [18].The work presented in this paper has the potential to be extended further for various otherforms of assembly process. For example, fitting a new gear into a partly assembled gearboxusing axial torque oscillations along with a compliant positioning, placing a piston into acylinder liner, a fuel pump plunger into its barrel, etc.

AcknowledgementsThe authors sincerely acknowledge the robotics group at Program for Autonomous RoboticsLab. of Indian Institute of Technology Delhi, New Delhi for their support during the experi-ments that was performed on KUKA LBR iiwa robot.The authors also would like to thank technical team of FARO Business Technologies Pvt. Ltd.,New Delhi, India, for their support while calibration and measurement of Stewart platformmounted on KUKA KR5 Arc robot.

FundingThe first part of the work presented here using joint-torque controlled robot, KUKA LBR iiwawas funded by BARC/BRNS, Mumbai through a project recently completed at Indian Instituteof Technology Delhi, New Delhi.The second part of the work with serial-parallel hybrid robot system was funded by BirlaInstitute of Technology, Mesra, India, under the funding scheme of UG/PG Projects and seed-money grant alloted to the first author by the institute.The major equipments used in this work like, KUKA KR5 Arc robot and 6-Axis SchunkForce/Torque Sensor were funded by a special grant alloted to Autonomous Systems Lab.in the Department of Mechanical Engineering by Birla Institute of Technology, Mesra.

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[18] Arun Dayal Udai. Video for the work presented in this paper (2018), https://youtu.be/Kuo8HSD9T28.

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