Feedforward Friction Compensation of Bowden-Cable Transmission Via Loop Routing

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1 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) Congress Center Hamburg Sept 28 - Oct 2, Hamburg, Germany Feedforward Friction Compensation of Bowden-Cable Transmission Via Loop Routing Useok Jeong, and Kyu-Jin Cho, Member, IEEE Abstract Friction along the Bowden-cable transmission degenerates control performance unless it is properly compensated. Friction is produced when the bending angle of the Bowden-cable changes as the relative position of the actuator and the end-effector changes. This study proposes a method, termed loop routing, to compensate friction along the Bowden-cable. Loop routing involves making a one-round loop along the sheath that continuously maintains the sheath s bending angle at 2π regardless of the end-effector s position in 2-D space. This minimizes the bending angle change of the sheath as the end-effector translates in a 3-D workspace, which minimizes the friction change and enables feedforward friction compensation of the Bowden-cable without employing a sensor. An experiment in open-loop tension control of the Bowden-cable was conducted to evaluate the performance of the proposed method. Results show that the output tension follows the reference tension well, with an RMS error of 4.3% and a peak error of 13.3% of maximum reference. I. INTRODUCTION Bowden-cable transmission (also referred to as tendon-sheath transmission) provides a high degree of freedom to the routing path because force is transmitted though the continuum and the flexible component (that is, sheath and wire), which have infinite degrees of freedom. It is also compact and lightweight compared to other transmission systems, such as geared transmission. Thanks to these advantages, the Bowden-cable has been widely used in mechanical systems, from bicycle brakes to a complex robotic hand and surgical tools. The Bowden-cable system is, though, subject to friction along the cable. Studies have been performed into methods to identify and compensate for this friction [1 7]. The first method uses closed-loop feedback of the output tension [1 3]. It measures the tension of the wire at the output side and controls the actuator so that output tension follows the reference. The second method identifies the friction along the Bowden-cable and compensates it with a feedforward control scheme [4]. In addition, above two methods can be combined to further increase tension control performance of the Bowden-cable [6, 7]. Other studies use position based impedance control [8] and decrease pre-tension [8, 10, 13] with a slack prevention actuator to reduce the effect of the friction. However, these friction-reduction methods are * This study was supported by a grant (NRCTR-EX15001) of the Translational Research Center for Rehabilitation Robots, Korea National Rehabilitation Center, Ministry of Health & Welfare, Korea. U. Jeong is with Biorobotics Laboratory, the School of Mechanical and Aerospace Engineering, Seoul National University, Daehak-dong, Gwanak-gu, Seoul, Korea ( snopyy@snu.ac.kr). K. J. Cho is with Biorobotics Laboratory, the School of Mechanical and Aerospace Engineering/IAMD, Seoul National University, Daehak-dong, Gwanak-gu, Seoul, Korea (Corresponding author kjcho@snu.ac.kr). limited to the case when the identified friction model is constant that is, when the bending angle of the sheath is constant for the feedforward friction compensation. However, many applications using a Bowden-cable change the bending angle of the sheath during operation. Examples include a soft wearable robotic hand for grasping assistance [10 12], LOPES for gait rehabilitation [1], a soft wearable lower limb assistance device [3], and surgical tools [9]. The relative position between actuator and end-effector changes as the end-effector moves within the allowable workspace. Therefore, the bending angle of the sheath should change without requiring any devices to maintain it. As a result, it is difficult to compensate the friction with a feedforward scheme without employing a sensor because the bending angle of the sheath continuously changes as the end-effector moves. This study proposes a new concept, loop routing, to maintain the bending angle of the sheath when the relative position of the actuator and the end-effector changes. Loop routing uses a one-round loop along the sheath to maintain the bending angle at 2π when the end-effector translates in 2-D space. This minimizes the bending angle change of the sheath when the end-effector moves within a 3-D workspace. As a result, loop routing allows open-loop tension control with feedforward friction compensation of the Bowden-cable transmission. Experiments conducted to test this model demonstrated that loop routing solves the problem of friction along the Bowden-cable during translation of the end-effector without employing a sensor. II. FRICTION ALONG THE BOWDEN-CABLE A. Friction Model of the Bowden-Cable System Figure 1. Schematic of the Bowden-cable transmission. Fig. 1 illustrates a static friction model of the Bowden-cable system. The normal force originating from the bent sheath creates friction force between the sheath and the wire. The friction force has a nonlinear tension distribution along the wire. The equations governing this phenomenon are represented in Eq. 1 3 [5]. T exp sign p L in 1 T p T L p /15/$ IEEE 5948

2 L min p T p T 1 0 T T p 0 in T T p L out where T(p) represents tension of the wire at position, p; μ is the kinetic friction coefficient between sheath and wire; φis the summation of the bent angle of each segment, dφ; υ is the velocity of the wire relative to the sheath; and L is the total length of the sheath. Fig. 3 shows how friction changes along the sheath when the position of the end-effector changes within the allowable workspace of the Bowden-cable. The transmission efficiency changes from 1 to 0.53 as the sheath bends from 0 to 2π with the translation of the end-effector. It is difficult to compensate the friction for such applications because the bending angle of the sheath is hard to measure; the bend sensor should measure the summation of the infinitesimal change of the angle. If the bending angle changes are not measured, uncertainty in the model results in degradation of control performance, whether output tension is controlled in a feedforward or feedback manner. III. LOOP ROUTING: MAINTAINING THE BENDING ANGLE A. Basic concept Figure 2. Characteristics of the relation between input and output Eq. 1 3 are illustrated graphically in Fig. 2, which shows the relation between input and output tension of the wire. The output tension, T out, increases proportional to the input tension, T in, with the transmission efficiency exp(-μφ). As input tension starts to decrease, the output tension experiences a dead zone until it reaches a line with a slope exp(μφ). Then the output tension decreases proportional to the input tension with the inverse of the transmission efficiency. If the input tension increases before dropping to zero tension, the output tension experiences a dead zone again. The friction described above can be properly compensated with feedforward control with a known value of friction coefficient and bending angle of the sheath [4, 6, 7]. B. Problem of Bending Angle Estimation Studies have been undertaken in methods to compensate the friction along the Bowden-cable transmission system, as noted in the previous section. However, these studies are limited to the case of the non-changing bending angle of the sheath. But there are many cases when the bending angle needs to change, especially when the end-effector moves during the application [1, 3, 9 12]. Figure 3. Friction characteristics change with the sheath bending angle. (a) (b) Figure 4. Bending angle change of a sagging sheath. (a) Free sagging sheath. The bending angle φ decreases as the end-effector moves away from the actuator. (b) Sheath with loop routing. The bending angle φ always maintains 2π regardless of the translation of the end-effector in 2-D space. Fig. 4 illustrates how the bending angle of the Bowden-cable transmission can be maintained while the end-effector translates within the workspace. Fig. 4 (a) shows the change of bending angle when the sheath is directly routed to the end-effector from the actuator. It is natural that the bending angle, φ, decreases as the end-effector moves away from the actuator. On the other hand, a sheath using loop routing, as shown in Fig. 4 (b), always maintains the bending angle at 2π regardless of the end-effector position in 2-D space. As the sheath goes from the actuator to the end-effector, it always makes one rotation, resulting in a bending angle of 2π. The above proposition is valid even though the end-effector moves to the left side of the actuator in Fig. 4 (b). To satisfy the proposition, the following conditions should be met: 1) The orientation of the end-effector does not change. 2) The movement of the sheath is not disturbed by the environment. 3) Sheath stiffness in the radial direction (that is, in the direction that causes bending) is uniform along the axial 5949

3 direction so that a loop on the sheath can move along the sheath when the end-effector translates. Free movement of a loop on the sheath is the key to the way in which loop routing maintains a constant bending angle in the sheath. It should allow propagation of a constant sign of curvature along the sheath. If the above conditions are satisfied, a loop on the sheath rolls along the axial direction as the end-effector translates. This occurs because the sheath changes its bending shape in a manner that minimizes the potential energy of bending. This results in turn in an unchanging sign of curvature of the sheath along the axial direction, and the sheath thereby always makes one rotation, 2π. Therefore, the bending angle will not change the end-effector position in 2-D space unless the relative orientation between the actuator and the end-effector changes. In addition, it is recommended to use a sheath with low stiffness in the radial direction (that is, one that is easy to bend) to avoid disturbing the movement of the end-effector. But the sheath should also be stiff along the axial compression direction to enable force transfer. This is because the sheath needs to endure the compression force, which equals the amount of tension in the wire. A long incompressible extension spring having the same value of pitch as the diameter of the spring wire is used in this study and illustrated in Fig. 5. Fig. 6 illustrates a sheath with a direct connection between the actuator, A, and the end-effector, C, in 3-D space. The sheath is represented by two straight lines, AB and BC, and five points, O, A, B, C and E. A C 0, 0, 0 x, y, z O A C E 0,1, 0 Eq. 4 describes the position of each point in 3-D space. The vectors OA and CE are set to unit vector in the Y axis to fix the relative orientation between the actuator and the end-effector. AB x, y, z The X and Y position of B is assumed to be a mid-point of A and C as in Eq. 5. AB BC L With the constraint that the length of the sheath is constant, L as in Eq. 6, z 0 in Eq. 5 can be derived. The total bending angle of Fig. 6 can then be described by the following equation: OA, AB AB, BC BC, CE free Figure 5. Schematic of the Bowden-cable used in this study. It consists of a sheath (incompressible extension spring), a liner (Teflon tube), and a cable (braided Dyneema). B. Bending Angle The bending angle of the sheath can be maintained during translation of the end-effector in 2-D space by implementing the concept of loop routing as described in the previous section. However the proposed concept does not compensate the bending angle change originating from the translation of the end-effector in an orthogonal direction. But a loop on the sheath could minimize the bending angle change when the end-effector moves in an orthogonal direction. Figure 6. Schematic of a sheath without loop routing. Fig. 7 shows the schematic of a sheath with loop routing in 3-D space. AB x y z Figure 7. Schematic of a sheath with loop routing. 0,, z x 0 1 x 2 z m 1 z y 0 1 y 2 z m 1 z z 0 1 z 2 z m z L x y m m The crossing point of a loop, B', changes as the position of the end-effector changes. The value x' 0 should be within the X position of A and C. Also, y' 0 should be within 0 to y, and it should change as z changes. It should be 0 when z has the 5950

4 highest position (z m ) and y when z has the lowest position (- z m ). In addition, the value z 0 should be within - z m and 0 because the direction of a loop should not change and the sign of curvature of a sheath does not change. The values x' 0, y' 0 and z' 0 can be determined via linear approximation as in Eq. 9. OA, AB AB, CB B C, CE loop The bending angle of the sheath in Fig. 7 can be derived as in Eq. 11. The angle between the two vectors in Eq. 7 and 11 can be calculated with the dot product property described in Eq. 12; P and Q represent the arbitrary vectors in a 3-D space. P Q P, Q ArcCos P Q C. Workspace The workspace of the end-effector is bounded by the length of the Bowden-cable. The working position of the end-effector, C, should satisfy the following condition: x y z L A sheath with loop routing loses workspace because the loop reduces the effective sheath length to AB' + B'C. However, the loss of workspace can be covered by increasing the length of the sheath, which does not change the 2π bending angle. D. Simulation A numerical simulation was conducted to validate the effectiveness of the proposed method. The bending angle was calculated within a range of workspaces using derived results from the previous section. ref Error % To compare the bending angle change within a workspace, an error of bending angle was calculated using Eq. 14 and plotted in Fig. 8 with a sheath length L of 1,000 mm. The reference bending angle, φ ref in Eq. 14, was selected to have 0 for the case without loop routing and 2π for the case with loop routing. half-sphere shape in accordance with Eq. 13. The colors of each point illustrate the bending angle error. The result of the case without loop routing (a) shows zero error on (0, 1000, 0) which has zero bending angle as shown in Fig. 3 (1). As the end-effector get closer to the actuator that is located on (0, 0, 0), the error increases with the increasing bending angle, as shown in Fig. 3 (2), (3) and (4). The bending angle change within the workspace is larger than the case with loop routing (Fig. 8 (b)), and this changing in the bending angle leads to friction model error and degrades control performance. On the other hand, the case with loop routing in Fig. 8 (b) shows a more uniform distribution of the bending angle error within the workspace, with a value around 0 (shown in the color blue). This is because the bending angle of the sheath with loop routing always maintains 2π on the YZ plane with x = 0. Although it has the highest error at around (±1000, 0, 0), it shows a lower error distribution within the workspace. The effectiveness of loop routing (that is, making a loop with a sheath) is verified by these simulation results. Therefore loop routing can be applied to feedforward friction compensation using the friction model that will be described in next section. IV. FRICTION COMPENSATION The friction along the Bowden-cable can be compensated with a determined model using the feedforward control scheme [6, 7]. With a newly proposed concept to minimize the bending angle change, the control error of friction compensation as the end-effector position changes can be minimized. This allows feedforward open-loop tension control of the end-effector. Figure 9. Control algorithm to evaluate the performance of friction compensation. Fig. 9 shows the control algorithm to evaluate the performance of friction compensation with loop routing. T T exp c ref sign dt ref dt The friction compensator in Fig. 9 is defined in Eq. 15 and 16. It uses the inverse of the friction model in Eq. 1 3 and computes the compensation tension, T c, so that the output tension, T out, can follow the reference tension, T ref. If δ in Eq. 16 equals to zero, it should maintain the last value of δ because the relation between input and output tension must always rely on the model illustrated in Fig. 2. Figure 8. Simulation results of the bending angle error comparison between (a) a case without loop routing and (b) a case with loop routing. Assume that the actuator is placed on (0,0,0). Fig. 8 shows the distribution of the bending angle error in the workspace of the end-effector. The workspace has a V. EXPERIMENTAL SETUP Fig. 10 shows the experimental setup, which can actuate the wire and measure the tension of the wire. The mechanism of the tendon actuator shares the same concept of the slack 5951

5 Output tension [N] Output tension [N] prevention tendon actuator [8, 13] to prevent tangling of the wire inside the actuator. The input tension was measured with a custom made tension sensor that was placed at the outlet of the tendon actuator. An incompressible extension coil spring with a length of 1,000 mm was used for a sheath. Applying a small amount of torsion to the sheath is recommended to maintain a loop. One Ф15 polymer ring was put on a sheath to prevent disassembly of the loop routing. A Teflon tube was inserted inside the sheath to reduce friction. Braided Dyneema, which has very high tensile strength, was used for the wire. An end-effector that can be placed on a desired 3-D space and can measure the output tension of the wire was designed. Figure 11. Result of input and output tension relation with the sheath bending angle 2π. Fig. 11 shows the experimental result of input and output tension relation. Data was fitted with a model in Eq. 1 and Fig. 2. A friction coefficient was determined to 0.075, which is within the range of the friction coefficient between Teflon lining and polymer wire [14]. About 0.5 N of offset of data was observed, which originated from the friction of the rollers in the tension sensor. B. Friction Changes with Different Positions Figure 10. Experimental setup with tendon actuator, sheath, and end-effector. The low level tension controller was implemented in FPGA with a PI feedforward scheme, and the friction compensator was implemented in a real-time operating system. Measured data was transmitted through a serial communication from the RT target to a PC and processed and saved with Labview. Table 1 describes the detailed specification of the experimental setup. TABLE I. Component Real-time controller Software Motor driver Motor Tension sensor SPECIFICATIONS OF EXPERIMENTAL SETUP Specification CompactRIO 9082 (include FPGA), National Instruments Labview, National Instruments ESCON 36/2 DC, Maxon RE25 20 W with 5.4:1 gearhead, Maxon Custom made (force sensor from Ktoyo) Actuation module Custom made slack prevention tendon actuator [8, 13] Sheath Incompressible extension coil spring: O.D. 2.5, I.D. 1.8, length 1,000 mm, Stiffness of 100 mm 1.5 N/cm Teflon lining: O.D. 1.5, I.D. 1.0 Cable Braided Dyneema, O.D. 0.4 VI. RESULTS A. Friction Characterization The input and output tension of the wire was measured while maintaining the bending angle of the sheath at 2π to determine the friction coefficient, μ. Input tension was gradually increased up to 24 N and decreased, over 3 seconds, and repeated 5 times. Figure 12. Position of the end-effector for the friction change experiment. The experiment conducted in section A was carried out again with different end-effector positions for cases without loop routing and with loop routing. Fig. 12 shows the position of the end-effector within the workspace conducted in this experiment Without a loop Input tension [N] Input tension [N] Fig. 13 shows the results of input and output tension relation in different end-effector positions shown in Fig. 12. It show the effectiveness of loop routing on a sheath maintaining constant friction along the Bowden-cable, although the end-effector moves within the workspace. While the case without loop routing in Fig. 13 (a) has a large friction variation, With a loop Figure 13. Results of input and output tension relation in different end-effector positions, (a) without loop routing, (b) with loop routing. 5952

6 a sheath with loop routing in (b) has relatively small variation that can be neglected for some cases. C. Friction Compensation with Different Positions Bowden-cable transmission, which may decrease the performance of a non-controlled system. Second, the proposed method does not cover the orientation change of the end-effector, which affects the bending angle change of the sheath. Loop routing may be helpful for a wide variety of applications that use a Bowden-cable to compensate friction without additional sensors. For example, a soft wearable robot [3, 10 12] can benefit from Bowden-cable actuation by placing the actuator away from the limbs [10]. Figure 14. Results of open-loop tension control with feedforward friction compensation. An open-loop tension control with feedforward friction compensation, introduced in section IV, was conducted with the identified friction property from the previous experiments. The sinusoidal reference tension, T ref, was applied as the end-effector changed its position. Fig. 14 shows the results of reference, input, and output tensions, and an error that is a difference between reference and output tension. The results show that the output tension can follow the reference tension with a small error (root mean square error of 0.65 N, which is 4.3 % of the maximum reference tension, 15 N, during the experiment), although the end-effector changes its position in 3-D space. The peak error (2 N, which is 13.3 % of the maximum reference) is originating from abrupt change of input tension when the direction of increment of reference tension changes. This abrupt change in tension causes an un-modeled phenomenon with friction and a bandwidth problem with the actuator. It is expected that the error can be decreased with exponential regulation [6, 7] or smooth inverse [9], either of which prevent the abrupt change of the tension. VII. CONCLUSION This study proposes a new concept called loop routing. Loop routing minimizes the bending angle change of the Bowden-cable transmission. Loop routing completely compensates for changes in the bending angle of the Bowden-cable originating from the translation of the end-effector in 2-D space. It also minimizes the bending angle change when the end-effector translates in the orthogonal direction. This resulted in a constant friction model of the system and allowed feedforward friction compensation with only a small error, which can be applied to open-loop tension control of the Bowden-cable transmission. In addition, it could increase the performance of a closed-loop control scheme by compensating the friction along the Bowden-cable. However, this study has limitations in several respects. First, it deliberately increases the bending angle of the sheath to maintain 2π. This increases the overall friction of the REFERENCES [1] J. F. Veneman, R. Kruidhof, E. E. G. Hekman, R. 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