ICABB-2010, Venice, Italy October 14-16, 2010

Development of a light-weight Forceps Manipulator using Pneumatic Artificial Rubber Muscle for Sensor-free Haptic Feedback Hongbing Li, Shameek Ganguly, Sumire Nakano, Kotaro Tadano and Kenji Kawashima

Abstract—Recently, in order to carry out more precise laparoscopic surgery, many types of master-slave surgical robot system have been developed. For this purpose, haptic feedback to the operator is essential. However, installation of a force sensor at the forceps tips is difficult because of space constraints and possible damage during conventional sterilization. In this work, a novel light-weight forceps manipulator is developed for sensor-less force estimation using Pneumatic artificial rubber muscles (PARM). The model of the PARM is obtained experimentally and used to develop a new position controller for the forceps manipulator. A disturbance observer is integrated into the controller to estimate the external force on the forceps tip. Experimental results verify high precision in position tracking and an accuracy of around 0.5 N in estimation of external force, which is deemed adequate for the required purpose. Keywords— Laparoscopic surgery, forceps manipulator, Pneumatic Artificial Muscle, sensor-free haptic feedback I. INTRODUCTION

M

INIMALLY invasive laparoscopic surgery is an effective alternative to open surgery. However the degrees of freedom (DOF) of typical surgical instruments in such procedures are restricted due to the use of trocars. Hence it demands expert skill on part of the surgeon. In order to solve this problem, multi-DOF robotic manipulators have been reported as an alternative to conventional instruments [1-7]. In order to carry out safer and more precise operations using robotic manipulators, especially in master-slave systems, force measurement and haptic feedback to the operator are very important factors [8-11]. To realize precise position control of the slave manipulator, the use of electric motors with high-reduction gears has proved to be effective. Advantages include a very small influence of gravity, inertia and friction on the actuators. But the ability to accurately H. Li is with the Department of Mechano-Micro Engineering, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, Japan. (email: [email protected]) S. Ganguly is with Department of Mechanical Engineering, Indian Institute of Technology, Guwahati, India.(email: [email protected]) S. Nakano is with Asahi Kasei Corporation, Japan. (email: [email protected]) K. Tadano and K. Kawashima are part of the Precision and Intelligence Laboratory, Tokyo Institute of Technology, Japan. (phone:+81-45-924-5032; Fax:+81-45-924-5486; email: tadano, [email protected])

Fig. 1. Developed slave-side surgical manipulator IBIS-IV consists of a 4-DOF supporting manipulator and a 3-DOF forceps manipulator.

sense the force being applied using such actuators requires a force sensor near the end-effecter of each manipulator. However, installation of a sensor at the tip of a forceps manipulator makes sterilizing and downsizing difficult [12]. On the other hand, the use of direct drive motors or small reduction motors with high back-drivability enables good estimation of the external force being applied without the use of force sensors [13]. However, the small power-to-weight ratio of these motors renders them bulky for use in compact robots. Moreover, in the event of a power interruption, the manipulators could hardly retain their posture. We have earlier proposed a slave-side surgical manipulator that is capable of estimating external force, without the use of force sensors, using pneumatic cylinders and rotary vane motors [14][15]. A sensitivity of around 1.0 N in external force estimation was achieved in this work [15]. However, recent investigations into the typical force estimations during laparoscopic surgeries suggest a range upto 10 N with the lower limit lying between 0.1 and 0.5 for different human tissues [16-18]. Hence, there is a clear need to improve the sensitivity of the estimate atleast to 0.5 N even though an even smaller value is more desirable. In this paper, we investigate the applicability of the Pneumatic artificial rubber muscle (PARM) to develop a new forceps manipulator with lighter weight and accurate force estimation. This motive is driven by the fact that the effect of inertia and gravity should be as small as possible, because it is

(a)

Fig. 3. Antagonistic tendon drive mechanism for tip rotational joint.

(b) Fig. 2. (a) Forceps tip showing gripping and rotational joints. Note the absence of any sensor (b) Forceps manipulator developed using PARMs.

impossible to model it perfectly. The modeling errors could be an obstacle to realize high accuracy force estimations. Also, the use of normally closed servo valves for supply flow control to the PARMs makes it possible to retain the posture even in the event of a power failure. II. DEVELOPED FORCEPS MANIPULATOR The developed surgical manipulator IBIS IV consists of a forceps part and a supporting part as shown in Fig. 1. The supporting manipulator has 4 DOFs. Pitch and yaw motion are achieved using pivotal motion centered at the inlet part of the trocar cannula. Roll motion and telescopic extension are achieved using a rotary vane type and cylinder type pneumatic actuator respectively. By combining two parallel link mechanisms and a gimbal mechanism, the pivot point at the trocar cannula is immovable mechanically without direct force as has been shown in [15]. This minimizes the load on the patient’s body, and the kinematics calculation does not need the coordinate of the port position. The 3-DOF forceps part includes a gripper as shown in

Fig. 4. Fiber knitted type PARM manufactured by FESTO. Rest length = 73 mm, inner diameter of tube = 5 mm.

Fig.2. The gripper is implemented using an embedded pneumatic cylinder in order to achieve large gripping force and to avoid interference with other joints. Gripper pitch and yaw motions are independently actuated by two PARMs each installed at the driving part in an antagonistic tendon drive as shown in Fig. 3. Drive wire is made of stainless steel. PARMs of the McKibben type are adopted in this work, composed of rubber tubes with embedded fiber knitting. The PARMs, manufactured by FESTO, have an inner diameter of 5mm and a rest length of 73 mm each (Fig. 4). The forceps manipulator is modularly attachable with the supporting part for quick change and fit. A 5-port normally closed spool type proportional-flow servo valve [5-M5-010B FESTO] is used to supply and exhaust air to each pair of PARMs. The difference in the contraction of the two PARMs results in the tip-joint torque. Linear potentiometers attached to the PARMs are used to calculate the contraction of each PARM and hence, the tip-joint angle. The hereby outlined forceps weighs 236 gm that is 27%

Fig. 6. Experimental set-up for PARM model determination at steady-state conditions. First set of experiments involve variation of the load under isobaric conditions while second set involves variation of working pressure under constant load conditions.

(a)

(b) Fig. 7. Experimental results and linear least square fits for first set of experiments. Typical hysteresis for McKibben type PARMs is observed.

Fig. 8. Determination of empirical relation between (a) slope a and (b) intercept y0 from (1) as a function of the operating pressure.

lesser than the existing forceps using pneumatic cylinders which weighs 325 gm including fitting, as detailed in [14].

where a(P) is the estimated slope from the least square fit and y0(P) is the intercept whose numerical values are presented in Fig.8. Subsequently, functions a(P) and y0(P) are determined using a least square fitting with a polynomial basis as shown in Fig.8. A second order relation is seen to be empirically suitable between the slope and the operating pressure while a first order relation seems adequate for the intercept. These relations are presented as follows:

III. MODELING OF PARM For designing a control for the tendon mechanism, the model of the PARM was determined experimentally. The experimental set-up is as shown in Fig.6. Two sets of independent experiments were performed for this purpose. In the first set, the pressure was controlled using a PI controller to maintain isobaric conditions in the PARM. Then the force was varied and the contraction of the PARM was recorded. Fig.7 shows the experimental results of the force-contraction characteristics of the PARM along with the linear least square fit at each operating pressure. Thus, the force F can be estimated to vary as a linear function of the contraction ɛ as follows: 𝐹 = 𝑎(𝑃)𝜀 + 𝑦0(𝑃)

(1)

𝑎(𝑃) = 𝛼2 𝑃2 + 𝛼1 𝑃 + 𝛼0 𝑦0 (𝑃) = 𝛽1 𝑃 + 𝛽0

(2) (3)

where α0, α1, α2, β0, β1 are parameters obtained from the least square fit in Fig. 8. The force was thus approximated in the following relation with the operating pressure P and the contraction ɛ:

the operating pressure to a range of 200 – 500 KPa as discussed in section III. B. It must be observed here that the model obtained in (4) differs from the more popular Chou-Hannaford model [19] for McKibben muscles which is generalized as follows: 𝐹 = 𝛿0 𝑃(1 − 𝜀)2 + 𝛿1 𝑃

(a) Force = 6 N

(b) Force = 12 N

Fig. 9. Correlation of model (4) with results from second set of experiments. The model fits the experimental data well between 200 to 500 KPa which is the operating pressure range for IBIS IV (refer section III. B ).

𝐹 = (𝛼2 𝑃2 + 𝛼1 𝑃 + 𝛼0 )𝜀 + 𝛽1 𝑃 + 𝛽0

(4)

𝐹 = (𝛼2 𝑃2 + 𝛼1 𝑃 + 𝛼0 )𝜀 + 𝛽1 𝑃 + 𝛽0 + 𝛾𝜀̇

(5)

Furthermore, to account for the friction in the PARM motion, an additional damping factor is added to (4) as follows:

where γ is the viscous damping co-efficient whose value is difficult to obtain experimentally with high accuracy. Hence, it is considered a free parameter and tuned optimally as presented in section IV A. In the second set of experiments, the contraction is noted by varying the operating pressure at steady state with constant force applied on the PARM. This is performed to verify the accuracy of the model obtained in (4). Results are shown in Fig. 9 where the red line indicates the experimental contraction-pressure curve and the blue line the empirical curve obtained from the hereby developed PARM model. It can be observed that the obtained model correlates well with the experimental data only above 200 KPa. This is taken into account by designing the position controller in a way to limit

(6)

where δ0, δ1 are experimentally determined model parameters. The authors attribute this to the construction of the PARMs which is of knitted fiber type rather than the external fiber braided type which are considered in the Chou-Hannaford model. Furthermore, the size of the PARMs adopted in this work is very small, which to the extent of the author’s knowledge, is one of the smallest reported in scientific literature. The small size also makes it difficult to assume the shape of the PARM to be cylindrical during operation. However, a detailed analytical procedure to model this type of PARM is out of the scope of this work. The rest of this paper uses the empirical model developed in (5). IV. CONTROLLER DESIGN A. Position control The proposed controller of the forceps is introduced in this section and is summarized in the block diagram of Fig.10. It consists of an outer position loop with a PD controller and feed-forward block, and an inner pressure loop with a PI controller. The output of the position control loop is the required torque at the tip joint which is obtained as follows: 𝜏𝑟𝑒𝑓 = 𝐾𝑝𝑝 �𝑞𝑟𝑒𝑓 − 𝑞� + 𝐾𝑝𝑑 �𝑞̇ 𝑟𝑒𝑓 − 𝑞̇ � + 𝑍(𝑞̇ 𝑟𝑒𝑓 ) (7)

where q indicates the joint angle, qref the desired joint angle and Z the dynamics of the forceps manipulator. Kpp and Kpd are the PD controller gains.

Fig. 10. Block diagram of position controller of the tendon drive. Reference torque 𝜏𝑟𝑒𝑓 for the driven joint is obtained from the output of the PD position controller and the system dynamics Z(𝑞̇ 𝑟𝑒𝑓 ), and used to obtain the reference pressure 𝑃𝑟𝑒𝑓 for each of the two PARMS using (5). A PI controller is used to set the desired pressure.

To model the dynamics of the forceps part, we neglect gravity and inertia effects since the weight of the tip part is very small and its movement is not so fast. Only friction caused in the transmission line is considered, which is simply presented as 𝑍(𝑞̇ ) = 𝑐𝑞̇ + 𝐷sgn(𝑞̇)

(8)

where c denotes viscous coefficient and D is the absolute value of Coulomb friction. These parameters are also used as free parameters and are optimally tuned during initial set-up (Table I). The desired joint torque from (7) is then used to calculate the required pressures in each of the two muscles in the tendon drive in the following manner. Firstly, we obtain the steady state kinematic and kinetic relations in the tendon drive from Fig. 3 as follows: 𝑟𝑞 = (𝜀0 − 𝜀1 )𝑙0 = −(𝜀0 − 𝜀2 )𝑙0 𝜏 = 𝑟(𝑇1 − 𝑇2 ) 𝑇𝑚 =

𝑇1 + 𝑇2

(9) (10)

where r denotes the radius of the pulley at the fore-end of a tendon drive, ɛ1 and ɛ2 the contraction of the left and right PARMs, T1 and T2 the tensions in the left and right wires, and Tm their mean value. Also, ɛ0 and l0 are the initial contraction and the rest length of the PARM respectively. T1 and T2 are thus obtained from the following equations:

𝑇2 = 𝑇𝑚 −

𝜏

(12)

𝜏

(13)

2𝑟 2𝑟

In order to realize a secure tendon drive, tension in the wire is required to be sufficiently high to prevent slacking. Denoting the minimum allowable tension as T0, we set the mean tension Tm in the wires as the following: 𝑇𝑚 = 𝑇0 +

1

2𝑟

|𝜏|

(14)

Thus combining (14) with (12) and (13), 𝑇1 = 𝑇0 +

𝑇2 = 𝑇0 +

|𝜏| + 𝜏 2𝑟

|𝜏|− 𝜏 2𝑟

≥ 𝑇0

≥ 𝑇0

(15) (16)

which assures that the wire will remain taut at all times. Hence, using (15) and (16), we can generate arbitrary drive torques τref while maintaining wire tension at a level of T0 or above as follows: 𝑇1 = 𝑇0 +

𝛼0 𝛼1 𝛼2 𝛽0 𝛽1 𝛾 𝐾𝑝𝑝

657.9 N 1.96 N/ KPa -0.003 N/ KPa2 -12.0 N 0.18 N/ KPa 45.06 N.s 800.0 mNm / rad

𝑇2 = 𝑇0 +

�𝜏𝑟𝑒𝑓 � + 𝜏𝑟𝑒𝑓 2𝑟

(17)

𝐾𝑝𝑑 𝐾𝑎𝑝 𝐾𝑎𝑖 𝑐 𝐷 𝑇0 r �𝜏𝑟𝑒𝑓 � − 𝜏𝑟𝑒𝑓

10.0 mNm/ rad 0.01 V/ N 0.33 V/ N.s 0.5 N.s/ mm 0.5 N 2.0 N 4.0 mm

(18)

2𝑟

Now, the tension in the wire is identical to the force applied by the corresponding driving PARM. Thus, given the joint torque 𝜏𝑟𝑒𝑓 , the reference pressures in the PARMs 𝑃𝑟𝑒𝑓1 and 𝑃𝑟𝑒𝑓2 can be derived from the PARM model using (5), (7), (17) and (18) as follows: where

𝐴𝑖 (𝑃𝑟𝑒𝑓𝑖 )2 + 𝐵𝑖 𝑃𝑟𝑒𝑓𝑖 + (𝐶𝑖 − 𝑇𝑖 ) = 0

(19)

𝐵𝑖 = 𝛼1 𝜀𝑖 + 𝛽1 ,

(21)

𝐴𝑖 = 𝛼2 𝜀𝑖 ,

(20)

𝐶𝑖 = 𝛼0 𝜀𝑖 + 𝛾𝜀̇𝑖 + 𝛽0 .

(22)

(11)

2

𝑇1 = 𝑇𝑚 +

TABLE I CONTROL PARAMETERS

Here, index i = 1, 2 denotes reference to each of the two PARMs. Thus, one of the two solutions to (19) is easily known to be 𝑃𝑟𝑒𝑓𝑖 =

−𝐵𝑖 −�𝐵𝑖 2 −4𝐴𝑖 (𝐶𝑖 − 𝑇𝑖 ) 2𝐴𝑖

.

(23)

It is to be noted here that the other root of (19) is also physically realizable although it requires higher operating pressures, which is undesirable, as the limiting pressure of the PARMs is 600 KPa. Furthermore, it can be observed from Fig. 9 that the operating pressure of the PARM should be higher than 200 KPa. This is achieved by adjusting T0 so that at T1 = T2 = T0, 𝑃𝑟𝑒𝑓1 = 𝑃𝑟𝑒𝑓2 = 350 KPa to maintain of operating range between 200 to 500 KPa for the tendon drive. Thus, (23) can be used to calculate the reference pressure for each PARM which is then input to the inner pressure control loop. B. Estimation of external force using disturbance observer The dynamics equation of the whole 6-DOF surgical manipulator is described as follows: 𝜏 = 𝜏𝑒𝑥𝑡 + 𝑍(𝑞, 𝑞̇ , 𝑞̈ ) 𝑓𝑒𝑥𝑡 = ( 𝐽𝑇 )−1 𝜏𝑒𝑥𝑡

where fext ∈ 6: External force on the manipulator

τ ∈ 6: Drive torque of the manipulator

(24) (25)

τext ∈ 6: External torque caused by the external force

Z ∈ 6: Impedance function

J ∈ 6×6: Jacobian matrix

Therefore, the external force fext can be obtained from the external torque τext which is estimated from the drive torque τ and the inverse dynamics model. In this calculation, the reference values for torque, velocity and acceleration are used as follows 𝜏𝑒𝑥𝑡 = 𝜏𝑟𝑒𝑓 − 𝑍(𝑞, 𝑞̇ 𝑟𝑒𝑓 , 𝑞̈ 𝑟𝑒𝑓 )

(26)

because the reference values have less noise and a slight phase lead compared to the actually measured values. V. EXPERIMENTS

Fig. 11. Position tracking control using sinusoidal input at amplitude of 30 degrees and frequency of 0.5 Hz.

A. Forceps position control Firstly, in order to evaluate the performance of the developed controller, joint position tracking was performed with a sinusoidal reference input. Movement was unhindered without contact with the external environment. The system was tested by varying amplitude of the reference angles from 0 to 30 deg, and frequencies of 0.1 to 1 Hz. This range of

(a)

(a)

(b) Fig. 12. External force estimation (a) Experimental set-up showing forceps tip gripping a suturing thread attached to a rigidly supported force sensor (b) Forceps tip motion during tracking control of a sinusoidal reference while gripping the suturing thread. The displacement of the tip is visibly impeded by the force applied by the suturing thread.

(b) Fig. 13. Force estimation performance (a) Correlation between estimated and measured force (b) Estimation error. Maximum error is around 0.5 N.

amplitude and frequency was chosen based upon the practical motion constraints on the manipulator during real-time master slave laparoscopic surgery. The free parameters presented in section III were tuned manually for optimal results and are shown in Table I. The experimental result at a frequency of 0.5 Hz is shown in Fig. 11. It is clear that the error in position tracking for the tip joints is negligibly small. Furthermore, no stick-slip phenomena can be seen that might be seen using pneumatic cylinders in slow movement. B. Force estimation In the second experiment a suture thread bound to a rigidly fixed force sensor (BL AUTOTEC.LTD., NANO2.5/2) was gripped and pulled by the forceps manipulator while tracking a sinusoidal reference, as shown in Fig. 12. The external force was estimated from (25) and (26). Fig. 13(a) shows the combined plot of the magnitude of the estimated force and the joint force obtained from the output of the force sensor. Fig. 13(b) shows the estimation error. It is observed that errors are within approximately 0.5 N that is around 16% of the maximum estimated force. Thus, it presents a 50% improvement over the previously achieved sensitivity in [15] which was 1.0 N and is adequate for typical laparoscopic surgery as suggested in [18]. The largest errors are observed during the unhindered motion when the output of the force sensor is zero. This error is attributed mainly to inadequate modeling of the frictional forces of the mechanism which are dominant during unhindered motion of the forceps. It is possible to prevent the errors during free motion being transmitted to the master side by using a low threshold cut-off range [14]. Also, in the future, the friction in the power transmission needs to be reduced further.

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VI. CONCLUSION In this paper, a light-weight forceps manipulator was developed using PARMs for accurate and sensor-free feedback of the external forces acting at the forceps tip. The model of the PARMs was determined empirically and applied for position control of the tip-joints. The designed controller incorporated a disturbance observer for force estimation. Experimental results indicate the adequacy of the tip-joint position control and external force estimation with the developed forceps using PARMs. A sensitivity of around 0.5 N is achieved which is a 50% improvement over the previous work using pneumatic cylinders. However, it is also observed that the friction in the mechanism needs to be reduced for further improvement in the force estimation during free motion.

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