Robust Control Theory and Applications Part 15 docx

Robust Bilateral Control for Teleoperation System with Communication Time Delay - Application to DSD Robotic Forceps for Minimally Invasive Surgery - 547 one joint is between -30 and +30 degrees since this is the allowable bending angle of the universal joint. One bending linkage allows for one-DOF bending motion, and by using two bending linkages and controlling their rotation angles, arbitrary omnidirectional bending motion can be attained. The total length of the bending part is 59 mm excluding a gripper. 2.3 Attachment and rotary gripper The gripper is exchangeable as an end effector and can be replaced with tools such as scalpels or surgical knives. Fig. 5 shows the attachment of the end effecter and mechanism of the rotary gripper. Gear 1 is on the tip of the grasping linkage and gear 2 is at the root of the jaw mesh. The gripper is turned by rotation of the grasping linkage. Although the rotary gripper can rotate arbitrary degrees, it should be rotated within 360 degrees to avoid winding of the wire which drives the jaw. Gear1 Gear2 End effecter End plate Gear1 Gear2 Gear1 Gear2 End effecter End plate End effecter End plate Fig. 5. Attachment and rotation of gripper 2.4 Open and close of jaws The opening and closing motions of the gripper are achieved by wire actuation. Only one side of the jaws can move, and the other side is fixed. The wire for actuation connects to the drive unit through the inside of the DSD mechanism and the rod, and is pulled by the motor. The open and closed states of the gripper are shown in Fig.6. Open Close Wire Open Close Wire Fig. 6. Grasping of gripper 2.5 Drive unit The feature of a drive unit for the DSD robotic forceps manipulator is shown in Fig.7. The total length of the drive unit is 274 mm, its maximum diameter is 50 mm, and its weight is 935 g. Driving forces from motors are transmitted to the linkages through the gears. There Robust Control, Theory and Applications 548 are four motors in the drive unit. Three motors are mounted at the center of the drive unit. Two of them are used for inducing bending motion and the third one is used for inducing rotary motion of the gripper. The fourth motor, which is mounted in the tail, is for the opening and closing motions of the gripper actuated by wire. The wire capstan is attached to the motor shaft of the forth motor and acts as a reel for the wire. The spring is used for maintaining the tension of the wire. DC micromotors 1727U024C (2.25W) produced by FAULHABER Co. were selected for the bending motion and the rotary motion of the gripper. For the opening and closing motions of the gripper, a DC micro motor 1727U012C (2.25W) produced by FAULHABER Corp. was selected. A reduction gear and a rotary encoder are installed in the motor. Wire CapstanWire 274 50 Spring Gear C Gear A Gear B Wire CapstanWire 274 50 Spring Gear C Gear A Gear B Fig. 7. Drive unit The inside part of the rod, as shown in Fig. 1, consists of three shafts, each 2 mm in diameter and 300 mm long. Each motor in the drive unit and each linkage in the DSD mechanism are connected to each other through a shaft. Therefore, the rotation of each motor is transmitted to each respective linkage through a shaft. 2.6 Built DSD robotic forceps manipulator The proposed DSD robotic forceps manipulator was built from stainless steel SUS303 and SUS304 to satisfy bio-compatibility requirements. The miniature universal joints produced by Miyoshi Co., LTD. were selected. The universal joints have a diameter of 3 mm and are of the MDDS type. The screws on both sides of the yokes were fabricated by special order. The built DSD robotic forceps manipulator is shown in Fig. 8. Its maximum diameter from the top of the bending part to the root of the rod is 10 mm. The total length of the bending part, including the gripper, is 85 mm. Fig. 8. Built DSD robotic forceps manipulator A transition chart of the rotary gripper is shown in Fig.9. Robust Bilateral Control for Teleoperation System with Communication Time Delay - Application to DSD Robotic Forceps for Minimally Invasive Surgery - 549 Fig. 9. Transition chart of the rotary gripper 2.7 Master manipulator for teleoperation In a laparoscopic surgery, multi-DOF robotic forceps manipulators are operated by remote control. In order to control the DSD robotic forceps as a teleoperation system, the joy-stick type master manipulator for teleoperation was designed and built in (Ishii et al., 2010) by reconstruction of a ready-made joy-stick combined with the conventional forceps, which enables to control bending, grasping and rotary motions of the DSD robotic forceps manipulator. In addition, the built joy-stick type master manipulator was modified so that the operator can feel reaction force generated by the electric motors. The teleoperation system and the force feedback mechanisms for the bending force are illustrated in Fig.10. The operation force is detected by the strain gauges, and variation of the position is measured by the encoders mounted in the electric motors. Strain gauge Bending Strain gauge Motor with rotary encoder Joystick Master Slave m x s x s f m f Strain gauge Bending Strain gauge Motor with rotary encoder Joystick Strain gauge Bending Strain gauge Motor with rotary encoder Joystick Master Slave m x s x s f m f Fig. 10. DSD robotic forceps teleoperation system 3. Bilateral control for one-DOF bending In this section, bilateral control law for one-DOF bending of the DSD robotic forceps teleoperation system with communication time delay is derived. 3.1 Derivation of Control Law Let the dynamics of the one-DOF master-slave teleoperation system be given by mm mm mm m m mx bx cx f++=τ+   , (1) Robust Control, Theory and Applications 550 ss ss ss s s mx bx cx f + +=τ−   , (2) where subscripts m and s denote master and slave respectively. x m and x s represent the displacements, m m and m s the masses, b m and b s the viscous coefficients, and c m and c s the spring coefficients of the master and slave devices. f m stands for the force applied to the master device by human operator, f s the force of the slave device due to the mechanical interaction between slave device and handling object, and m τ and s τ are input motor toques. As shown in Fig.11, there exists constant time delay T in the network between the master and the slave systems. Human operator Master Slave Environment m x s x m f s f T T Communication Time Delay Human operator Master Slave Environment m x s x m f s f T T Communication Time Delay Fig. 11. Communication time delay in teleoperation systems Define motor torques as mmmmmmmm xcxbxm + − − = λ λ τ τ  , (3) ssssssss xcxbxm + − − = λ λ τ τ  , (4) where λ is a positive constant, and m τ and s τ are coupling torques. Then, the dynamics are rewritten as follows. mmmmmm frbrm + = + τ  , (5) ssssss frbrm − = + τ  , (6) where r m and r s are new variables defined as mmm xxr λ +=  , (7) sss xxr λ + =  . (8) Control objective is described as follows. [Design Problem] Find a bilateral control law which satisfies the following two specifications. Specification 1: In both position tracking and force tracking, the motion scaling, which can adequately reduce or enlarge the movements and tactile senses of the master device and the slave device, is achievable. Specification 2: The stability of the teleoperation system in the presence of the constant communication time delay between master device and slave device, is guaranteed. Robust Bilateral Control for Teleoperation System with Communication Time Delay - Application to DSD Robotic Forceps for Minimally Invasive Surgery - 551 Assume the following condition. Assumption: The human operator and the remote environment are passive. In the presence of the communication time delay between master device and slave device, the following fact is shown in (Chopra et al., 2003). Fact: In the case where the communication time delay T is constant, the teleoperation system is passive. From Assumption and Fact, the following inequalities hold. 00 0, 0 tt mm ss rfd rfd − τ≥ τ≥ ∫∫ , (9) () () 00 0, 0 tt sm ms rf Td rf Td − τ− τ≥ τ− τ≥ ∫∫ . (10) Using inequalities (9) and (10), define a positive definite function V as follows. () () () () () 22 222 1 00 00 21 2 1 22 t mm p ss m p s tT tt mmmpfsss tt ps sm f m ms Vmr Gmr K r Grd KrfdGGKrfd GK rf Td GK rf Td − =+ + + τ − +τ+ +τ − τ− τ+ τ− τ ∫ ∫∫ ∫∫ , (11) where 1 K , m K and s K are feedback gains, and 1 p G ≥ and 1 f G ≥ are scaling gains for position tracking and force tracking, respectively. The derivative of V along the trajectories of the systems (5) and (6) is given by ( ) () () () () () () () ()() () () () () () () () () () 222 1 222 1 1 1 22 21 2 1 22 22 21 mmm p sss m p s mps mmmpfsss pssm f mms mmmmm p sssss ps m ps m mpsmps m Vmrr GmrrKr Gr Kr tT Gr tT KrfGGKrf GKrf tT GKrftT rbr f Grbr f KGrtT r GrtT r KrtT Gr rtT Gr K =+ ++ −−+− −+ + + −−+ − =−+τ++ −+τ− −−− −+ −−− −+ −+   () () () 21 22. mm p f s ss pssm f mms rf G GK rf GKrf tT GKrftT ++ −−+ − (12) Let the coupling torques be given as follows. () ( ) () ( ) 1m p smm f sm KGrtT r K G f tT f τ= − − − − − , (13) () ( ) () ( ) 1sm p ssm f s KrtT Gr K f tT G f τ= − − + − − . (14) Robust Control, Theory and Applications 552 Using (13) and (14), (12) is rewritten as follows. () () {} () () {} () () {} () () {} () () () () 22 1 1 1 1 2 2222 2 2 2 2 21 2 1 22 2 mm m m m m p ss ps s ps s mmfs m m mmfs m ssm fs ps ssm fs mmmpfss pssm f mms mm Vbr r rfGbrGr Grf K GftT f r K K GftT f KftT Gf Gr K KftT Gf KrfGGKrf GKrf t T GK r f t T br − − =− + τ + − + τ − ⎡ ⎤ +τ+ − − + τ+ − − ⎢ ⎥ ⎣ ⎦ ⎡ ⎤ −τ− − − + τ− − − ⎢ ⎥ ⎣ ⎦ −+ + + −−+ − =−  () () {} () () {} () () () () 2 22 11 11 22 11 2 . pss m m fs m s s m fs ps m m ps Gbr K K GftT f K Kf tT Gf KGrtT r KrtT Gr −− − −τ+ −− −τ− −− ≤− − − − − − (15) Thus, stability of the teleoperation system is assured in spite of the presence of the constant communication time delay, and delay independent exponential convergence of the tracking errors of position to the origin is guaranteed. Finally, motor torques (3) and (4) are given as follows. () () 11 11 () () () () mps ps mfs mm m m m mm KGx t T KGx t T K G f t T Kmxc KbxKf τ =−+λ−− − −+λ +−λ+ +   , (16) ()( ) 11 11 () () () () sm m sm p ss s p ss ss Kx t T Kx t T Kf t T KG m x c KG b x K f τ =−+λ−+− −+λ+−λ+−   . (17) 3.2 Experiments In order to verify an effectiveness of the proposed control law, experimental works were carried out for the developed DSD robotic forceps teleoperation system. Here, only vertical direction of the bending motion is considered. Namely, bending motion of the DSD robotic forceps is restricted to one degree of freedom. Then, the dynamics of the master-slave teleoperation system are given by equations (1) and (2), since only one bending linkage is used. Parameter values of the system are given as m m = 0.07 kg, m s = 0.025 kg, b m = 0.25 Nm/s, b s = 2.5 Nm/s, c m = 9 N/s and c s = 9 N/s. The control system is constructed under the MATLAB/Simulink software environment. In the experiments, 200g weights pet bottle filled with water was hung up on the tip of the forceps, and lift and down were repeated in vertical direction. Appearance of the experiment is shown in Fig. 12. First, in order to see the effect of the motion scaling, experimental works with the following conditions were carried out. a. Verification of the effect of the motion scaling. i) G p = G f = 1 and T = 0 ii) G p = 2, G f = 3 and T = 0 Second, in order to see the effect to the time delay, comparison of the proposed bilateral control scheme and conventional bilateral control method was performed. Robust Bilateral Control for Teleoperation System with Communication Time Delay - Application to DSD Robotic Forceps for Minimally Invasive Surgery - 553 Fig. 12. Appearance of experiment b. Verification of the effect to the time delay. i) G p = G f = 1 and T = 0.125 ii) Force reflecting servo type bilateral control law with constant time delay T = 0.125 In b-ii), the force reflecting servo type bilateral control law is given as follows. ( ) () mfms Kf ftTτ= − − , (18) ( ) () s p ms KxtT xτ= − − , (19) where K f and K p are feedback gains of force and position. The time delay T = 0.125 is intentionally generated in the control system, whose value was referred from (Arata et al., 2007) as the time delay of the control signal between Japan and Thailand: approximately 124.7 ms. 0 5 10 15 20 25 30 35 -4 -2 0 2 4 Force Time [s] f s and f m [N] 0 5 10 15 20 25 30 35 -30 -20 -10 0 10 20 30 Position Time [s] x s and x m [mm] xs xm fs fm Fig. 13. Experimental result for a-i) Robust Control, Theory and Applications 554 0 5 10 15 20 25 30 35 40 45 -4 -2 0 2 4 6 8 Force Time [s] f s and f m [N] 0 5 10 15 20 25 30 35 40 45 -30 -20 -10 0 10 20 30 Position Time [s] x s and x m [mm] xs xm fs fm Fig. 14. Experimental result for a-ii) Note that the proposed bilateral control scheme guarantees stability of the teleoperation system in the presence of constant time delay, however, stability is not guaranteed in use of the force reflecting servo type bilateral control law in the presence of constant time delay. Feedback gains were adjusted by trial and error through repetition of experiments, which were determined as λ = 3.8, K 1 = 30, K m = 400, K s = 400, K p = 60 and K f = 650. Experimental results for condition a) are shown in Fig. 13 and Fig. 14. As shown in Fig. 13 and Fig. 14, it is verified that the motion of slave tracks the motion of master with specified scale in both position tracking and force tracking. Experimental results for condition b) are shown in Fig. 15 and Fig. 16. 0 5 10 15 20 25 30 -4 -2 0 2 4 Force Time [s] f s and f m [N] 0 5 10 15 20 25 30 -30 -20 -10 0 10 20 30 Position Time [s] x s and x m [mm] xs xm fs fm Fig. 15. Experimental result for b-i) Robust Bilateral Control for Teleoperation System with Communication Time Delay - Application to DSD Robotic Forceps for Minimally Invasive Surgery - 555 0 5 10 15 20 25 30 35 -4 -2 0 2 4 Force Time [s] f s and f m [N] 0 5 10 15 20 25 30 35 -30 -20 -10 0 10 20 30 Position Time [s] x s and x m [mm] xs xm fs fm Fig. 16. Experimental result for b-ii) As shown in Fig. 15 and Fig. 16, tracking errors of both position and force in Fig. 15 are smaller than those of Fig. 16. From the above observations, the effectiveness of the proposed control law for one-DOF bending motion of the DSD robotic forceps was verified. 4. Bilateral control for omnidirectional bending In this section, the bilateral control scheme described in the former session is extended to omnidirectional bending of the DSD robotic forceps teleoperation system with constant time delay. 4.1 Extension to omnidirectional bending As shown in Fig.10, master device is modified joy-stick type manipulator. Namely, this is different structured master-slave system. The cross-section views of shaft of the joy-stick and the DSD robotic forceps are shown in Fig.17. Due to the placement of strain gauges and motors with encoder of the master device, the dynamics of the master device are given in x-y coordinates as follows. mm mm mm xm xm mx bx cx f + +=τ+   , (20) mm mm mm ym ym m y b y c yf + +=τ+   . (21) When only motor A drives, bending direction of the DSD robotic forceps is along A-axis, and when only motor B drives, bending direction of the DSD robotic forceps is along B-axis. Thus, due to the arrangement of the bending linkages, the dynamics of the slave device are given in A-B coordinates as follows. ss ss ss As As mA bA cA f ++=τ−   , (22) ss ss ss Bs Bs mB bB cB f ++=τ−   . (23) Robust Control, Theory and Applications 556 B A ),( mm yxr ),( ss yxr Slave device ym τ xm τ Master device :Strain gauge Bs τ As τ y x Motor1 Motor2 Motor A Motor B ：Shaft of joystick ：Cross-section of DSD forceps ：Bending linkage y x s A s B m x m y ：Grasping linkage B A ),( mm yxr ),( ss yxr Slave device ym τ xm τ Master device :Strain gauge:Strain gauge Bs τ As τ y x Motor1 Motor2 Motor A Motor B ：Shaft of joystick：Shaft of joystick ：Cross-section of DSD forceps：Cross-section of DSD forceps ：Bending linkage ：Bending linkage y x s A s B m x m y ：Grasping linkage：Grasping linkage Fig. 17. Coordinates of master device and slave device In order to extend the proposed bilateral control law to the omnidirectional bending motion of the DSD robotic forceps, the coordinates must be unified. As shown in Fig. 17, x m and y m are measured by encoders. f xm , f ym , f xs , and f ys are measured by strain gauges. xm τ , y m τ , xs τ and y s τ are calculated from the bilateral control laws. These values are obtained in x-y coordinates. Therefore, consider to unify the coordinates in x-y coordinates. While, displacement of the slave A s and B s are measured by encoder, which are obtained in A-B coordinates. These values must be changed into x-y coordinates. y x B A ),( yxr ),( BAr θ °30 °60 °90 x-y coordinate A-B coordinate : Angle of Rotation: Angle of Bend θ φ φ °120 y x B A ),( yxr ),( BAr θ °30 °60 °90 x-y coordinate A-B coordinate : Angle of Rotation: Angle of Bend θ φ φ °120 Fig. 18. Change of coordinates The change of coordinates for position r(A,B) given in A-B coordinates to r(x,y) given in x-y coordinates (Fig. 18) is given as follows. [...]... effectiveness of the proposed control scheme was verified 558 Robust Control, Theory and Applications Force fxs and fxm [N] 1 fxs fxm 0.5 0 -0.5 -1 0 5 10 x s and x m [m] 25 30 xs xm 20 0 -20 -40 0 5 10 15 Time [s] 20 25 30 Force 1 fys and fym [N] 20 Position 40 fys fym 0.5 0 -0.5 -1 0 5 10 15 Time [s] 20 25 30 Position 40 ys and ym [m] 15 Time [s] ys ym 20 0 -20 -40 0 5 10 15 Time [s] 20 25 30 Fig 19... Li, B and Yu, F (2010) Design of a vehicle lateral stability control system via a fuzzy logic control approach, Proc Instn Mech Engrs Part D: J Automobile Engineering Vol 224, 313-326 576 Robust Control, Theory and Applications Mirzaei, M., Alizadeh, G., Eslamian, M and Azadi, S (2008) An optimal approach to nonlinear control of vehicle yaw dynamics, Proc Instn Mech Engrs Part I: J Systems and Control. .. constraints and tyre-road conditions must be considered so that the implementation of the controller can be more practical In this chapter, a nonlinear observer based robust yaw moment controller is designed to improve vehicle handling and stability with considerations on cornering stiffness uncertainties, actuator saturation limitation, and measurement noise The yaw moment 562 Robust Control, Theory and Applications. .. M., Fagiano, L., Milanese, M and Borodani, P (2007) Robust vehicle yaw control using an active differential and IMC techniques, Control Engineering Practice Vol 15, 923-941 Cao, Y.-Y and Lin, Z (2003) Robust stability analysis and fuzzy-scheduling control for nonlinear systems subject to actuator saturation, IEEE Transactions on Fuzzy Systems 11(1): 57-67 Du, H., Lam, J and Sze, K Y (2005) H∞ disturbance... for uncontrolled system Dotted line is sideslip angle for controlled system with the designed controller, and solid line is sideslip angle estimated from observer 1000 500 Moment (Nm) 0 -500 -1000 -150 0 -2000 -2500 -3000 0 1 2 3 4 5 Time (s) 6 7 8 9 10 Fig 8 Yaw moment under J-turn manoeuvre on a dry road with measurement noise 574 Robust Control, Theory and Applications To further validate the robustness... vehicle dynamic control system, Transportation Research Part C: Emerging Technologies Vol 18, No 2, 213–224 Tanaka, K andWang, H O (2001) Fuzzy control systems design and analysis: A linear matrix inequality approach, John Wiley & Sons, Inc., New York Yang, X., Wang, Z and Peng, W (2009) Coordinated control of AFS and DYC for vehicle handling and stability based on optimal guaranteed cost theory, Vehicle... and control for improving handling and active safety: from four-wheel steering to direct yaw moment control, Proc Instn Mech Engrs Part K: J Multi-body Dynamics Vol 213, 87-101 Antonov, S., Fehn, A and Kugi, A (2008) A new flatness-based control of lateral vehicle dynamics, Vehicle System Dynamics Vol 46, No 9, 789-801 Boada, B L., Boada, M J L and Diaz, V (2005) Fuzzy-logic applied to yaw moment control. .. velocity and is often used for controller design and evaluation Fig 1 Vehicle lateral dynamics model In this model, the vehicle has mass m and moment of inertia Iz about yaw axis through its center of gravity (CG) The front and rear axles are located at distances lf and lr, respectively, from the vehicle CG The front and rear lateral tyre forces Fyf and Fyr depend on slip angles αf and αr, respectively, and. .. oxygen control in the literature: PI and PID -control, fuzzy logic, robust control, model based control etc (Garcia-Sanz et al., 2008), (Olsson & Newell, 1999) Recently the control problem of nitrate and phosphate level also became a priority The control based on mathematical model of the wastewater treatment process has known many developing, depending on the type of the mathematical model used in the control. .. 180rpm and 300rpm The aeration tank working volume is 35L The treatment temperature can be on-line monitored and controlled through a temperature probe and an electric heating resistance both mounted inside the tank The pH can also be on-line monitored and controlled through a pH electrode connected to a pH controller and two peristaltic pumps, one for acid and the other for base (acid tank [3] and base . of the proposed control scheme was verified. Robust Control, Theory and Applications 558 0 5 10 15 20 25 30 -40 -20 0 20 40 Position Time [s] x s and x m [m] 0 5 10 15 20 25 30 -1 -0.5 0 0.5 1 Force Time. [s] x s and x m [mm] xs xm fs fm Fig. 13. Experimental result for a-i) Robust Control, Theory and Applications 554 0 5 10 15 20 25 30 35 40 45 -4 -2 0 2 4 6 8 Force Time [s] f s and. vehicle handling and stability with considerations on cornering stiffness uncertainties, actuator saturation limitation, and measurement noise. The yaw moment Robust Control, Theory and Applications