Visual Servo Control of Cabledriven Soft Robotic Manipulator

Transcription

1 Shanghai Jiao Tong University Visual Servo Control of Cabledriven Soft Robotic Manipulator Hesheng Wang ( 王贺升 ) Shanghai Jiao Tong University China

2 Outline Introduction Background System Design Kinematics Controller Design Experimental results Conclusion

3 Background Minimally Invasive Surgery (MIS) On the surface of the beating heart Inside the beating heart

4 Background Concentric Tube Robot HARP Heart Lander

5 Background Not Soft Enough Not Safe Enough Not Practical Enough

6 Background Soft robotic systems -Conform to the surroundings -Ease of operation - Fit to Dynamic environments

7 Research Background Soft robots: material, manufacturing, Control Theory, computer simulation Applications: minimally invasive surgery, military, exploration, rescue (1) Starfish robot (2)Quadruped deformable robot (3) Caterpillar robot (4)Mechanical octopus tentacle

8 Characters of soft robot Characters Rigid robots Redundant robot Hard continuum robot Soft robot DOF Small Many Infinite Infinite Material strain None None Low High Accuracy Very High High High Low Safety Low Low Medium High Flexibility Low High High High Compatibility with obstacles None Good Medium Very good Controllability Easy Medium Hard Hard Positioning Easy Medium Hard Hard

9 System Design Soft Robotic Manipulator Kinematics - hyper-redundancy

10 System Design System Composition A soft manipulator A drive base frame Control and display system

11 System Design The Soft Manipulator 30mm silicone rubber (ECOFLEX ) 8 non-abrasive fiber cables (DyneemaTM) plastic caps ablation tools and a micro CCD camera

12 System Design The Drive Base Frame Linear motion system Rotational motion system

13 System Design Control and Display System Joystick Control Cameral Display Control Software

14 System Manipulation Manipulate method Manual Mode The cable tension can be changed by setting the Head angle Adding functional buttons - functional buttons for each behavior - buttons for selecting which cables are being controlled - buttons for emergency Automatic Mode Path planning & Localization on the surface of the heart

15 System Manipulation Behavior Implementation 1. Blending 2. Contracting 3. Advancing/Retreating 4. Wriggling 5. Blending and Wriggling partly 6. S shape

16 Movie 5

17 Experiments Unconstrained Environment -with a plastic thorax and a silicone heart -different simulated paths on the surface -to identify the geometrical shape and flexibility

18 Experiment Video

19 Experiments Limited Environment - made of balloons to imitate the human tissue - complicated path to guide the soft probe - effects of the gravity and surroundings

20 Experiment Video 2

21 Experiment Video 3

22 Experiment Video 4

23 System Manipulation KEY ISSUES Kinematics Modeling - Influence of gravity - Influence of Surroundings Environment Dynamics Modeling - Modeling Method - Calculation efficiency Controller

24 Constant curvature hypothesis Constant curvature hypothesis :dividing the whole body of the soft robotic manipulator into n segments, and each segment can be treated as a cylinder that the radius of section is constant three spaces and two mappings r denotes the angle between the bending plane and the positive direction of x axis, denote the curvature angle of the bending plane respectively. denote the curvature radius of the bending plane respectively.

25 Kinematics For i-th segment the length variables of 4 cables: the current length of 4 cables: q, q, q, q l1 l2 l3 l4,,, n n n n the central axis of the i-th segment l n

26 Actuation space - Virtual joint space 柔性机械臂运动学模型驱动空间 - 虚拟关节空间映射 i tan q q q q i q q q q nR i r i 2L q Ri q q q q

27 Virtual joint space Task space 柔性机械臂运动学模型虚拟关节空间 - 任务空间映射 i1 T A A A A A i i1 i2 i3 i4 i c i c i s ic i c i c is i rc i i c i s c c s c ss rs c i i i i i i i i i i cs ss c rs i i i i i i i i 1 T T1 T2 T i

28 Perspective Projection u v ( t ( t 1 ) ) Π Π z( t) Camera coordinate frame c O x( t) 1 c the magnifications cot sin 0 u v y C zc x C principal angle between pointu and v axes Ĉ vˆ pˆ û Normalized image plane C u ( u 0, v0) v p Physical retina z y World coordinate frame x P

29 Projection Model the projection of the feature point on the image plane Interaction matrix 1 e x() t yqt ( ( )) P zqt ( ( )) 1 e T x() t zqt ( ( )) m vt () yqt ( ( )) Ayt ( ( ), qt ( )) zqt ( ( )) wt () vt () zqt ( ( )) bqt ( ( )) wt ()

30 Property 1 For any homogenous vector, the product can be written in the following form: A( t)ρ Q(ρ, y( t) )θ Q( ρ, y( t)) where is a regressor matrix without depending on the unknown parameters. σ ρ A (t) ρ

31 Kinematic-based and Dyanmic Visual Servoing + - Control law Joint velocity Robot controller Robot Camera Joint angle sensors Visual information Robot Camera + - Control law Visual information

32 Kinematic-based Visual Servoing Kinematic-based controller T () ( ()) ˆ T qt J qt A ( yt (), qt ()) Kyt () 1 T ˆT T J ( qt ( )) b ( qt ( )) y ( tk ) 1yt ( ) 2 Adaptive law 1 b 1 T xt ˆ( ) Y ( y(), t q()) t q() t

33 Stability analysis Applying the image-based visual servo controller and adaptive algorithm, it can be proved that the position error of the feature point on the image plane will be convergent to zero when time approaches to the infinity lim yt ( ) 0 t a Lyapunov-like function is defined as follows: Finally 1 T 1 b T b V t y () t K1z( q()) t y() t x () t x() t 2 2 V () t y () t Dˆ ( y(), t q()) t JK J Dˆ ( y(), t q()) t y() t T T 2 T 1 By Babarrat s Lemma, the stability could be proved.

34 Experimental system

35 Experimental results

36 Experimental Results Initial position: y 0 208,166 实验与分析 T 三种情况下的实验 Desired position: y 50,150 T d Initial estimated feature 3D position: gains: K b x T 50 Trajectory Desired position u v v(pixel) Position Error(pixel) u(pixel) Time(s) The trajectory of the feature point on the image plane. The image errors between current position and desired position.

37 Conclusion and future work A cable-driven soft manipulator for cardiac ablation -completely made of soft materials -high degree of freedom -high flexibility A modified behavior-based control method is presented crowded pericardial environment A kinematic model of the soft robotic manipulator with the concept of piecewise constant curvature is presented. An adaptive controller for image-based visual servoing of the soft robotic manipulator is developed. The performances of the proposed method are verified by experiments on a soft robotic manipulator. Future work includes considering dynamic visual servoing and environment effects on the robot.

38 Shanghai Jiao Tong University Thank you!

39 Shanghai Jiao Tong University Thank you!