1、Conguration and Joint Feedback for Enhanced Performance of Multi-Segment Continuum Robots Andrea Bajo, Roger E. Goldman, and Nabil Simaan* AbstractMulti-segment continuum robots offer enhanced safety during surgery due to their inherent passive compliance. However, they suffer poor position tracking
2、 performance due to exibility of their actuation lines, structural compliance, and actuation coupling effects between segments. The need for control methods addressing accurate tracking for multi- segment continuum robots is magnied by increased precision requirements of surgical procedures employin
3、g these structures. To address this need, this paper proposes a tiered controller that uses both extrinsic and intrinsic sensory information for improved performance of multi-segment continuum robots. The higher tier of this controller uses conguration space feedback while the lower tier uses joint
4、space feedback and a feed-forward termobtainedwithactuation compensation techniques.Weprove the stability of this controller using Lyapunovs direct method and experimentally evaluate its performance on a three-segment multi-backbonecontinuumrobot.Resultsdemonstrateitsefcacy in enhancing regulation a
5、nd tracking performance. It is shown that the controller mitigates the effects of actuation coupling be- tweenrobotssub-segmentsanddecreasesphaselag.Theseresults suggest that this tiered controller will enhance telemanipulation performance of multi-segment continuum robots. I. INTRODUCTION In the pa
6、st decade, continuum robots gained popularity in the medical robotics community for their dexterity and innate compliance. These devices address a growing need to reach deeper into the human anatomy while minimizing or eliminating skin incisions. The development of new surgical paradigms such as Min
7、imally Invasive Surgery (MIS) in deep surgical elds and Natural Orice Transluminal Endoscopic Surgery (NOTES) emphasize this need. Current designs of continuum robots that provide deep access into the human body continue to present new theoretical and practical chal- lenges. These designs include wi
8、re-actuated articulated robots 1 and 2, passively exible stems with wire-actuated wrists 3, rigid-exible locking access sheaths 47, steerable robots 810, and multi-backbone continuum robots 11 and Fig. 1. These robotic slaves offer advantages in terms of miniaturization while supporting multiple app
9、lications 12 and 13. However, they require novel control algorithms in ordertomeetthedesiredaccuracy.Thelackofaccuracyisdue to friction,extensionand torsionoftheir actuationlines, shape discrepancy from nominal kinematics, and actuation coupling between segments. This work was supported by NSF Caree
10、r grant #IIS-0844969. A. Bajo and N. Simaan are with the Department of Mechanical Engineering, Vanderbilt University, Nashville, TN 37212, USA (e-mail: fandrea.bajo,nabil.simaangvanderbilt.edu). R. E. Goldman is with the Department of Biomedical Engi- neering, Columbia University, New York, NY 10027
11、, USA (e-mail: reg2117columbia.edu). * corresponding author Fig. 1. The experimental setup consist of a nine-axis actuation unit, a 3-segment continuum robot, a magnetic eld generator, and four magnetic sensors attached to the robots base (0), the end disk of the rst segment (1), the end disk of the
12、 second segment (2), and robots end-effector (3) The theoretical foundations of kinematics and dynamics of continuum robots are built upon the work on hyper-redundant robots by Chirikjian and Burdick 1416. Previous works on control of continuum robots include the work of Gravagne and Walker 17 on as
13、ymptotic regulation for wire-actuated continuumsegments, the work of Webster et al. on kinematics and visual servoing for concentric-tube robots 18, and the workofDupontetal.ondesignandcontrolofconcentrictube- robots 19. Several other researchers focused on overcoming exibilities, friction, backlash
14、, and hysteresis in continuum robots. For example, Xu and Simaan 20 presented a model- based recursive estimation framework that uses extrinsic mea- surements of the end-effector orientation for multi-backbone continuumsegments.Simaanetal.12extendedthisapproach to multi-segment multi-backbone contin
15、uum robots using a hybrid approach. The nominal parameters of the robot were corrected based on joint-space information for each segment of a multi-segment robot. Additional coupling effects between segments were overcome by conguration space compensa- tion. Agrawal et al. 21 designed a feed-forward
16、 smooth backlash inverse and a recursive estimator for unknown pa- rameters in wire-actuated robots. Kesner and Howe 22 used 2011 IEEE International Conference on Robotics and Automation Shanghai International Conference Center May 9-13, 2011, Shanghai, China 978-1-61284-385-8/11/$26.00 2011 IEEE 29
17、05a model-based actuation compensation technique in bowden wire actuated catheters. Camarillo et al. 23 used vision feedback with wire-actuated multi-segment catheters. Croom etal.24investigatedtheuseofself-organizedmapsforshape estimation of concentric-tube robots. Despite these works, there is a l
18、ack of delineation of the role of extrinsic feedback for improving the performance of continuum robots. Our investigation makes a small step towards lling this gap by proposing a mixed feedback controller and by experimentally evaluating its performance on a continuum robot with compa- rable dimensi
19、ons to conventional MIS surgical instruments. Future surgical continuum robots with multiple segments will operate deep inside the human anatomy. For this reason, we are designing our continuum robots with embedded mag- netic sensors that provide position and orientation information about the base a
20、nd tip of each segment. These sensors are suitable and approved for surgery and can provide valuable in-vivo sensory information. In our investigation, we assume that a source of extrinsic measurement exists. This extrinsic measurement can be provided by both a vision system or an electromagnetic de
21、vice as shown in Fig. 1. This paper proposes the design of a controller that uses this extrinsic information online for improving the congura- tion tracking and for overcoming modeling uncertainties. We exploretheutility ofthismixedfeedbackcontrollerinenhanc- ing regulation and tracking control of e
22、xible multi-segment continuum robots. The conguration space controller runs on top of the low level, joint-space, PD controller based on the instantaneous inverse kinematics model of the robot. Section II summarizes the forward kinematics of the three-segment continuum robot based on 2527. Section I
23、II introduces the Conguration Space Controller (CSC) and carries out the proof of stability. Section IV presents the experimental setup andtrackingperformanceoftherobotscongurations.Section V compares the phase lag of the system with and without CSC, singleCongurationSpaceDegreeofFreedom(CSDoF) trac
24、king, multi CSDoF tracking, the controller response to external wrench disturbances, and an evaluation of the pose of a single continuum segment. II. KINEMATIC MODELING OF THE 3-SEGMENT CONTINUUM ROBOT The multi-backbone robot of Fig. 1 is composed of three multi-backbone segments. Each segment is m
25、ade from three circumferentially located super elastic NiTi secondary back- bones and one centrally located super elastic NiTi primary backbone. By controlling the length of the secondary back- bones each segment may be actively bent according to the kinematics dened below. The conguration of each s
26、egment k=1,2,3 can be characterized by two angles: the bending angle L k and the angle characterizing the plane in which the segment bends k as shown in Fig. 2. The conguration space vector for each segment is dened as k = L k , k T . An augmented conguration space vector is constructed for 1 2r x b
27、1 x p1 y p1 y b1 z b1 =z p1 y p2 y b2 x p2 z b2 =z p2 =z g2 x e2 x g2 y e2 y g2 z e2 =z g2 L2 L1 2 2 1 1 Fig. 2. Kinematic nomenclature of a two-segment robot all three segments as:=T 1 , T 2 , T 3T . (1) For each segment,positionp b k g k and orientationR b k g k of the end disk with respect to the
28、 segment base disk are given by p b k g k = L k L k 0 cos( k )(sin( L k )1) sin( k )(sin( L k )1) cos( L k ) (2) R b k g k =R b k p k R p k e k R e k g k (3) where R b k p k = e k e3 , R p k e k = e (0L k )e2 , and R e k g k = e k e3 denote the exponential forms for these rotations, e j denotethecan
29、onicalbasisunitvectorsforR 3 , ndesignates the skew-symmetric cross product matrix of vector n, and 0 = /2. Using (2) and (3), one can write the direct kinematics of any segment (k 1) with respect to the robots base: p b1 g k =p b1 g k1 +R b1 g k1 p b k g k (4) R b1 g k =R b1 g k1 R b k g k . (5) Given the length of the primary backbone L k , and the lengths of the secondary backbones L k,i , i = 1,2,3, we dene the following joint space variables q k,i = L k L k,i . The inverse kinematics that relates the conguration space vector k to 2906
