Kinematic modelling and trajectory planning for a tele-laparoscopic manipulating system Ali Faraz and Shahram Payandeh Experimental Robotics Laboratory (ERL), School of Engineering Science, Simon Fraser University, Burnaby, British Columbia V5A 1S6 (Canada) E-mail: shahram@cs.sfu.ca (Received in Final Form: September 4, 1999) SUMMARY This paper addresses the kinematic modelling, solutions and trajectory planning of a tele-laparoscopic manipulator. This type of manipulator can be used in remote positioning of laparoscopic tools through tele-operating system. Speci- fically the paper models kinematics of a typical manipulating system which can be used in such tele-surgery. Inverse kinematics solutions are also obtained for two kinematically constraint motions which are part of a typical trajectory of the laparoscopic tools. These are fixed axis rotation of the tool and its straight line motion. Simulation results are presented to demonstrate the validity of such models and solutions. KEYWORDS: Tele-laparoscopic system; Kinematic modelling; Trajectory planning 1. INTRODUCTION The remote manipulation in laparoscopy introduces kine- matic motion problems described as: (a) spherical movements of tool at the port of entry on the abdomen, and (b) lack of dexterity inside the abdomen. There are a number of works in the literature addressing robotic applications for laparoscopy, which can be categorized in two main types: Automated Positioners. This type is basically a posi- tioner for laparoscopic tools and a navigating system which in addition to locking tools in a desired configuration, it also can reposition the tool to a previously defined location (e.g. for changing the angle of endoscopic view to a previously stored orientation). This type of positioner is also commer- cially available by Computer Motion Inc. (AESOP units). 1–3 Taylor et al, 4 have developed an automated positioner with a parallelogram configuration to provide remote center of rotation for laparoscopic tools. Also the commercial devel- opment (EndoSista) by Armstrong Projects, is a specially designed positioner to control laparoscopic view directly by head movements of the surgeon. Tele-Operated Extenders. One of the main areas of potential application for robotic extenders in laparoscopy, is in the field of tele-operated master-slave system. This is due to the fact that laparoscopic surgery with inverse hand motion and limited force sensing is very unnatural to control and physically demanding for the surgeons. As a result, this motivates to develop tele-operated extenders so that the surgeon can control the direct motion of the tool’s tip on the monitor, instead of reverse motion at the handle which is the case in manual operations currently performed. 5 There are also other research works proposing the general concept of tele-surgical workstations for laparoscopy, which are based on master-slave tele-operated systems. 6,7 However, there has not been any specific design for implementation or experi- mental developments for laparoscopy. The only tele-operated surgical development belongs to SRI Inter- national. 8 However their current design configuration is only suitable for open surgery, since it does not have any DOF to perform spherical movements at the port of entry which is a primary requirement for laparoscopy. This paper presents a kinematic model and solution to a laparoscopic manipulating system which can be used in the context of automated positioning systems and/or tele- operating system. The paper is organized as follows: Section (2) presents the mechanical configuration of the system; Section (3) presents the kinematic model of the manipulating system and the inverse kinematic solutions; Section (4) presents solutions for trajectory generation for two types of motions: (a) fix-point rotation and (b) linear motion. Finally Section (5) presents some concluding remarks. 2. CONFIGURATION OF ROBOTIC EXTENDERS The design configuration of robotic extenders for laparo- scopic applications should generally meet the two primary requirements: (a) to comply with the kinematic constraint at the port of entry; (b) to provide sufficient DOF inside the abdomen for the specific surgical task. Generally laparoscopic positioners are used either for positioning the laparoscope, or surgical tools (such as retractors, graspers, etc), which both cases require two positioning DOF (i.e.  1 , and  2 , Figure 1). In the case of laparoscope, 2 additional DOF at the port of entry are needed. One DOF for the rotational adjustment of laparo- scope around its longitudinal axis ( 3 ), so that the image on the monitor obtains the upright orientation. The second DOF for translating the laparoscope in and out of abdomen for zooming purposes. Also, in the case of surgical tools same 2 DOF are required for proper orientation and axial reach at the surgical site. Therefore for this type of positioner, generally a total of 4 DOF (i.e.  1 ,  2 ,  3 , and l at the port of entry, Figure 1) is adequate. The design of Robotica (2000) volume 18, pp. 347–360. Printed in the United Kingdom © 2000 Cambridge University Press