Degrees of freedom of a manipulator 38
Kind of joints possibly involved in a manipulator 38
Kinematic structures 38
Robot actuators 43
Speed-to-torque converters 46
Motors encoders and brakes 46
Knowing and ordering the pose of a robot: computational kinematics 46
Trajectory planners 46
Robot movement dynamics 47
Controlling a robot (the control loop) 48
Robot end effector precision 49
Working volume 50
Manipulability index 51
Regardless of purpose, robotics fundamentally describes a combination of mechanics, sensors, electronics and software. Since surgical manipulators can be extremely specific depending of their intended application, it is not possible to consider surgical robotics without a basic knowledge of what a robot is made of—in the same way as it is impossible to discuss surgery without a knowledge of fundamental anatomy. In this chapter we will try to provide some basic information about the technology upon which surgical manipulators rely. It is of course beyond the scope of this chapter to provide an in depth analysis of every possible technical aspect, but rather to provide a common vocabulary with the aim of attempting to fill the gap existing between biomedical engineers and surgeons, the futures of whom will probably need to be shared.
The origin of the term “robot” is explained chapter 1 . This is simply a generic term for machines which vary from roboticized car, exoskeleton, drone, or, more generally, any unmanned moving system controlled by a computer. The exact technical term used when discussing surgical robots , should actually be surgical manipulators . However, we will use the terms “robot” and “manipulator” interchangeably, as they are commonly understood as meaning the same thing.
Degrees of freedom of a manipulator
Any mechanical system able to move have a certain degree of freedom (DOF). The more DOF it has, the more complex its movement may be. A degree of freedom is nothing else than a unique translation on, or a unique rotation about, an axis. For example, a 1 DOF manipulator can only provide rotation or translation, and 2 DOF allow either a planar movement, or one translation and one rotation.
Depending of their application, surgical robots currently have 2 to 8 DOF. Systems with 6 DOF can usually adopt any pose in the 3D-space whereas larger numbers of DOF are named redundant manipulators and allow the same pose to be achieved by using different combinations. This can be an advantage when multiple arms need to work in the same surgical field without colliding. However, more is not necessarily better as the higher the DOF level of a surgical robot, the more complex it is in terms of design and price, and it has the greatest constraints to resolve to keep it steady and accurate with soft motions.
Kind of joints possibly involved in a manipulator
Robots are simply made of links connected together by joints, but the nature of these joints and the way they are combined give the robot most of its specifications. Five types of joints may be involved ( Table 4.1 ).
The most common joint type is revolute, due to the fact that actuators are generally themselves made of revolute motors. Prismatic joints are favored when a pure translation motion is required (Cartesian motion) and are particularly good choice when highly accurate micromotion is required.
Joints and the way they are assembled via links are critical as these have to deal with opposing constraints: very low friction and the smallest possible clearance between moving parts. High friction not only will increase the force required to move the joint, but also will introduce non-linear parameters in the movement equations making accurate joint control difficult or impossible. This problem is increased when links are long and the payload is heavy as such designs generate high friction.
A new kind of joint not listed above is currently emerging: the magnetic joint, that is a magnet shaped as a ball joint with very limited friction and an extended range of motion which produces low force but extremely agile robots [ ].
Some authors have proposed disposable plastic joints for cost-effective surgical robot components [ ]. These would have the significant advantage of being low-cost and single use, but still remain to be assessed in real-life surgery.
Manipulators can be categorized into two main classes: serial and parallel structures. These classes are opposing in nature and strongly influence the properties of any manipulator using them.
Serial manipulators have links which connect serially from the one joint to the next. Conversely, parallel manipulators have serially linked parts which finally connect together to form a closed loop. Hybrid manipulators are simply the combination of both types: a serial manipulator can be mounted at the end of a parallel one, or vice versa.
Both have advantages and drawbacks and the choice of one type over the other greatly depends on the required specification of the robot [ ]. They are equally used in surgical robotics.
A basic knowledge of the fundamental properties of these kinematics is crucial to understand the possibilities and the limitations of surgical manipulators [ ].
Serial manipulators are the oldest concept and are the most commonly used in industry due to their versatility.
They are constructed by addition of segments usually connected by revolute or prismatic joints. This kind of kinematic allows large workspaces with a comfortable reach while maintaining a compact size with limited footprint [ ].
While 6 DOF are sufficient to perform any pose, some serial robots have an additional DOF in order to simulate the large range of motions of the human arm. Such robots, which are known as anthropomorphic manipulators, have 3 coaxially located DOF at the base (like the human shoulder), 3 other coaxial DOF at the end (like the wrist) and are connected by another DOF, the elbow.
Due to their capabilities to simulate a human arm, these anthropomorphic robots are extremely useful for surgical applications, particularly to restrict the likelihood of collision when multiple arms are used.
An example of an industrial robot commonly used in experimental surgery is the KUKA iiwa™ manipulator. Which has 7 DOF kinematics that mimic the human arm.
These are made up of a complex association of segments collaborating together in a closed loop. Their workspaces are smaller and more complex than serial manipulators and some poses inside the workspace may be unreachable (due to singularities ). However, they exhibit high stiffness and accuracy, making them a good choice for surgical applications where the workspace is generally very limited, but accuracy is demanded. Furthermore, their closed structure allows better payload capabilities than that of serial manipulators, as each actuator collaborate with the others to cumulate their force/torque [ ]. This allows the power of each actuator to be reduced, making the whole robot both smaller and safer.
Hybrid kinematics combines both serial and parallel manipulators. Generally, the parallel structure is used for the proximal DOF, whereas the serial part is located at the terminal end of the manipulator. This combination provides better stiffness and increased force/torque where it is most required (the base) with greater agility at the end effector. Examples of such kinematic are shown Figure 4.3 and see also chapter 10 (SurgiDelta system, prototype k-3).
Continuum robots form a new class of manipulators, derived from the serial type. Most of these have been developed for surgical purpose [ ] and rely on observations from nature. They try to imitate the structure and motion of snakes, whose spine is made of a huge number of vertebrae, each with limited individual mobility but producing segments with different directions when summated. This in practice allows turning movement around a structure and then multiple changes in direction. These kinematics are particularly useful when an instrument needs to follow a non-linear path in order to reach a structure, while preserving another critical structure located along the same path, a rather common situation in surgery.
Spine continuum manipulators
Spine continuum manipulators have raised a lot of interest for abdominal and cardiothoracic surgery ( Figure 4.4 ) due to their relatively good force control and stiffness [ ]. Some attempts have been made in vitro to use them in laryngeal endosurgery [ ]. An example of such a manipulator is described chapter 9 under the trade name Flex™.
Concentric tubes form the second class of continuum robot with “virtual” joints. These are made of precurved hyperelastic tubes inserted telescopically into each other. The combination of translation and rotation motions of one tube with regard to the others allows the whole system to reshape. Two tubes with same curvature summate their angulations whereas in opposition they cancel each other out ( Figure 4.5 ). The major drawback of this technology is that the radius of curvature (ROC) cannot be made small enough in many clinical circumstances. Using small diameter tubes allows a smaller ROC but significantly decreases the overall stiffness of the system.
Some teams have considered the possibility of using these to perform transnasal sellar surgery, although they are still in the laboratory evaluation stage [ ] and the cumbersome mechanics involved make them hard to integrate in a surgical set-up.
Virtual RCM kinematics
As minimal invasive surgery aims to target anatomical structures within natural orifices or via the smallest possible incisions, the medical instrument has to be constrained in such a small hole, usually called a port . Obviously, only rotations around and coaxial translation within the port are allowed in order to maintain the smallest size of the incision. Thus, the surgical port is a fulcrum point around which instruments are manipulated from outside to inside the body.
Because it is unpractical or impossible to place robot joints close to the entry port, a general-purpose robot would need a special arrangement of joints in order to move its end effector instrument around this fulcrum point ( Figure 4.6 ). To circumvent this issue, some specific mechanics may be designed in order to distance the joints from the port while maintaining the fulcrum point at the correct location. These kinematics were first studied by Taylor et al. [ ] in order to best match manipulators to surgical requirements and are named virtual remote center of motion (RCM). Figure 4.7 shows a common embodiment of a virtual RCM system. Many arrangements are possible, as described in references [ ].
One advantage of the virtual RCM based manipulators is that their working volumes are not drastically restricted by the RCM constraint, unlike industrial robots which are not specifically designed for surgical purposes. Another advantage of virtual RCM based manipulators is their intrinsically safe structure [ , ]. Because their kinematic do not permit motion outside the pivot point (the instrument entry point), the risk of patient injury is minimized compared to kinematics where the pivoting motion is made up of a combination of multiple motions (as shown in Figure 4.7 ). Furthermore, as the kinematics control relies on a less complex computation, the risk of a mathematical singularity occurrence that could lead to a dangerous motion is also reduced, while at the same time the response time is improved [ ].
Other designs of systems involving single-revolute and circular-prismatic joints, or spherical 5-bar linkages, are possible [ , ], mainly depending of the expected accuracy and space available for the mechanism ( Figure 4.8 ).
The drawback of virtual RCM is that it is a fixed point, the location of which depends on both the robot position and the geometry of the surgical instrument. It has to be accurately located on the patient entry port and any change in the instrument geometry needs to be compensated.
One issue with manipulators is the fact that they have to cope with the influence of gravity which depends of the orientation of each joint axis with respect to the axis of gravity. In order to cancel out or decrease this effect, a SCARA structure (selective compliance articulated arm) can be used. This acronym simply means that each joint axis is designed to be parallel with the axis of gravity (an example of a SCARA structure is shown Figure 6.2 ).
Actuators are the technical name for robot motors. As high demands are placed on surgical manipulators, they can use a wide variety of means of motion, depending of the intended application. Actuators are one of the key parts of any robot.
This is the most common technology. The motors rely on Lorentz magnetic force to move a rotor relative to its stator. They have a high rotational speed and very low output torque, which requires the speed to be reduced while increasing the torque using, for example, a gearbox. Their flexibility of electronic control makes them the first choice for robot actuators.
Some modern motors are “direct-drive” type, avoiding the problem of using a speed-to-torque transformer. The standard motors are steppers, coreless, or brushless technologies. Steppers (typically used in printers) are bigger and noisy but as digital motors they are very simple and effective to be directly and accurately controlled, up to a 0.06° by step. Brushless motors are much expensive and require sophisticated electronics to be driven, but they are light, noiseless, as or more accurate than steppers, thus making them the most common choice for a surgical robot.
Electromagnetic motors exist also in the form of linear motor: magnets are aligned rather to be arranged in a circular way. Although they have a lower power to size ratio, they are useful for linear movement of a surgical instrument with simple and direct control.
Also called ultrasonic motors (due to their kilohertz band frequency excitation), piezoelectric actuators are newcomers to this area. They rely on certain ceramics properties to bend when a high voltage is applied to them. They transmit their force by a slip-stick mechanism allowing both translational and rotational motion. These motors are useful for microsurgery due to their capability to move an extremely small distance, allowing nanometer granularity and therefore, extremely small movements. Furthermore, they can be produced without any ferromagnetic parts to be compatible with interventional magnetic resonance imaging (MRI) [ ]. They have the drawback that they require a complicated high voltage electronic driver, which make them less desirable where electric safety may be a critical concern.
Pneumatic actuators use a gas (often mixed with oil vapors), to move a piston, elongate a curved tube or simply inflate a bladder. Their advantage is their low inertia allowing high speed motions and a very high power to footprint ratio, consistent with miniaturized actuators. They can be made with no ferromagnetic parts, allowing them to be used in a MRI unit [ ]. They come in 2 main types: piston-rod system and artificial pneumatic muscles. Their drawback is the cumbersome, noisy and dirty air compression system which is mandatory to generate the force. They also require a demanding servicing.
The IBIS system developed by the Tokyo Institute of Technology illustrates the possibilities of pneumatically actuated surgical manipulators. The IBIS has a parallel 4 DOF base manipulator with 2 additional serial DOF in the forceps manipulator.
Pneumatic actuators provide soft and progressive motions in a compact size [ ]. Haptic feedback is made possible without cumbersome force sensors by directly measuring pressure variations in pneumatic ducts. The force at the instrument tip of the IBIS is estimated by a neural network with a resolution of 0.1 N [ ].
Another significant achievement in pneumatic robotics is the EMARO pneumatic laparoscope holder, again from Tokyo Institute of Technology, for which pose is controlled via the surgeon’s head onto which gyroscopes are fixed [ ].
Hydraulic actuators are similar to pneumatic actuators, except that they use a liquid (oil or water) to transmit power to joint units. As liquids are incompressible, they can develop a huge amount of force while using very thin ducts, as narrow as 1 mm and they have the best-known power-to-size ratio. A good example is the system developed by the Osaka Institute of Technology [ ] which allows laparoscope manipulation and has the novel feature of being single use.
Cartesian direct magnetic actuators
These use a direct magnetic force from a set of electromagnets to move a magnetic target in 3D space. Their greatest advantage is that the target can move freely without any other linkage.
Developed by Stereotaxis Inc. (St-Louis Missouri, USA), this technology is currently used clinically to move a magnetic catheter wirelessly toward intracardiac cavities, specifically to treat arrhythmias ( Figure 4.9 ). This technology is very complex because magnetic force decreases with the cube of the distance between target and magnet. The highly non-linear servo-loop used to finely control in the millimeter range the 3D magnetic force produced by magnets is very challenging [ , ].
Another application, still under preclinical assessment, is the octomag system ( Figure 4.10 ), designed to move inside the globe of the eye a rare earth magnetic target under a millimiter in size [ ]. The force experienced by the magnetic target is between 25 and 90 μN, depending of target orientation. Such forces, although rather weak, could be sufficient, if applicable, for intracochlear cell surgery.
This family of surgical robots uses cables to actuate manipulator joints from motors located away from the surgical field. The obvious advantage is a compact system not crowding the operating field with bulky machinery. Theoretically, as the motors do not have to move themselves but are, rather, in a fixed place, the power required is decreased, making the whole system safer.
These rely on Bowden cables (the name of the inventor of bicycle brakes) which permit simple designs. However the displacement of the cable in its sleeve has the huge drawback of producing a significant amount of friction, especially when the cable has a short radius of curvature. This friction introduces non-linearities in the control of motion, which are very difficult to compensate for, limiting its capabilities for smooth accurate motions [ , ]. An example of this actuating technology is the Laprotek system, an experimental laparoscope holder [ ].
Cables and pulleys
Pulleys are used to guide actuation cables around each joint. This allows virtually no friction at the expense of much greater manufacturing complexity, which drastically increases with the number of DOF of the manipulator. The best example of this technology is the Intuitive Surgical Inc. da Vinci® system (see chapter 6 ). Another interesting example is the Raven System, a surgical manipulator developed at the University of California, on an open source basis [ , ] ( Figure 4.11 ). These systems however suffer from a lack of accuracy as position encoders are usually located on the motor side. Perfect rope tensioning is mandatory for precise transmission of the angular motion of each drive motor, while temperature variations or wear of the pulleys detrimentally affects correct tensioning [ ]. Another drawback is the very limited capability to provide the user with haptic feedback because of the noise introduced by the whole transmission.