Page 26 - Flexible Robotics in Medicine

8 Chapter 1

1.3.1 Kinematics

The kinematic model of snake-like surgical robots has been intensively surveyed by
Burgner-Kahrs et al. [2] and Li et al. [38]. As a complementary, here we will summarize
the kinematic modeling methods of the platforms that emerged in the recent 3 5 years. As
is known to all, the earliest modeling of the continuum robot configuration stemmed from
the backbone curve proposed by Chirikjian [39]. Most of the snake-like surgical robots,
especially the cable-driven ones, were modeled based on the piecewise constant curvature
assumption. In the constant curvature model, once the length of the backbones of the robot
is known, the configuration depends on the bending angle of the tip and the rotating angle
of the bending plane with respect to the plane that is defined by the base disk. Simaan et al.
[40], Kato et al. [41], Haraguchi et al. [31], Ding et al. [42,43], Li et al. [10,20,38,44 46],
Smoljkic et al. [32], Lau et al. [33], Qi et al. [47], and Roy et al. [48] have validated their
platforms using the kinematic modeling based on constant curvature assumption.

The conventional D-H method for rigid-link robots has been widely used too. Garg et al.
[1] adopted the D-H parameter table on a wire-driven rigid-link snake robot to build its
kinematic model. For a notched dexterous continuum manipulators in the work of Gao et al.
[49,50], the interconnected rigid links and flexible links, transformation matrices were
obtained respectively and construct the whole kinematic model based on D-H method.
Murphy et al. [51] proposed a wire-driven continuum robot composed of two nested tubes
and used the single-chain D-H method to build the kinematic model. As a notched and
nested assembly, the snake-like robot’s kinematic model in the study of Kutzer et al. [52]
was built by 35 parameters from the pin joints and vertebrae one by one.

1.3.2 Statics and dynamics

A snake-like surgical robot’s static modeling solves the relationship of the force, moment,
and deformation. For tendon-driven snake-like surgical robots, statics is usually combined
with kinematics when Cosserat Rod Theory is applied in the modeling. Based on Cosserat
Rod Theory, Gao et al. [17] built a shape prediction model for a helical spring backboned
snake robot, in which the deformation of the robot is related to the tendon force, friction
force, and external forces. Lumped-parameter model is an alternative basis for static
analysis, for example, Kato et al. [16] built the tension propagation model with friction
between the wires and the robot body. The principle of virtual work was used to compute
the actuation force on building a load transmission model in the work of Roy et al. [48].
Dong et al. [29] analyzed the cable tension and stiffness of a compliant joint backboned
snake robot based on the Jacobian. A dynamic model to compensate for the uncertainty and
asymmetry has been proposed by Haraguchi et al. [31] by defining the driving forces
related to the bending angle, friction force, and elastic forces.