Non-iterative geometric approach for inverse kinematics of redundant lead-module in a radiosurgical snake-like robot

Abstract

BackgroundSnake-like robot is an emerging form of serial-link manipulator with the morphologic design of biological snakes. The redundant robot can be used to assist medical experts in accessing internal organs with minimal or no invasion. Several snake-like robotic designs have been proposed for minimal invasive surgery, however, the few that were developed are yet to be fully explored for clinical procedures. This is due to lack of capability for full-fledged spatial navigation. In rare cases where such snake-like designs are spatially flexible, there exists no inverse kinematics (IK) solution with both precise control and fast response.MethodsIn this study, we proposed a non-iterative geometric method for solving IK of lead-module of a snake-like robot designed for therapy or ablation of abdominal tumors. The proposed method is aimed at providing accurate and fast IK solution for given target points in the robot’s workspace. n-1 virtual points (VPs) were geometrically computed and set as coordinates of intermediary joints in an n-link module. Suitable joint angles that can place the end-effector at given target points were then computed by vectorizing coordinates of the VPs, in addition to coordinates of the base point, target point, and tip of the first link in its default pose. The proposed method is applied to solve IK of two-link and redundant four-link modules.ResultsBoth two-link and four-link modules were simulated with Robotics Toolbox in Matlab 8.3 (R2014a). Implementation result shows that the proposed method can solve IK of the spatially flexible robot with minimal error values. Furthermore, analyses of results from both modules show that the geometric method can reach 99.21 and 88.61% of points in their workspaces, respectively, with an error threshold of 1 mm. The proposed method is non-iterative and has a maximum execution time of 0.009 s.ConclusionsThis paper focuses on solving IK problem of a spatially flexible robot which is part of a developmental project for abdominal surgery through minimal invasion or natural orifices. The study showed that the proposed geometric method can resolve IK of the snake-like robot with negligible error offset. Evaluation against well-known methods shows that the proposed method can reach several points in the robot’s workspace with high accuracy and shorter computational time, simultaneously.

Self-Collision Avoidance Control of Dual-Arm Multi-Link Robot Using Neural Network Approach

“…All the above methods are united by the fact that the solution of the kinematic problems necessary for their implementation is performed based on classical approaches. At the same time, a number of articles [26][27][28][29][30][31][32] propose approaches to design kinematic control of multilink manipulators based on neural networks, where the data obtained because of solving the direct kinematics problem (DKP) are used as a set of training parameters. At the same time, there are studies that show the effectiveness of the neural network approach, primarily in terms of computational speed.…”

Axis manipulation to solve Inverse Kinematics of Hyper-Redundant Robot in 3D Space

“…In the iterative approach, several strategies have been proposed, such as Artificial Neural Network [11] [12], iterative algorithm [13], genetics algorithm, ANFIS, Fuzzy Logic, evolution algorithm (EA) [14] [15], and iterative algorithm [16] [17]. The geometric approach offers a simpler calculation such as repetitive basic inverse kinematics of a two-link [18], the angular deflection of the upper platform concerning the lower platform [19], a non-iterative geometric approach for inverse kinematics [20], and a modified modal method [21] [22].…”

Design and motion control of an under-actuated snake arm maintainer

“…Bending curves in the kinematics modeling of the snake arm can be described through differential geometry, and the forward kinematics can be implemented by a modified Denavit-Hartenberg program [15]. The traditional generalized inverse matrix method is unsuitable for solving the inverse kinematics and trajectory planning of snake arms, because a snake arm includes many joints and degrees of freedom [16][17][18]. With recent computational developments, the inverse kinematics of hyper-redundant robots can be solved by neural network methods and various genetic algorithms [19,20].…”