Solving the Time-Varying Inverse Kinematics Problem for the Da Vinci Surgical Robot

Specifying Inputs for the Computational Structure of a Surgical System via Optical Method and DLT Algorithm Based on In Vitro Experiments on Cardiovascular Tissue in Minimally Invasive and Robotic Surgery

With the application of four optical CMOS sensors, it was possible to capture the trajectory of an endoscopic tool during an in vitro surgical experiment on a cardiovascular preparation. This was due to the possibility of obtaining a path when a reflective marker was attached. In the work, APAS (Ariel Performance Analysis System) software and DLT (direct linear transformation) algorithm were used. This made it possible to acquire kinematic inputs to the computational model of dynamics, which enabled, regardless of the type of surgical robot structure, derivation of the analogous motion of an endoscopic effector due to the mathematical transformation of the trajectory to joints coordinates. Experiments were carried out with the participation of a practiced cardiac surgeon employing classic endoscopic instruments and robot surgical systems. The results indicated by the experiment showed that the inverse task of kinematics of position for the surgical robot with RCM (remote center of motion) structure was solved. The achieved results from the experiment were used as inputs for deriving a numerical dynamics model of surgical robot during transient states that was obtained by applying the finite element method and by driving dynamics moments acquired through the block diagrams method using a steering system with DC (direct current) motor and PID (proportional–integral–derivative) controller. The results section illustrates the course of kinematic values of endoscopic tools which were employed to apply numerical models as inputs, the course of the driving torque of the model of the surgical robot that enabled the selection of the drive system and the strength values, stresses and displacements according to von Mises hypothesis in its structure during the analysis of transient states that made it possible to establish the strength safety of the surgical robot. For the conducted experiments, the accuracy was ±2 [mm]. In the paper, the employment of optical CMOS sensors in surgical robotics and endoscopy is discussed. The paper concludes that the usage of optical sensors for determining inputs for numerical models of dynamics of surgical robots provides the basis for setting the course of physical quantities that appear in their real object structure, in manners close to reality.

Design and Implementation of a Graphic Simulator for Calculating the Inverse Kinematics of a Redundant Planar Manipulator Robot

In this paper, a graphics simulator that allows for characterizing the kinematic and dynamic behavior of redundant planar manipulator robots is presented. This graphics simulator is implemented using the Solidworks software and the SimMechanics Toolbox of MATLAB/Simulink. To calculate the inverse kinematics of this type of robot, an algorithm based on the probabilistic method called Simulated Annealing is proposed. By means of this method, it is possible to obtain, among many possibilities, the best solution for inverse kinematics. Without losing generality, the performance of metaheuristic algorithm is tested in a 6-DoF (Degrees of Freedom) virtual robot. The Cartesian coordinates (x,y) of the end effector of the robot under study can be accessed through a graphic interface, thereby automatically calculating its inverse kinematics, and yielding the solution set with the position adopted by each joint for each coordinate entered. Dynamic equations are obtained from the Lagrange–Euler formulation. To generate the joint trajectories, an interpolation method with a third order polynomial is used. The effectiveness of the developed methodologies is verified through computational simulations of a virtual robot.

Existence Conditions and General Solutions of Closed-form Inverse Kinematics for Revolute Serial Robots

This study proposes a method for judging the existence of closed-form inverse kinematics solutions based on the Denavit–Hartenberg (DH) model. In this method, serial robots with closed-form solutions are described using three types of sub-problems from the viewpoint of solving algebraic equations. If a serial robot can be described using these three types of sub-problems, i.e., if the inverse kinematics problems can be solved by several basic problems, then there is a closed-form solution. Based on the above method, we design a set of universal closed-form inverse kinematics solving algorithms. Since there is a definite formula solution for the three types of sub-problems, the joint angles can be rapidly determined. In addition, because the DH parameters can directly reflect the linkage of the robot, the judgment of the sub-problems is also quick and accurate. More importantly, the algorithm can be applied to serial robots with low degrees of freedom. This enables the algorithm to not only quickly and accurately solve inverse kinematics problems but also to exhibit high universality. This proposed theory improves the existence conditions for closed-form reverse solutions and further promotes the development of motion control techniques for serial robots.

Medical Robotics in Bone Fracture Reduction Surgery: A Review

Since the advantages of precise operation and effective reduction of radiation, robots have become one of the best choices for solving the defects of traditional fracture reduction surgery. This paper focuses on the application of robots in fracture reduction surgery, design of the mechanism, navigation technology, robotic control, interaction technology, and the bone-robot connection technology. Through literature review, the problems in current fracture reduction robot and its future development are discussed.