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

Bai, Long; Yang, Jie; Chen, Xiaohong; Jiang, Pei; Liu, Fuqiang; Fan, Zheng; Sun, Yuanxi

doi:10.3390/app9030546

Cited by 12 publications

(4 citation statements)

References 24 publications

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“…The paper [ 15 ] illustrates a method of solving the inverse kinematics problem about the position using the PSO algorithm (particle swarm optimization) for the creation of a surgical robot with three linear and three rotary axes that is intended to provide treatment of fractures. The iterative solution of inverse kinematics of a da Vinci robot in a controller-responder system using the Newton method is shown in work [ 16 ], while the inverse kinematics solution of a surgical robot with six degrees of freedom implemented upon a model in CATIA program and D-H (Denavit and Hartenberg) notation is shown in work [ 17 ]. Beyond the aforementioned, a comprehensive analysis of dynamics based on the energy method of a robot with a remote center of motion mechanism is shown in work [ 18 ].…”

Section: Literature Reviewmentioning

confidence: 99%

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

Ilewicz

Ładyżyńska-Kozdraś

2022

Sensors

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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.

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Section: Literature Reviewmentioning

confidence: 99%

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

Ilewicz

Ładyżyńska-Kozdraś

2022

Sensors

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“…The method considers weight matrices to prioritize tasks, thus controlling the robot behavior efficiently. A quasi-analytic inverse kinematics approach has been suggested for an active slave manipulator in the surgical robot by Bai et al [44]. The approach can meet the real-time and high-accuracy requirements of control for the robot.…”

Section: Advanced Mobile Roboticsmentioning

confidence: 99%

Special Feature on Advanced Mobile Robotics

Kim

2019

Applied Sciences

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“…Da Vinci system also adopted the inverse Jacobian method solving the joint angles (Niemeyer, 2004). A dialytic-elimination and Newton-iteration-based quasi-analytic inverse kinematics approach was proposed for the 6 degrees of freedom (DOFs) active slave manipulator in the Da Vinci surgical robot (Bai et al , 2019), and the error of this method is less than 0.0004° (or mm). Ma (2013) proposed a two-stage calculation method and constructed a master–slave control strategy based on the separation of position and pose.…”

Section: Introductionmentioning

confidence: 99%

A novel closed-form solutions method based on the product of exponential model for the minimally invasive surgical robot

Song

Pan

Niu

et al. 2022

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Purpose This study aims to represent a novel closed-form solutions method based on the product of the exponential model to solve the inverse kinematics of a robotic manipulator. In addition, this method is applied to master–slave control of the minimally invasive surgical (MIS) robot. Design/methodology/approach For MIS robotic inverse kinematics, the closed-form solutions based on the product of the exponential model of manipulators are divided into the RRR and RRT subproblems. Geometric and algebraic constraints are used as preconditions to solve two subproblems. In addition, several important coordinate systems are established on the surgical robot and master–slave mapping strategies are illustrated in detail. Finally, the MIS robot can realize master–slave control by combining closed-form solutions and master–slave mapping strategy. Findings The simulation of the instrument manipulator based on the RRR and RRT subproblems is executed to verify the correctness of the proposed closed-form solutions. The fact that the accuracy of the closed-form solutions is better than that of the compensation method is validated by the contrastive linear trajectory experiment, and the average and the maximum tracking errors are 0.1388 mm and 0.3047 mm, respectively. In the animal experiment, the average and maximum tracking error of the left instrument manipulator are 0.2192 mm and 0.4987 mm, whereas the average and maximum tracking error of the right instrument manipulator are 0.1885 mm and 0.6933 mm. The successful completion of the animal experiment comprehensively demonstrated the feasibility and reliability of the master–slave control strategy based on the novel closed-form solutions. Originality/value The proposed closed-form solutions are error-free in theory. The master–slave control strategy is not affected by calculation error when the closed-form solutions are used in the surgical robot. And the accuracy and reliability of the master–slave control strategy are greatly improved.

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

Cited by 12 publications

References 24 publications

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

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

Special Feature on Advanced Mobile Robotics

A novel closed-form solutions method based on the product of exponential model for the minimally invasive surgical robot

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