Abstract
The paper presents a complete geometric analysis of a novel parallel medical robotic system designed for minimally invasive treatment of hepatic tumors using brachytherapy, ablation or targeted chemotherapy. An algebraic method based on the study parameters of the special Euclidean transformation Lie group SE(3) was used to determine the mechanism kinematics singularities and workspace. Moreover, two particular medical tool manipulations for the minimally invasive medical procedures are defined in terms of the Study parameters. The first manipulation of the medical tool refers to the linear insertion (of e.g., needles) and the second one is the remote center of motion manipulation of specific medical instruments (e.g., ultrasound probes). The constraint equations of the robotic system are derived and then, the operational workspace is illustrated for the novel parallel robotic system. Lastly, a numerical simulation is presented showing the behavior of the robotic system manipulating the ultrasound probe constrained by the remote center of motion. The geometric analysis of the operational workspace and the numerical simulation show promising results that validate the novel robotic system (safe-wise) for the medical procedure.
Highlights
In robotics and in mechanism analysis and synthesis there exists various mathematical approaches to describe the mechanism kinematics, singularities and workspace, which have both advantages and disadvantages [1]
The authors exploited the advantages of the algebraic method based on the Study parameters to achieve two main objectives: (i) a complete geometric analysis of the Pro-Hep-LCT robotic system, and (ii) the analysis of the behavior of the robotic system while it performs the medical task
The paper is structured as follows: Section 2 presents the mathematical framework of the Study parameters and it defines the mathematical relations for the linear insertion/retraction of a medical instrument and for the Remote Center of Motion (RCM) manipulation; Section 3 presents the Pro-Hep-LCT robotic system and shows the kinematics, the singularity analysis and the workspace of the robotic system; Section 4 presents some numerical simulations for the Pro-Hep-LCT robotic system based on the previous obtained results; Section 5 presents the conclusions and future work
Summary
In robotics and in mechanism analysis and synthesis there exists various mathematical approaches to describe the mechanism kinematics, singularities and workspace, which have both advantages and disadvantages [1]. The motivation of using the Study parameters for the first objective is due to the fact that the Study parameters offer a description of the global kinematics of the mechanism which in turn shows all the kinematic solutions, all the singularities and all the working modes of the robotic system All this information, especially the singularities of the mechanism (since they define configurations where the control of the robotic system may be lost), should be valuable for understanding the robotic system capabilities to perform the medical task from the safety point of view. The paper is structured as follows: Section 2 presents the mathematical framework of the Study parameters and it defines the mathematical relations for the linear insertion/retraction of a medical instrument and for the RCM manipulation; Section 3 presents the Pro-Hep-LCT robotic system and shows the kinematics, the singularity analysis and the workspace of the robotic system; Section 4 presents some numerical simulations for the Pro-Hep-LCT robotic system based on the previous obtained results; Section 5 presents the conclusions and future work
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