A method for mapping the boundaries of collision-free reachable workspaces

Yang, Xiangdong; Wang, Hongbo; Zhang, Chuanqing; Chen, Ken

doi:10.1016/j.mechmachtheory.2010.02.002

Cited by 15 publications

(7 citation statements)

References 40 publications

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“…Once the mathematical descriptions of the obstacles and the needle j are obtained, based on our previous work [ 34 ], the collision-free equation Φ ' between the needle j and obstacles can be formulated as: where a g = [ a x , a y , a z ] T and b g = [ b x , b y , b z ] T are the point coordinates on curved surfaces of both the obstacles and needle j in Σ, is a 6×1 vector, ; λ = [ λ 1 , λ 2 ] T is a 2×1 vector of Lagrange multipliers, L is a 2×2 diagonal matrix of λ 1 and λ 2 , S is a 2×2 diagonal matrix of the slack variables s 1 and s 2 , s = [ s 1 , s 2 ] T is a 2×1 vector; e = [1, 1] T , and γ > 0 is the safe-distance parameter, which can be decided by clinical needs to avoid a needle insertion trajectory too close to important organs. We can set the value based on the clinical experience; μ is the barrier parameter and s d is a slack variable.…”

Section: Methodsmentioning

confidence: 99%

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Automatic Multiple-Needle Surgical Planning of Robotic-Assisted Microwave Coagulation in Large Liver Tumor Therapy

et al. 2016

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The “robotic-assisted liver tumor coagulation therapy” (RALTCT) system is a promising candidate for large liver tumor treatment in terms of accuracy and speed. A prerequisite for effective therapy is accurate surgical planning. However, it is difficult for the surgeon to perform surgical planning manually due to the difficulties associated with robot-assisted large liver tumor therapy. These main difficulties include the following aspects: (1) multiple needles are needed to destroy the entire tumor, (2) the insertion trajectories of the needles should avoid the ribs, blood vessels, and other tissues and organs in the abdominal cavity, (3) the placement of multiple needles should avoid interference with each other, (4) an inserted needle will cause some deformation of liver, which will result in changes in subsequently inserted needles’ operating environment, and (5) the multiple needle-insertion trajectories should be consistent with the needle-driven robot’s movement characteristics. Thus, an effective multiple-needle surgical planning procedure is needed. To overcome these problems, we present an automatic multiple-needle surgical planning of optimal insertion trajectories to the targets, based on a mathematical description of all relevant structure surfaces. The method determines the analytical expression of boundaries of every needle “collision-free reachable workspace” (CFRW), which are the feasible insertion zones based on several constraints. Then, the optimal needle insertion trajectory within the optimization criteria will be chosen in the needle CFRW automatically. Also, the results can be visualized with our navigation system. In the simulation experiment, three needle-insertion trajectories were obtained successfully. In the in vitro experiment, the robot successfully achieved insertion of multiple needles. The proposed automatic multiple-needle surgical planning can improve the efficiency and safety of robot-assisted large liver tumor therapy, significantly reduce the surgeon’s workload, and is especially helpful for an inexperienced surgeon. The methodology should be easy to adapt in other body parts.

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Section: Methodsmentioning

confidence: 99%

“…The analytical criterion of needle CFRW for needle j can be given by [ 34 ]: where u = [ x , y ] T , , is a unit 13-dimensional vector, because and Eq 12 contains 27 equations, is a 1D curve on z h -plane.…”

Section: Methodsmentioning

confidence: 99%

Automatic Multiple-Needle Surgical Planning of Robotic-Assisted Microwave Coagulation in Large Liver Tumor Therapy

et al. 2016

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“…In order to avoid damaging the obstacles, we introduce safety distance constant 0 γ > , so we can ensure that the distance of the needle and obstacles is farther than safety distance if the needle gesture satisfies the following condition: (4) According to [16], we introduce slack variable d s , then formula 4 could be rewritten as: (5) The combination of (3) and (5) constructs the constraint equation, which ensures that the needle-insertion path does not damage obstacles.…”

Section: Physical Model Of the Surgical Planning For The Raltctmentioning

confidence: 99%

Interior point-based method for surgical planning and risk analysis of robot-assisted liver tumor coagulation therapy system

Liu

Yang

et al. 2011

2011 IEEE International Conference on Robotics and Biomimetics

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Due to the lack of surgical planning, the needle-insertion path planning still depends on the surgeon's operation experience and the reconstructed 3D operation environment in the robot-assisted liver tumor coagulation therapy system. So, the study of the surgical planning strategy is an important task to reduce the surgeon workload and improve the therapy efficiency and quality. To this end, according to the operation characteristics, the surgical planning is divided into two parts: pre-operative surgical planning and intra-operative risk analysis in this paper. In the pre-operative stage, the interior point method is used to obtain the constraint equations which prohibit the needle-insertion path from damaging important organs or tissues, e.g., ribs or primary blood vessels. In the intra-operative stage, a rapid risk analysis of previous planning is performed to assist surgeons in determining the final needle-insertion path. In this paper, the needle's collision-free reachable workspace is successfully solved. The simulation results indicated that the needle-insertion path selected in the needle's collision-free reachable workspace can avoid the collision with important organs or tissues. The risk analysis algorithm can quickly calculate the nearest distance between the pre-planned insertion path and the important organs, which could assist surgeons in evaluating the pre-planned needle-insertion path. The proposed surgical planning strategy can significantly reduce the surgeon workload and improve the efficiency and safety of operation.

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“…Therefore, to avoid collisions and improve efficiency, some scholars have begun to study the collision-free workspace. [16][17][18] A notable example is an obstacle-free workspace of the parallel mechanisms with an intervalbased approach obtained Farzanehkaloorazi et al 19 In this article, a bogie 6-degree-of-freedom (6-DOF) dynamic simulation test bench 20 was analyzed. It is a parallel mechanism composed of three 6-DOF motion platforms, there are 21 actuators to drive it.…”

Section: Introductionmentioning

confidence: 99%

Workspace analysis of the bogie 6-degree-of-freedom dynamic simulation test bench

Liu

Zhuang

Wang

et al. 2019

Advances in Mechanical Engineering

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The bogie 6-degree-of-freedom dynamic simulation test bench can simulate various operating conditions of the bogie through coordinated movement of the three parallel 6-degree-of-freedom motion platforms; however, the motion of the platforms will be interfered by some space obstacles. In order to obtain the collision-free workspace of the 6degree-of-freedom motion platforms, a limit boundary-search method based on the collision-detection model is proposed. The structure of three parallel 6-degree-of-freedom motion platforms is analyzed, and its inverse kinematics model is established. Considering its internal constraints, the constraint models of the actuators' stroke and the spherical hinges angle are established. Based on the collision-detection method between convex polygons, the minimum distancedetection models between platforms and obstacles as well as between actuators and obstacles are established. Then the limit boundary-search method is used to search for all boundary points that satisfy the constraint conditions. Finally, the correctness and feasibility of the proposed method and models are verified by some simulation examples. The proposed research avoids collisions effectively and provides a reference for the optimal design of the test bench.

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A method for mapping the boundaries of collision-free reachable workspaces

Cited by 15 publications

References 40 publications

Automatic Multiple-Needle Surgical Planning of Robotic-Assisted Microwave Coagulation in Large Liver Tumor Therapy

Automatic Multiple-Needle Surgical Planning of Robotic-Assisted Microwave Coagulation in Large Liver Tumor Therapy

Interior point-based method for surgical planning and risk analysis of robot-assisted liver tumor coagulation therapy system

Workspace analysis of the bogie 6-degree-of-freedom dynamic simulation test bench

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