Research On Optimal Design And Motion Control Of A Surgical Concentric Tube Robot

Minimally invasive surgery(MIS)robots represent an innovative achievement of robotics technology in clinical medicine.This field is a novel cross-disciplinary research area that integrates multiple research fields,including robotics,mechanical engineering,medicine,computer science,materials science,and information technology.The related technologies have increasingly become a prominent focus of scientific research.Compared to traditional open surgery,robot-assisted minimally invasive surgery enables more precise surgical operation,increases comfort for the surgeon,and reduces pain for the patient.Therefore,research in this field holds significant scientific and societal value.Currently,there are still various problems and challenges in the use of surgical robots for MIS.In order to address the technical challenges encountered in robot-assisted MIS and advance the widespread application of robots in MIS,this dissertation focuses on the key technologies of concentric tube robot(CTR)for MIS.Specifically,the research involves modeling,parameter design,mechanism optimization,and motion control of CTR.This dissertation simplifies the physical and motion models of CTR,analyzes the joint degrees of freedom and kinematic parameters of the robot arm.The relationship between the physical parameters and spatial geometric parameters of CTR is established.Based on the motion model and rigid torsion assumption of CTR,the curvature of concentric tube pair is calculated using the moment equilibrium equation,and the transformation relationship between the kinematic parameters of CTR in the driving space,configuration space,and operation space is studied.By transforming the motion of CTR in the configuration space into three screw motions,a rigid torsion kinematic model of CTR based on POE is proposed.Drawing on the Cosserat rod theory,the compliant torsion kinematic model of CTR is constructed,and the kinematic problem is transformed into a BVP problem.Then,by adding a "virtual segment" to define the variable domain uniformly and setting boundary conditions for concentric tubes,the curvature and pose of CTR are calculated using a numerical BVP solver.By transforming the compliant torsion kinematic equations of CTR into the form of first-class elliptic integrals and analyzing the solutions of the equations,the parameter design conditions for stable operation of CTR are proposed.Based on the kinematic models,design principles for CTR are established.The parameter design problem for piecewise constant curvature CTR arm is solved by transforming it into a geometric problem.To meet the customized design requirements of robots for surgical tasks,a method for design and optimization of CTR arm parameters is proposed.This is achieved by the construction of virtual surgical environment,the design of an objective function,and the design of fixed-point propagation algorithm and the expanded mesh adaptive pattern search algorithm.In order to address issues of rotation angle hysteresis in transmission tubes and large footprint of multi-arm CTR,a multiobjective optimization function is constructed by parameterizing the diameter constraints,length constraints,collision avoidance constraints,and deformation constraints of CTR.The Pareto optimal front is then utilized to design the structure of multi-arm CTR.Finally,a design and optimization method for parallel tower-shaped multi-arm CTR is proposed.For the preoperative motion planning problem,a SI-RRT* path planning algorithm is proposed by adding robot global shape constraints and setting differentiated spatial sampling rates based on prior information in path planning.By transforming the trajectory planning problem of CTR into a quadratic programming problem and setting three types of constraints for trajectory planning problems,a CCMJ trajectory planning algorithm based on cube constraints is proposed.The SI-RRT* and CCMJ algorithm can control CTR to move in a way that approximates "follow-the-leader" in complex environments.By discretizing the continuous arms of CTR,a method for collision detection between CTR and task environment is designed.Meanwhile,a method for collision detection between CTR arms is designed.In response to the problem of singularity-induced illconditioning of CTR’s Jacobian matrix when the robot approaches singular positions,a JVC-LM algorithm based on joint velocity constraints is designed using the Lagrange multiplier method.The Jacobian null space method is applied to intraoperative operations,and a safety operation strategy based on task priority is constructed for CTR.To address the issue of the differential impact of rotation and translation degrees of freedom of CTR on the end-effector pose and to avoid the overshoot phenomenon for small errors during servoing process,an adaptive servo controller is designed for CTR to accelerate the process of visual servoing tasks.For overcoming the difficulties in conputing accurate kinematic model of CTR and solving the problem of inaccurate handeye calibration,the dissertation analyzes the calculation process of the Jacobian matrix in visual servoing of CTR and proposes a method based on modified MASR-UKF for online estimation of the combined Jacobian matrix.A method of initializing combined Jacobian matrix and an algorithm of image feature extraction are designed to achieve image based model-free visual servo control of CTR.On the basis of the above studies,the dissertation sets up a serial single-arm CTR and a parallel tower-shaped multi-arm CTR.By designing an objective function similar to that of the least squares method and using image processing algorithms,a method for calibrating the curvature of concentric tubes is proposed.For the errors introduced during installation,a joint zero-position correction method based on least squares method is proposed,which helps to improve the control accuracy.Finally,experiments are conducted on the concentric tube robots built in this dissertation,including joint zero-position correction experiments,trajectory tracking experiments,motion planning experiments,and multi-arm operation experiments.The experiments validate the effectiveness of the kinematic model,the design method and the motion control method presented in this dissertation for CTR.