| Percutaneous pedicle screw fixation is a commonly used minimally invasive surgical method for the treatment of spinal compression fracture,spinal injury and degeneration.Percutaneous pedicle puncture localization and spinal drilling are the important steps.In terms of spinal drilling,most hospitals in China are carried out by doctors holding bone drills for spinal drilling.Fatigue and physical tremors caused by holding the bone drill for a long time increase the potential risk of spinal drilling.The doctor directly drags and controls the spine surgery drilling assisted robot（SSDAR）to perform interventional therapy,which has become a new solution.In this paper,the kinematics,working space and deformation of the SSDAR was systematically studied,and a control algorithm based on nonlinear disturbance observer（NDO）and feedback linearization（FL）was proposed to realize the passive compliance of the SSDAR,thereby making it can assist doctors in performing spinal surgery.The main research content and results of the thesis are as follows.（1）The workspace requirements,structure composition and working principle of the SSDAR were described,and its forward/inverse kinematics were analyzed.Based on the DH parameter method,the forward kinematics equation of the SSDAR was derived.The ZYX Euler angle transformation was used to establish the homogeneous transformation matrix of the target coordinate system of the SSDAR relative to its base coordinate system,and a discrete method was proposed to discretize the possible drilling directions of the spine.The numerical solution of inverse kinematics of the SSDAR showed that the end effector of the robotic arm can reach at least 90 drilling directions within a vertical 20°taper range.（2）Based on the forward kinematics of the SSDAR,the Monte Carlo method was used to establish the reachable space model of the spine surgery drilling assistant robot.The reachable space can include a rectangular parallelepiped space of0.2m*0.3m*0.8m,which is 77.78%larger than the position adjustment range0.3m*0.3m*0.3m required by the SSDAR;at x=0.7m,the end effector of the SSDAR can cover a width of 0.8m in the Y direction,and its reachable space can meet the patient’s spine surgery space requirements.The manipulability model of the SSDAR in the reachable space was established,and the manipulability of the positioning and orientation of the assistant robot’s end effector was quantitatively described.（3）Static analysis,modal analysis in the frequency range of 0-100Hz and harmonic response analysis in the range of 0-60Hz of the drilling assisted robot for spine surgery were completed.The static deformation of the SSDAR is mainly the deflection in the+Y direction of the column,and the maximum displacement at the end effector is about 1.15mm.In the analyzed frequency range,the SSDAR has6-order mode shapes（MS）.The first to third modes of the SSDAR in the X direction are the second,third and sixth modes respectively,and the first and second modes in the Y direction are the first and sixth modes of the SSDAR,and the first and third modes in the Z direction are the fourth modes of the SSDAR.The modal analysis results also further show that the stiffness of the SSDAR in the X and Y directions is lower than that in the Z direction.The main deformation of the SSDAR under the action of harmonic loads occurs near the first,second,and fourth NF,and its main deformation occurs in the Y direction and the Z direction.The maximum displacement response in the X direction is 1.42*10-5m,while the maximum displacement responses in the Y and Z directions are 4.514*10-4m and 7.562*10-4m,respectively.The maximum displacement in the X direction is 96.85%smaller than the maximum displacement in the Y direction.It is 98.12%smaller than the maximum displacement in the Z direction.The SSDAR with small deformation under the reaction force of spinal drilling,and the structure of the SSDAR is reliable.（4）The feedback linearization control algorithm based on the nonlinear disturbance observer（FL+NDO）was established,and the outer-loop reference speed trajectory generator,the inner-loop position controller and the nonlinear disturbance observer were specifically designed.The stability of the NDO and the tracking error system was strictly proved theoretically,and the stability of the internal dynamics was briefly described.The derivation proved that under the FL control algorithm based on the NDO,the end effector of the manipulator has the isotropic acceleration capability.The NDO compensates for the error and increases the stability of the system.The simulation experiment shows that the FL control algorithm based on the NDO can make the manipulator have better passive compliance ability.The FL control algorithm based on the NDO was simulated with the constant force in the same direction,the variable force in the same direction,and the constant force in different directions.The results show that the velocity tracking errors are in the order of 10-3m/s,10-4m/s and 10-3m/s respectively,and the end-effector velocity almost has no overshoot.Compared with the force-free control algorithm and admittance control algorithm,under the FL control algorithm based on the NDO,the speed of the end effector of the manipulator has nothing to do with the process of the drag force,and is only determined by the current towing force.The FL control algorithm based on the NDO is more suitable for the passive compliance of the spine robot,in other words,it is more suitable for the doctor to directly drag the spine robot to realize the direct interaction between the doctor and the SSDAR.The numerical simulation results show that in the directions of 45°,-45°,135°and-135°in cartesian space,the relationship between the drag force and the velocity of the end-effector always follows the reference velocity trajectory generator under the FL control based on NDO.Based on the NDO and FL control algorithm,the performance is superior,and it is suitable for the surgeon to directly drag and control the SSDAR to intervene in the spine surgery treatment. |
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