立體定位手術為腦神經外科手術的核心手術，近年來已被應用於活體組織切片、深腦電刺激和燒灼術等手術中，先前研究團隊已完成具有觸覺回饋系統之五軸磁振造影相容立體定位手術機器人，透過將觸覺回饋系統拆分為觸覺回饋系統傳達使用者操作資訊的主系統與傳達感測力量的從系統。完成觸覺回饋系統的設計，提升手術安全性與成功率。
然而在觸覺回饋系統的控制器上，先前研究並未建立獲得觸覺回饋系統的數學模型，因此僅採用不需依靠數學模型的PI控制器與模糊控制器，可能無法應對系統的不確定性。為了解決此問題，本研究選擇了模型預測控制策略中的動態矩陣控制，利用觸覺回饋系統的步階響應取得觸覺回饋系統的動態矩陣，在應用動態矩陣控制於觸覺回饋系統。
此外，本研究透過F-8艦載機之模擬，驗證線性動態矩陣控制是否能應用於非線性系統上，最後，透過先前研究團隊已完成之大腦假體與腫瘤假體，完成模擬手術過程的穿刺實驗，實驗結果顯示，在針對步階響應前處理後，動態矩陣控制仍然能完成非線性系統的追蹤控制，在穿刺實驗部分，使用步階響應的動態矩陣控制在上升時間與超越量PI相比，性能均有改善，因此，本研究採用動態矩陣控制可進一步提升大腦穿刺手術安全性與成功率。

Stereotactic surgery is a core technique in neurosurgery and is widely used in procedures such as biopsy, deep brain stimulation, and thermal ablation. To improve surgical safety and precision, an MRI-compatible stereotactic surgical robot equipped with a haptic feedback system has been developed. The haptic feedback architecture consists of a master system that conveys the surgeon’s operational input and a slave system that transmits interaction forces between the surgical instrument and biological tissues, enabling surgeons to perceive tissue stiffness variations and puncture events during needle insertion.
In previous studies, proportional–integral (PI) and fuzzy control strategies were adopted for the haptic feedback system due to the lack of an explicit mathematical model. Although these methods are easy to implement, their performance is sensitive to parameter tuning and system uncertainties, particularly in the presence of nonlinear dynamics and time delays. To address these limitations, this study proposes the application of Dynamic Matrix Control (DMC), a model predictive control approach based on experimentally identified step response data, to the haptic feedback system.
The feasibility of applying linear DMC to nonlinear systems is first investigated through simulations using the F-8 aircraft model. Subsequently, experimental validation is conducted using brain and tumor phantoms to simulate needle insertion during stereotactic surgery. The results demonstrate that, after appropriate preprocessing of step response data, DMC achieves accurate tracking control in nonlinear conditions and outperforms conventional PI control in terms of reduced rise time and overshoot. These findings indicate that DMC can further enhance the safety and success rate of robotic-assisted stereotactic neurosurgery.

[1]A. Compston, “The structure and functions of the cerebellum examined by a new method. By Sir Victor Horsley, FRS, FRCS and R.H. Clarke, MA, MB. Brain 1908: 31; 45-124.,” Brain, vol. 130, no. 6, pp. 1449–1452, Apr. 2007.
[2]E. A. Spiegel, H. T. Wycis, M. Marks, and A. J. Lee, “Stereotaxic Apparatus for Operations on the Human Brain,” Science, vol. 106, no. 2754, pp. 349–350, Oct. 1947.
[3]C. C. McIntyre, A. Chaturvedi, R. R. Shamir, and S. F. Lempka, “Engineering the Next Generation of Clinical Deep Brain Stimulation Technology,” Brain Stimulation, vol. 8, no. 1, pp. 21–26, Jan. 2015.
[4]M. Ahmed, C. L. Brace, F. T. Lee, and S. N. Goldberg, “Principles of and Advances in Percutaneous Ablation,” Radiology, vol. 258, no. 2, pp. 351–369, Feb. 2011.
[5]L. Leksell and B. Jernberg, “Stereotaxis and tomography a technical note,” Acta neurochir, vol. 52, no. 1, pp. 1–7, Mar. 1980.
[6]. Grimm, G. Naros, A. Gutenberg, N. Keric, A. Giese, and A. Gharabaghi, “Blurring the boundaries between frame-based and frameless stereotaxy: feasibility study for brain biopsies performed with the use of a head-mounted robot,” Sep. 2015.
[7]“Elekta, ‘Leksell Stereotactic System.’” https://www.elekta.com/neurosurgery/leksell-stereotactic-system/
[8]. W. Roberts, J. W. Strohbehn, J. F. Hatch, W. Murray, and H. Kettenberger, “A frameless stereotaxic integration of computerized tomographic imaging and the operating microscope,” J Neurosurg, vol. 65, no. 4, pp. 545–549, Oct. 1986.
[9]Y. Lu, C. Yeung, A. Radmanesh, R. Wiemann, P. M. Black, and A. J. Golby, “Comparative effectiveness of frame-based, frameless, and intraoperative magnetic resonance imaging-guided brain biopsy techniques,” World Neurosurg, vol. 83, no. 3, pp. 261–268, Mar. 2015.
[10]T. Hartkens et al., “Measurement and analysis of brain deformation during neurosurgery,” IEEE Transactions on Medical Imaging, vol. 22, no. 1, pp. 82–92, Jan. 2003.
[11]H. Elhawary, Z. T. H. Tse, A. Hamed, M. Rea, B. L. Davies, and M. U. Lamperth, “The case for MR-compatible robotics: a review of the state of the art,” Int J Med Robot, vol. 4, no. 2, pp. 105–113, Jun. 2008.
[12]“何炳林, ‘磁振造影相容之神經外科用立體定位手術機器人之發展’,國立成功大學機械工程學系碩士論文, 台南市, 2015.”
[13]“陳煌霖, ‘磁振造影相容之神經外科手術用五軸立體定位機器系統研究’,國立成功大學機械工程學系碩士論文, 台南市, 2017.”
[14]“彭郁濃, ‘術中核磁共振影像導引立體定位手術機器人’,國立成功大學機械工程學系碩士論文, 台南市, 2019.”
[15]“陳承寬, ‘術中磁共振影像導引與光纖力回授立體定位手術機器人’,國立成功大學機械工程學系碩士論文, 台南市, 2021.”
[16]K. Miller and K. Chinzei, “Constitutive modelling of brain tissue: Experiment and theory,” Journal of Biomechanics, vol. 30, no. 11, pp. 1115–1121, Nov. 1997.
[17]P. Aimedieu and R. Grebe, “Tensile strength of cranial pia mater: preliminary results,” J Neurosurg, vol. 100, no. 1, pp. 111–114, Jan. 2004.
[18]X. Jin, J. B. Lee, L. Y. Leung, L. Zhang, K. H. Yang, and A. I. King, “Biomechanical response of the bovine pia-arachnoid complex to tensile loading at varying strain-rates,” Stapp Car Crash J, vol. 50, pp. 637–649, Nov. 2006.
[19]X. Jin et al., “Biomechanical response of the bovine pia-arachnoid complex to normal traction loading at varying strain rates,” Stapp Car Crash J, vol. 51, pp. 115–126, Oct. 2007.
[20]X. Jin, K. H. Yang, and A. I. King, “Mechanical properties of bovine pia–arachnoid complex in shear,” Journal of Biomechanics, vol. 44, no. 3, pp. 467–474, Feb. 2011.
[21]D. Chauvet et al., “In Vivo Measurement of Brain Tumor Elasticity Using Intraoperative Shear Wave Elastography,” Ultraschall Med, vol. 37, no. 6, pp. 584–590, Dec. 2016.
[22]A. Abiri et al., “Multi-Modal Haptic Feedback for Grip Force Reduction in Robotic Surgery,” Sci Rep, vol. 9, no. 1, p. 5016, Mar. 2019.
[23]M. Tavakoli, A. Aziminejad, R. V. Patel, and M. Moallem, “High-Fidelity Bilateral Teleoperation Systems and the Effect of Multimodal Haptics,” IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), vol. 37, no. 6, pp. 1512–1528, Feb. 2007.
[24]T. Yoshikawa, “Dynamic hybrid position/force control of robot manipulators description of hand constraints and calculation of joint driving force,” in 1986 IEEE International Conference on Robotics and Automation Proceedings, Apr. 1986, pp. 1393–1398.
[25]A. Abdossalami and S. Sirouspour, “Adaptive Control for Improved Transparency in Haptic Simulations,” IEEE Transactions on Haptics, vol. 2, no. 1, pp. 2–14, Jan. 2009.
[26]P. M. Kebria, A. Khosravi, S. Nahavandi, P. Shi, and R. Alizadehsani, “Robust Adaptive Control Scheme for Teleoperation Systems With Delay and Uncertainties,” IEEE Transactions on Cybernetics, vol. 50, no. 7, pp. 3243–3253, Jul. 2020.
[27]“張洪瑞,”磁振造影相容立體定位手術機器人觸覺回饋系統開發與設計國立成功大學機械工程學系碩士論文, 台南市, 2022.”
[28]M. Morari, C. E. Garcia, and D. M. Prett, “Model predictive control: Theory and practice,” IFAC Proceedings Volumes, vol. 21, no. 4, pp. 1–12, Jun. 1988.
[29]R. Rouhani and R. K. Mehra, “Model algorithmic control (MAC); basic theoretical properties,” Automatica, vol. 18, no. 4, pp. 401–414, Jul. 1982.
[30]C. E. GARCIA and A. M. MORSHEDI, “Quadratic Programming Solution of Dynamic Matrix Control (qdmc),” Chemical Engineering Communications, vol. 46, no. 1–3, pp. 73–87, Jul. 1986.
[31]E. F. Camacho and C. Bordons, “Nonlinear Model Predictive Control: An Introductory Review,” in Assessment and Future Directions of Nonlinear Model Predictive Control, R. Findeisen, F. Allgöwer, and L. T. Biegler, Eds., Berlin, Heidelberg: Springer, 2007, pp. 1–16.
[32]Y. Shi, S. Kumar Singh, and L. Yang, “Classical Control Strategies Used in Recent Surgical Robots,” J. Phys.: Conf. Ser., vol. 1922, no. 1, p. 012010, May 2021.
[33]B. Kehoe et al., “Autonomous multilateral debridement with the Raven surgical robot,” in 2014 IEEE International Conference on Robotics and Automation (ICRA), Hong Kong, China: IEEE, May 2014, pp. 1432–1439.
[34]A. Safavi and M. H. Zadeh, “Model-Based Haptic Guidance in Surgical Skill Improvement,” in 2015 IEEE International Conference on Systems, Man, and Cybernetics, Oct. 2015, pp. 1104–1109.
[35]K. S. Holkar and L. M. Waghmare, “An Overview of Model Predictive Control,” International Journal of Control and Automation, vol. 3, no. 4, pp. 47–64, Dec. 2010.
[36]S. J. Qin and T. A. Badgwell, “A survey of industrial model predictive control technology,” Control Engineering Practice, vol. 11, no. 7, pp. 733–764, Jul. 2003.
[37]E. F. Camacho and C. Bordons, Model predictive control, 2nd ed. in Advanced textbooks in control and signal processing. London New York: Springer, 2004.
[38]Y. P. Gupta, “Control of Integrating Processes Using Dynamic Matrix Control,” Chemical Engineering Research and Design, vol. 76, no. 4, pp. 465–470, May 1998.
[39]R. Shridhar and D. J. Cooper, “A Tuning Strategy for Unconstrained SISO Model Predictive Control,” Ind. Eng. Chem. Res., vol. 36, no. 3, pp. 729–746, Mar. 1997.
[40]W. L. Garrard and J. M. Jordan, “Design of nonlinear automatic flight control systems,” Automatica, vol. 13, no. 5, pp. 497–505, Sep. 1977.
[41]E. Kaiser, J. N. Kutz, and S. L. Brunton, “Sparse identification of nonlinear dynamics for model predictive control in the low-data limit,” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 474, no. 2219, p. 20180335, Nov. 2018.
[42]“蕭正豪, ‘機械性值與磁振造影仿真之大腦假體研究’,國立成功大學機械工程學系碩士論文, 台南市, 2020.”
[43]“賴郁欣, ‘磁振造影仿真大腦及病灶假體與其穿刺力學之研究’,國立成功大學機械工程學系碩士論文, 台南市, 2021.”