Research Article
Dört Ayaklı Robotlar için Üç Serbestlik Dereceli Bacak Tasarımı ve Kesir Dereceli PID (PIλDμ) Tabanlı Kontrolü
Abstract
Dört ayaklı robotlar, tekerlekli sistemlere kıyasla farklı arazi şartlarında yüksek hareket kabiliyetine
sahip, karmaşık dinamik yapısı nedeniyle robotik ve kontrol alanında popülerliğini artıran, bacaklı mobil
robotlardır. Bu çalışmada; yürüyüş planlaması, adım yörüngesi tasarımı, gövdenin denge kontrolü gibi
konularda hızlı ve etkili bir benzetim yapabilmek amacıyla, üç serbestlik dereceli doğrusal bacak modeli
ve kontrolü sunulmuştur. Uzuv boyutlar, kütle, atalet, eklem sertlik ve sönüm değerleri vb. gibi dinamik
parametreleri içeren gerçekçi bir fiziksel model Matlab/Simulink/ Simscape’de tasarlandı ve benzetimi
gerçekleştirildi. Robotun yürüyüşü boyunca standart bir adım yörüngesini gerçekleştirmek için gerekli
eklemlere ait açısal konum aralıkları dikkate alınarak, fiziksel model üzerinden doğrusallaştırma araçları
kullanılarak, girişi tork-çıkışı açısal konum olacak şekilde, sistemin doğrusal Durum-Uzay modeli elde
edilmiştir. Sistemin doğrusal model ile fiziksel modelinin, sabit tork girişine karşın birim basamak
cevapları karşılaştırılmış ve küçük hata değerleri ile modellere ait cevapların birbirine benzer sonuçlar
verdiği görülmüştür. Doğrusal model üzerinden sistemin, farklı kesir dereceleri seçilerek tasarlanan PIλDμ kontrolcüleri ile açısal konum kontrolü, klasik PID kontrolcü ile karşılaştırmalı olarak gerçekleştirmiştir. Benzetim sonuçları sunulmuş ve değerlendirilmiştir.
References
- Bakırcıoglu, V., Sen, M.A. and Kalyoncu, M., 2016a, “Optimization of PID Controller Based on the Bees Algorithm for One Leg of a Quadruped Robot”, MATEC Web of Conferences, Vol. 42, No. 03004, pp. 1-4.
- Bakırcıoglu, V., Sen, M.A. and Kalyoncu, M., “Adaptive Neural-Network Based Fuzzy Logic (ANFIS) Based Trajectory Controller Design for One Leg of a Quadruped Robot”, 5th International Mechatronics and Control Engineering (ICMCE 2016), Venice, Italy, 82-85, 14-17 December, 2016b.
- Bakırcıoğlu, V., Sen, M.A. and Kalyoncu, M., “Motıon Analysıs of The Robotıc Leg Mass Centre Durıng Reference Trajectory Trackıng” 2018 International Vocational Science Symposium (IVSS 2018), Antalya, Turkey, 420, 26-29 April, 2018.
- Baudoin, Y. and Maki K. Habib, 2010, Using Robots in Hazardous Environments: Landmine Detection, De- Mining and Other Applications, Woodhead Publishing, Cambridge, London, England.
- Boston Dynamics Company, https://www.bostondynamics.com/robots, access date: 12.09.2019.
- Focchi, Michele, et al. “Control of A Hydraulically-Actuated Quadruped Robot Leg”, 2010 IEEE International Conference on Robotics and Automation (ICRA2010), IEEE, Alaska, United States, 4182-4188, 4-8 May, 2010.
- Hutter, M., et al., “StarlETH: A Compliant Quadrupedal Robot for Fast, Efficient, and Versatile Locomotion”, International Conference on Climbing and Walking Robots (CLAWAR), Baltimore, USA 483-490, 23-26 July, 2012.
- Hutter, M., et al., 2017, “Anymal-Toward Legged Robots for Harsh Environments”, Advanced Robotics, Vol. 31, No. 17, pp. 918-931.
- Podlubny, I., 1999, “Fractional-Order Systems and PIλDμ Controllers”, IEEE Transactions on Automatic Control, Vol. 44, No. 1, pp. 208-214.
- Podlubny, I., Dorcak L. and Kostial I., “On Fractional Derivatives, Fractional-Order Dynamic Systems and PIλDμ Controllers”, 36th IEEE Conference on Decision and Control, IEEE, Kobe, Japan, 1-5, 13-13 December, 1997.
- Raibert, M., Blankespoor, K., Nelson, G. and Playter, R., “Bigdog, The Rough-Terrain Quadruped Robot”, In 17th World Congress the International Federation of Automatic Control, Seoul, South Korea, 10822- 10825, 6-11 July, 2008.
- Raibert, M.H., 1986, Legged Robots That Balance. MIT Press, Cambridge, London, England.
- Rossell, J. M., et al. “Tracking Control for A Stewart Platform Prototype” 2015 International Conference on Advanced Mechatronics, Intelligent Manufacture, and Industrial Automation (ICAMIMIA), IEEE, Resort, Surabaya, 58-63, 15-16 October, 2015.
- Semini, C., 2010, Hyq-Design and Development of a Hydraulically Actuated Quadruped Robot, Doctor of Philosophy (Ph.D.), University of Genoa, Italy.
- Semini, C., et al., 2017, “Design of the Hydraulically-Actuated Torque-Controlled Quadruped Robot HyQ2Max”, IEEE/ASME Transactions on Mechatronics, Vol. 22, No. 2, pp. 635-646.
- Sen, M.A. and Kalyoncu M., 2018, “Optimal Tuning of PID Controller Using Grey Wolf Optimizer Algorithm for Quadruped Robot”, Balkan Journal of Electrical and Computer Engineering, Vol. 6, No. 1, pp. 29-35.
- Sen, M.A. and Kalyoncu M., 2019, “Grey Wolf Optimizer Based Tuning of a Hybrid LQR-PID Controller for Foot Trajectory Control of a Quadruped Robot”, Gazi University Journal of Science, Vol. 32, No. 2, pp. 674-684.
THREE DEGREE OF FREEDOM LEG DESIGN FOR QUADRUPED ROBOTS AND FRACTIONAL ORDER PID (PIλDμ) BASED CONTROL
Abstract
Quadruped robots are legged mobile robots that increase their popularity in
robotic and control areas due to their complex dynamic structure with high
mobility in different terrain conditions compared to wheeled systems. In this
study; A 3-DoF linear leg model and its control are provided in order to enable
quickly and effectively simulate about on such subjects that walking planning,
foot trajectory design and body stability control of robot. A realistic physical
model with parameters such as the dimensions, masses, inertia of limbs and the stiffness
and damping values of joints is designed on Matlab/SimMechanics and simulated
on Simulink environments. By taking into account the angular position ranges of
the joints required for the robot to perform a standard step trajectory during
the walk, the linear state-space model of the system (torque input- angular
position output) is obtained using the linearization tools over the physical
model. The unit step responses of the physical model are compared with the
obtained linear model responses under constant torque input and it is
understood to give similar results with small error values. Using the linear
model, the angular position control of the system is achieved with PIλDµ
controllers designed by selecting various parameters of fraction
orders as comparatively the classical PID. Simulation results are presented
and investigated.
robotic and control areas due to their complex dynamic structure with high
mobility in different terrain conditions compared to wheeled systems. In this
study; A 3-DoF linear leg model and its control are provided in order to enable
quickly and effectively simulate about on such subjects that walking planning,
foot trajectory design and body stability control of robot. A realistic physical
model with parameters such as the dimensions, masses, inertia of limbs and the stiffness
and damping values of joints is designed on Matlab/SimMechanics and simulated
on Simulink environments. By taking into account the angular position ranges of
the joints required for the robot to perform a standard step trajectory during
the walk, the linear state-space model of the system (torque input- angular
position output) is obtained using the linearization tools over the physical
model. The unit step responses of the physical model are compared with the
obtained linear model responses under constant torque input and it is
understood to give similar results with small error values. Using the linear
model, the angular position control of the system is achieved with PIλDµ
controllers designed by selecting various parameters of fraction
orders as comparatively the classical PID. Simulation results are presented
and investigated.
References
- Bakırcıoglu, V., Sen, M.A. and Kalyoncu, M., 2016a, “Optimization of PID Controller Based on the Bees Algorithm for One Leg of a Quadruped Robot”, MATEC Web of Conferences, Vol. 42, No. 03004, pp. 1-4.
- Bakırcıoglu, V., Sen, M.A. and Kalyoncu, M., “Adaptive Neural-Network Based Fuzzy Logic (ANFIS) Based Trajectory Controller Design for One Leg of a Quadruped Robot”, 5th International Mechatronics and Control Engineering (ICMCE 2016), Venice, Italy, 82-85, 14-17 December, 2016b.
- Bakırcıoğlu, V., Sen, M.A. and Kalyoncu, M., “Motıon Analysıs of The Robotıc Leg Mass Centre Durıng Reference Trajectory Trackıng” 2018 International Vocational Science Symposium (IVSS 2018), Antalya, Turkey, 420, 26-29 April, 2018.
- Baudoin, Y. and Maki K. Habib, 2010, Using Robots in Hazardous Environments: Landmine Detection, De- Mining and Other Applications, Woodhead Publishing, Cambridge, London, England.
- Boston Dynamics Company, https://www.bostondynamics.com/robots, access date: 12.09.2019.
- Focchi, Michele, et al. “Control of A Hydraulically-Actuated Quadruped Robot Leg”, 2010 IEEE International Conference on Robotics and Automation (ICRA2010), IEEE, Alaska, United States, 4182-4188, 4-8 May, 2010.
- Hutter, M., et al., “StarlETH: A Compliant Quadrupedal Robot for Fast, Efficient, and Versatile Locomotion”, International Conference on Climbing and Walking Robots (CLAWAR), Baltimore, USA 483-490, 23-26 July, 2012.
- Hutter, M., et al., 2017, “Anymal-Toward Legged Robots for Harsh Environments”, Advanced Robotics, Vol. 31, No. 17, pp. 918-931.
- Podlubny, I., 1999, “Fractional-Order Systems and PIλDμ Controllers”, IEEE Transactions on Automatic Control, Vol. 44, No. 1, pp. 208-214.
- Podlubny, I., Dorcak L. and Kostial I., “On Fractional Derivatives, Fractional-Order Dynamic Systems and PIλDμ Controllers”, 36th IEEE Conference on Decision and Control, IEEE, Kobe, Japan, 1-5, 13-13 December, 1997.
- Raibert, M., Blankespoor, K., Nelson, G. and Playter, R., “Bigdog, The Rough-Terrain Quadruped Robot”, In 17th World Congress the International Federation of Automatic Control, Seoul, South Korea, 10822- 10825, 6-11 July, 2008.
- Raibert, M.H., 1986, Legged Robots That Balance. MIT Press, Cambridge, London, England.
- Rossell, J. M., et al. “Tracking Control for A Stewart Platform Prototype” 2015 International Conference on Advanced Mechatronics, Intelligent Manufacture, and Industrial Automation (ICAMIMIA), IEEE, Resort, Surabaya, 58-63, 15-16 October, 2015.
- Semini, C., 2010, Hyq-Design and Development of a Hydraulically Actuated Quadruped Robot, Doctor of Philosophy (Ph.D.), University of Genoa, Italy.
- Semini, C., et al., 2017, “Design of the Hydraulically-Actuated Torque-Controlled Quadruped Robot HyQ2Max”, IEEE/ASME Transactions on Mechatronics, Vol. 22, No. 2, pp. 635-646.
- Sen, M.A. and Kalyoncu M., 2018, “Optimal Tuning of PID Controller Using Grey Wolf Optimizer Algorithm for Quadruped Robot”, Balkan Journal of Electrical and Computer Engineering, Vol. 6, No. 1, pp. 29-35.
- Sen, M.A. and Kalyoncu M., 2019, “Grey Wolf Optimizer Based Tuning of a Hybrid LQR-PID Controller for Foot Trajectory Control of a Quadruped Robot”, Gazi University Journal of Science, Vol. 32, No. 2, pp. 674-684.
There are 17 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Engineering |
| Journal Section | Research Article |
| Authors | |
| Publication Date | June 3, 2020 |
| Submission Date | September 16, 2019 |
| Acceptance Date | October 10, 2019 |
| Published in Issue | Year 2020 Volume: 8 Issue: 2 |
