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Estimation of Ground Reaction Force for Quadruped Robot Control Using a High-Gain Observer

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Ground reaction force is one of the most important information for legged-locomotion control. This paper presents a novel design of an observer for estimating the ground reaction force of a quadruped robot without force sensors. Simple dynamics model of a general quadruped robot is derived by assuming that the robot’s fore and hind legs can be treated separately, and they can support force provided by opposite legs and the ground reaction force are considered as external disturbance force to be estimated by a disturbance observer. Simulation results show that the proposed observer can successfully estimate the ground reaction force even though the leg is in its swing phase. The estimation of the ground reaction force by the proposed observer may be applied to the controller design using the ground reaction force such as Zero-Moment Point and Central Pattern Generator modulated by the ground reaction force.
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Disturbance Observer; Ground Reaction Force; High-Gain Observer; Nonlinear Observer; Quadruped Robot

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Robot start inc., Boston Dynamics “SpotMini” is evaluated in demonstration experiment for practical application in 2019, (in Japanese)

The Guardian, SpotMini: headless robotic dog to go on sale in 2019,

SONY, aibo,

Shuuji Kajita, Fumio Kanehiro, Kenji Kaneko, Kiyoshi Fujiwara, Kensuke Harada, Kazuhito Yokoi and Hirohisa Hirukawa, Biped Walking Pattern Generation by using Preview Control of Zero-Moment Point, IEEE International Conference on Robotics & Automation, pp. 1620-1626, Taipei, Taiwan, September 2003.

M. Vukobratovic and J. Stepanenko, On the stability of anthropomorphic systems, Mathematical Biosciences, Vol. 15, (Issue 1):1-37, October 1972.

Satoshi Kitano, Shigeo Hirose, Atsushi Horigome and Gen Endo, TITAN-XIII sprawling-type quadruped robot with ability of fast and energy-efficient walking, ROBOMECH Journal, Vol. 3, (Issue 8), 2016.

Michele Focchi, Andrea Del Prete, Ioannis Havoutis, Roy Featherstone, Darwin G. Caldwell and Claudio Semini, High-slope Terrain Locomotion for Torque-Controlled Quadruped Robots, Autonomous Robotics, 2015.

Alfayad, S., Bruneau, O., Ouezdou, F., Fouz, M., Doubliez, P., Analytical Energetic Approach for Predictive Generation of Dynamic Biped Walking - Use of Average Energies, (2016) International Review of Mechanical Engineering (IREME), 10 (7), pp. 461-473.

X. Li, H. Imanishi, M. Minami, T. Matsuno, and A. Yanou, Dynamical Model of Walking Transition Considering Nonlinear Friction with Floor, Journal of Advanced Computational Intelligence and Intelligent Informatics, Vol. 20, (Issue 6): 974-982, 2016.

Syuhri, A., Basuki, H., Syuhri, S., Kinematics Analysis of a Leg Mechanism as a Motion Converter, (2016) International Review of Mechanical Engineering (IREME), 10 (6), pp. 409-418.

Haibo Gao, Yufei Liu, Liang Ding, Guangjun Liu, Zongquan Deng, Yiqun Liu and Haitao Yu, Low Impact Force and Energy Consumption Motion Planning for Hexapod Robot with Passive Compliant Ankles, Journal of Intelligent & Robotic Systems, 2018.

Ryosuke Horio, Naoki Uchiyama and Shigenori Sano, Trot Gait Control of Quadruped Robot Based on Inclination of Body, IEEE International Conference on Robotics and Biomimetics, pp. 2062-2067, Bali, Indonesia, December 2014.

Ryosuke Horio, Naoki Uchiyama and Shigenori Sano, Observer Design for Estimating Support Force Applied by a Human Operator of a Biped Robot, Journal of Advanced Computational Intelligence and Intelligent Informatics, Vol. 21 (Issue 4):744-750, 2017.

Andre Rosendo, Shogo Nakatsu, Xiangxiao Liu, Masahiro Shimizu and Koh Hosoda, Quadrupedal locomotion based on a muscular activation pattern with stretch-reflex, IEEE International Conference on Robotics and Biomimetics, pp. 773-778, Bali, Indonesia, December 2014.

M. Mutlu, S. Hauser, A. Bernardino and A. J. Ijspeert, Effects of passive and active joint compliance in quadrupedal locomotion, Advanced Robotics, Vol. 32, (Issue 15):809-824, 2018.

S. Hauser, M. Mutlu, P. Banzet and A.J. Ijspeert, Compliant universal grippers as adaptive feet in legged robots, Advanced Robotics, Vol. 32, (Issue 15):825-836, 2018.

Zhigailov, S., Musalimov, V., Aryassov, G., Penkov, I., Modelling and Simulation of Human Lower–Limb Motion, (2016) International Review on Modelling and Simulations (IREMOS), 9 (2), pp. 114-123.

Caceres, C., Puerta, J., Jiménez, R., Rojas, D., Design of a Bio-Inspired Equine Robot Prototype, (2016) International Review of Mechanical Engineering (IREME), 10 (1), pp. 12-17.

Alexander Spröwitz, Alexandre Tuleu, Massimo Vespignani, Mostafa Ajallooeian, Emilie Badri, Auke Jan Ijspeert, Towards Dynamic Trot Gait Locomotion—Design, Control, and Experiments with Cheetah-cub, a Compliant Quadruped Robot, International Journal of Robotics Research, Volume 32 (Issue 8): pp. 933­951, July 2013.

Ludovico Minati, Mattia Frasca, Natsue Yoshimura and Yasuharu Koike, Versatile Locomotion Control of a Hexapod Robot Using Hierarchical Network of Nonlinear Oscillator Circuits, IEEE Access, Vol. 6:8042-8065, 2018.

Kassim, A., Yasuno, T., Abas, N., Aras, M., Rashid, M., Performance Study of Reference Height Control Algorithm for Tripod Hopping Robot, (2013) International Review of Mechanical Engineering (IREME), 7 (5), pp. 784-789.

Yasuhiro Fukuoka, Yasushi Habu and Takahiro Fukui, A simple rule for quadrupedal gait generation determined by leg loading feedback: a modeling study, Scientific Reports,

Dai Owaki and Akio Ishiguro, A Quadruped Robot Exhibiting Spontaneous Gait Transitions from Walking to Trotting to Galloping, Scientific Reports, 2017.

A. Fukuhara, D. Owaki, T. Kano, R. Kobayashi and A. Ishiguro, Spontaneous gait transition to high-speed galloping by reconciliation between body support and propulsion, Advanced Robotics, Vol. 32, (Issue 15): 794-808, August 2018.

Marco Camurri, Maurice Fallon, Stéphane Bazeille, Andreea Radulescu, Victor Barasuol, Darwin G. Caldwell and Claudio Semini, Probabilistic Contact Estimation and Impact Detection for State Estimation of Quadruped Robots, IEEE Robotics and Automation Letters, 2017.

Russell Smith, Open Dynamics Engine v0.5 User Guide,

Hassan. K. Khalil, Nonlinear Systems, Third Edition (Prentice-Hall, 2002, pp. 610-613).

Win, T., Hesketh, T., Eaton, R., Robotic Tower Crane Modeling and Control (RTCMC) with LQR-DRO and LQR-LEIC for Linear and Nonlinear Payload Swing Minimization, (2016) International Review of Automatic Control (IREACO), 9 (2), pp. 72-87.

Chalawane, H., Essadki, A., Nasser, T., Impact of Increasing Stator Resistance on Active Disturbance Rejection Control Based Sensorless Induction Motor Compared with a Conventional PI and Fuzzy Logic Control, (2018) International Review of Automatic Control (IREACO), 11 (5), pp. 217-225.


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