Momentum-Based Push Recovery Control of Bipedal Robots Using a New Variable Power Reaching Law for Sliding Mode Control

Ibrahim Al-Tameemi, Duc Doan, Abizer Patanwala, Mahdi Agheli

Abstract


A significant challenge in deploying bipedal robots for human-oriented real-world applications is their ability to maintain balance when externally disturbed. Current momentum-based balance control strategies often exhibit inadequate robustness to disturbances due to reliance on simple proportional controllers and imprecise incorporation of desired angular momentum changes. Furthermore, the sequential activation of momentum and posture correction controllers compromises system stability when confronted with consecutive disturbances. This paper proposes and validates a new Variable Power Reaching Law for Sliding Mode Control (SMC) to enhance the regulation of linear momentum against disturbances. The proposed reaching law adjusts dynamically to the system's errors, ensuring fast convergence and minimal chattering. In this paper, we precisely define the desired angular momentum change in relation to the Center of Pressure (CoP), a crucial stability metric, as well as the desired linear momentum and ground reaction forces.  The null-space method, which allows for simultaneous task execution by using unused degrees of freedom, is employed to ensure effective balance and upright posture without interference. The posture correction control is projected onto the null-space of momentum control. Simulation results confirm that the proposed control system effectively stabilizes the robot against external disturbances, regulating momentum and restoring upright posture. The null-space method proves effective in maintaining balance under multiple disturbances by simultaneously controlling momentum and posture. Comparative evaluations show that our approach outperforms traditional momentum-based controls and nonadaptive reaching laws, reducing CoP fluctuations, managing disturbances up to 117 N, and minimizing chattering and steady-state error. These advancements underscore the potential for deploying bipedal robots in dynamic environments.

Keywords


Push Recovery; Dynamic Stability; Bipedal Robots; Sliding Mode Control; Null-Space Method; Center of Pressure.

Full Text:

PDF

References


X. Yang, H. She, H. Lu, T. Fukuda, and Y. Shen, “State of the Art: Bipedal Robots for Lower Limb Rehabilitation,” Applied Sciences, vol. 7, no. 11, p. 1182, 2017, doi: 10.3390/app7111182.

K. Yin, Y. Wang, P. Li, K. Dai, Y. Xue, and L. Yang, “Adaptive ankle impedance control for bipedal robotic upright balance,” Expert Systems, vol. 40, no. 5, p. e13168, 2023, doi: 10.1111/exsy.13168.

Y. Cao, K. Xiang, B. Tang, Z. Ju, and M. Pang, “Design of Muscle Reflex Control for Upright Standing Push-Recovery Based on a Series Elastic Robot Ankle Joint,” Frontiers in Neurorobotics, vol. 14, p. 20, 2020, doi: 10.3389/fnbot.2020.00020.

E. Chumacero-Polanco and J. Yang, “Effect of disturbances and sensorimotor deficits on the postural robustness of an ankle–hip model of balance on a balance board,” Nonlinear Dynamics, vol. 99, no. 3, pp. 1959–1973, 2020, doi: 10.1007/s11071-019-05403-w.

P. Morasso, “Integrating ankle and hip strategies for the stabilization of upright standing: An intermittent control model,” Frontiers in Computational Neuroscience, vol. 16, p. 956932, 2022, doi: 10.3389/fncom.2022.956932.

K. Yin, Y. Xue, Y. Yu, and S. Xie, “Variable Impedance Control for Bipedal Robot Standing Balance Based on Artificial Muscle Activation Model,” Journal of Robotics, vol. 2021, no. 1, p. 8142161, 2021, doi: 10.1155/2021/8142161.

N. Nernchad and P. Artrit, “Stand balancing strategies for a humanoid robot with slidable floor,” International Journal of Mechanical Engineering and Robotics Research, vol. 9, no. 4, pp. 511–515, 2020, doi: 10.18178/ijmerr.9.4.511-515.

C. Li, R. Xiong, Q. guo Zhu, J. Wu, Y. liang Wang, and Y. ming Huang, “Push recovery for the standing under-actuated bipedal robot using the hip strategy,” Frontiers of Information Technology and Electronic Engineering, vol. 16, no. 7, pp. 579–593, 2015, doi: 10.1631/FITEE.14a0230.

M. Shafiee-Ashtiani, A. Yousefi-Koma, M. Shariat-Panahi, and M. Khadiv, “Push recovery of a humanoid robot based on model predictive control and capture point,” in 2016 4th International Conference on Robotics and Mechatronics (ICROM), pp. 433–438, 2016, doi: 10.1109/ICRoM.2016.7886777.

D. N. Nenchev and A. Nishio, “Experimental validation of ankle and hip strategies for balance recovery with a biped subjected to an impact,” IEEE International Conference on Intelligent Robots and Systems, vol. 26, no. 5, pp. 4035–4040, 2007, doi: 10.1109/IROS.2007.4399038.

K. Shen, A. Chemori, and M. Hayashibe, “Human-Like Balance Recovery Based on Numerical Model Predictive Control Strategy,” IEEE Access, vol. 8, pp. 92050–92060, 2020, doi: 10.1109/ACCESS.2020.2995104.

Y. Liu, J. Shen, J. Zhang, X. Zhang, T. Zhu, and D. Hong, “Design and Control of a Miniature Bipedal Robot with Proprioceptive Actuation for Dynamic Behaviors,” in Proceedings - IEEE International Conference on Robotics and Automation, pp. 8547–8553, 2022, doi: 10.1109/ICRA46639.2022.9811790.

J. Li, Z. Yuan, S. Dong, J. Zhang, and X. Sang, “External force observer aided push recovery for torque-controlled biped robots,” Autonomous Robots, vol. 46, no. 5, pp. 553–568, 2022, doi: 10.1007/s10514-022-10038-9.

B. J. Stephens and C. G. Atkeson, “Dynamic balance force control for compliant humanoid robots,” in IEEE/RSJ 2010 International Conference on Intelligent Robots and Systems, IROS 2010 - Conference Proceedings, pp. 1248–1255, 2010, doi: 10.1109/IROS.2010.5648837.

C. Ott, M. A. Roa, and G. Hirzinger, “Posture and balance control for biped robots based on contact force optimization,” in IEEE-RAS International Conference on Humanoid Robots, pp. 26–33, 2011, doi: 10.1109/Humanoids.2011.6100882.

Z. Wang et al., “A Spring Compensation Method for a Low-Cost Biped Robot Based on Whole Body Control,” Biomimetics, vol. 8, no. 1, p. 126, 2023, doi: 10.3390/biomimetics8010126.

Y. Yang et al., “Balanced Standing on One Foot of Biped Robot Based on Three-Particle Model Predictive Control,” Biomimetics, vol. 7, no. 4, p. 244, 2022, doi: 10.3390/biomimetics7040244.

J. Cui, Z. Li, Y. Kuang, and H. Cheng, “Standing balance maintenance by virtual suspension model control for legged robot,” Advances in Mechanical Engineering, vol. 12, no. 9, p. 1687814020954975, 2020, doi: 10.1177/1687814020954975.

R. Zhang, M. Zhao, and C. L. Wang, “Standing Push Recovery Based on LIPM Dynamics Control for Biped Humanoid Robot,” in 2018 IEEE International Conference on Robotics and Biomimetics, ROBIO 2018, pp. 1732–1737, 2018, doi: 10.1109/ROBIO.2018.8664792.

A. MacChietto, V. Zordan, and C. R. Shelton, “Momentum control for balance,” in ACM Transactions on Graphics, vol. 28, no. 3, 2009, pp. 1–8. doi: 10.1145/1531326.1531386.

S. Kajita et al., “Resolved Momentum Control: Humanoid Motion Planning Based on the Linear and Angular Momentum,” in IEEE International Conference on Intelligent Robots and Systems, pp. 1644–1650, 2003, doi: 10.1109/iros.2003.1248880.

S. H. Lee and A. Goswami, “A momentum-based balance controller for humanoid robots on non-level and non-stationary ground,” Autonomous Robots, vol. 33, no. 4, pp. 399–414, 2012, doi: 10.1007/s10514-012-9294-z.

M. Abdallah and A. Goswami, “A biomechanically motivated two-phase strategy for biped upright balance control,” in Proceedings - IEEE International Conference on Robotics and Automation, pp. 1996–2001, 2005, doi: 10.1109/ROBOT.2005.1570406.

A. Hofmann, M. Popovic, and H. Herr, “Exploiting angular momentum to enhance bipedal center-of-mass control,” in Proceedings - IEEE International Conference on Robotics and Automation, pp. 4423–4429, 2009, doi: 10.1109/ROBOT.2009.5152573.

R. Schuller, G. Mesesan, J. Englsberger, J. Lee, and C. Ott, “Online Centroidal Angular Momentum Reference Generation and Motion Optimization for Humanoid Push Recovery,” IEEE Robotics and Automation Letters, vol. 6, no. 3, pp. 5689–5696, 2021, doi: 10.1109/LRA.2021.3082023.

H. Dai, A. Valenzuela, and R. Tedrake, “Whole-body motion planning with centroidal dynamics and full kinematics,” in IEEE-RAS International Conference on Humanoid Robots, pp. 295–302, 2015, doi: 10.1109/HUMANOIDS.2014.7041375.

H. J. Lee and J. Y. Kim, “Balance Control Strategy of Biped Walking Robot SUBO-1 Based on Force-Position Hybrid Control,” International Journal of Precision Engineering and Manufacturing, vol. 22, no. 1, pp. 161–175, 2021, doi: 10.1007/s12541-020-00438-1.

Y. Lu, J. Gao, X. Shi, D. Tian, and Y. Liu, “Sliding balance control of a point-foot biped robot based on a dual-objective convergent equation,” Applied Sciences (Switzerland), vol. 11, no. 9, 2021, doi: 10.3390/app11094016.

M. Sobirin and H. Hindersah, “Stability Control for Bipedal Robot in Standing and Walking using Fuzzy Logic Controller,” in Proceedings - 2021 IEEE International Conference on Industry 4.0, Artificial Intelligence, and Communications Technology, IAICT 2021, pp. 1–7, 2021, doi: 10.1109/IAICT52856.2021.9532516.

M. Popovic, A. Hofmann, and H. Herr, “Angular momentum regulation during human walking: Biomechanics and control,” in Proceedings - IEEE International Conference on Robotics and Automation, pp. 2405–2411, 2004, doi: 10.1109/robot.2004.1307421.

S. Bakhtiari, M. Razzaghi, and A. Samiee, “A sliding mode controler of hips actuated for passive walking robots,” Journal of Computer & Robotics, vol. 12, no. 1, pp. 103–112, 2019.

G. Chen, B. Jin, and Y. Chen, “Accurate and robust body position trajectory tracking of six-legged walking robots with nonsingular terminal sliding mode control method,” Applied Mathematical Modelling, vol. 77, pp. 1348–1372, 2020, doi: 10.1016/j.apm.2019.09.021.

S. A. Ghoreishi, A. F. Ehyaei, and M. Rahmani, “Double hyperbolic sliding mode control of a three-legged robot with actuator constraints,” IET Control Theory and Applications, vol. 16, no. 15, pp. 1573–1585, 2022, doi: 10.1049/cth2.12326.

A. Sajedifar, M. H. Korayem, and F. Allahverdi, “Dynamic Modelling and Optimal Sliding Mode Control of the Wearable Rehabilitative Bipedal Cable Robot with 7 Degrees of Freedom,” Journal of Intelligent and Robotic Systems: Theory and Applications, vol. 110, no. 2, pp. 1–16, 2024, doi: 10.1007/s10846-024-02122-2.

M. M. Kakaei and H. Salarieh, “New Robust Control Method Applied to the Locomotion of a 5-Link Biped Robot,” Robotica, vol. 38, no. 11, pp. 2023–2038, 2020, doi: 10.1017/S0263574719001796.

Y. Gao, W. Wei, X. Wang, D. Wang, Y. Li, and Q. Yu, “Trajectory tracking of multi-legged robot based on model predictive and sliding mode control,” Information Sciences, vol. 606, pp. 489–511, 2022, doi: 10.1016/j.ins.2022.05.069.

L. Alnufaie, “Fuzzy nonsingular fast terminal sliding mode controller for a robotic system,” International Journal of Advanced and Applied Sciences, vol. 10, pp. 166–173, 2023, doi: 10.21833/ijaas.2023.10.019.

T. Sun, L. Cheng, Z. Hou, and M. Tan, “Novel sliding-mode disturbance observer-based tracking control with applications to robot manipulators,” Science China Information Sciences, vol. 64, no. 7, p. 172205, 2021, doi: 10.1007/s11432-020-3043-y.

Z. Anjum, H. Zhou, S. Ahmed, and Y. Guo, “Fixed time sliding mode control for disturbed robotic manipulator,” JVC/Journal of Vibration and Control, vol. 30, no. 7–8, pp. 1580–1593, 2024, doi: 10.1177/10775463231165094.

C. Jing, H. Zhang, Y. Liu, and J. Zhang, “Adaptive Super-Twisting Sliding Mode Control for Robot Manipulators with Input Saturation,” Sensors, vol. 24, no. 9, p. 2783, 2024, doi: 10.3390/s24092783.

R. Li, L. Yang, Y. Chen, and G. Lai, “Adaptive Sliding Mode Control of Robot Manipulators with System Failures,” Mathematics, vol. 10, no. 3, p. 339, 2022, doi: 10.3390/math10030339.

Z. Dachang, H. Pengcheng, D. Baolin, and Z. Puchen, “Adaptive nonsingular terminal sliding mode control of robot manipulator based on contour error compensation,” Scientific Reports, vol. 13, no. 1, p. 330, 2023, doi: 10.1038/s41598-023-27633-0.

Y. Xu, R. Liu, J. Liu, and J. Zhang, “A novel constraint tracking control with sliding mode control for industrial robots,” International Journal of Advanced Robotic Systems, vol. 18, no. 4, p. 17298814211029778, 2021, doi: 10.1177/17298814211029778.

Y. Pan, C. Yang, L. Pan, and H. Yu, “Integral Sliding Mode Control: Performance, Modification, and Improvement,” IEEE Transactions on Industrial Informatics, vol. 14, no. 7, pp. 3087–3096, 2018, doi: 10.1109/TII.2017.2761389.

N. Qiao, L. Wang, M. Liu, and Z. Wang, “The sliding mode controller with improved reaching law for harvesting robots,” Journal of Intelligent and Robotic Systems: Theory and Applications, vol. 104, no. 1, pp. 1–13, 2022, doi: 10.1007/s10846-021-01536-6.

C. J. Fallaha, M. Saad, H. Y. Kanaan, and K. Al-Haddad, “Sliding-mode robot control with exponential reaching law,” IEEE Transactions on Industrial Electronics, vol. 58, no. 2, pp. 600–610, 2011, doi: 10.1109/TIE.2010.2045995.

F. Xu, N. An, J. Mao, and S. Yang, “A New Variable Exponential Power Reaching Law of Complementary Terminal Sliding Mode Control,” Complexity, vol. 2020, no. 1, p. 8874813, 2020, doi: 10.1155/2020/8874813.

H. Wang, X. Zhao, and Y. Tian, “Trajectory tracking control of XY table using sliding mode adaptive control based on fast double power reaching law,” Asian Journal of Control, vol. 18, no. 6, pp. 2263–2271, 2016, doi: 10.1002/asjc.1322.

Z. Kang, H. Yu, and C. Li, “Variable-parameter double-power reaching law sliding mode control method*,” Automatika, vol. 61, no. 3, pp. 345–351, 2020, doi: 10.1080/00051144.2020.1757965.

L. Wang et al., “A sliding mode control method based on improved reaching law for superbuck converter in photovoltaic system,” Energy Reports, vol. 8, pp. 574–585, 2022, doi: 10.1016/j.egyr.2022.03.159.

V. Nayak and S. K. Gudey, “An Enhanced Exponential Reaching Law Based Sliding Mode Control Strategy for a Three Phase UPS System,” Serbian Journal of Electrical Engineering, vol. 17, no. 3, pp. 313–336, 2020, doi: 10.2298/SJEE2003313N.

B. Jiang, J. Li, and S. Yang, “An improved sliding mode approach for trajectory following control of nonholonomic mobile AGV,” Scientific Reports, vol. 12, no. 1, p. 17763, 2022, doi: 10.1038/s41598-022-22697-w.

S. Li, H. Wang, H. Li, and C. Yang, “PMSM sliding mode control based on novel reaching law and extended state observer,” Advances in Mechanical Engineering, vol. 14, no. 8, p. 16878132221119960, 2022, doi: 10.1177/16878132221119960.

Y. Wang, Y. Feng, X. Zhang, J. Liang, and X. Cheng, “New reaching law control for permanent magnet synchronous motor with extended disturbance observer,” IEEE Access, vol. 7, pp. 186296–186307, 2019, doi: 10.1109/ACCESS.2019.2956846.

H. Armghan, M. Yang, N. Ali, A. Armghan, and A. Alanazi, “Quick reaching law based global terminal sliding mode control for wind/hydrogen/battery DC microgrid,” Applied Energy, vol. 316, p. 119050, 2022, doi: 10.1016/j.apenergy.2022.119050.

Y. Zhao, M. Noori, and W. A. Altabey, “Reaching law based sliding mode control for a frame structure under seismic load,” Earthquake Engineering and Engineering Vibration, vol. 20, no. 3, pp. 727–745, 2021, doi: 10.1007/s11803-021-2049-0.

A. G. Iyer, J. Samantaray, S. Ghosh, A. Dey, and S. Chakrabarty, “Sliding Mode Control Using Power Rate Exponential Reaching Law for Urban Platooning,” IFAC-PapersOnLine, vol. 55, no. 1, pp. 516–521, 2022, doi: 10.1016/j.ifacol.2022.04.085.

S. Wang, C. Jiang, Q. Tu, and C. Zhu, “Sliding mode control with an adaptive switching power reaching law,” Scientific Reports, vol. 13, no. 1, p. 16155, 2023, doi: 10.1038/s41598-023-43304-6.

P. Leśniewski and A. Bartoszewicz, “Reaching law based sliding mode control of sampled time systems,” Energies, vol. 14, no. 7, p. 1882, 2021, doi: 10.3390/en14071882.

W. Gao and J. C. Hung, “Variable Structure Control of Nonlinear Systems: A New Approach,” IEEE Transactions on Industrial Electronics, vol. 40, no. 1, pp. 45–55, 1993, doi: 10.1109/41.184820.

M. Mori and M. Sugihara, “The double-exponential transformation in numerical analysis,” Journal of Computational and Applied Mathematics, vol. 127, no. 1–2, pp. 287–296, 2001, doi: 10.1016/S0377-0427(00)00501-X.

T. Ooura and M. Mori, “A robust double exponential formula for Fourier-type integrals,” Journal of Computational and Applied Mathematics, vol. 112, no. 1–2, pp. 229–241, 1999, doi: 10.1016/S0377-0427(99)00223-X.

L. Aceto and P. Novati, “Exponentially Convergent Trapezoidal Rules to Approximate Fractional Powers of Operators,” Journal of Scientific Computing, vol. 91, no. 2, p. 55, 2022, doi: 10.1007/s10915-022-01837-4.

G. Notomista, S. Mayya, M. Selvaggio, M. Santos, and C. Secchi, “A Set-Theoretic Approach to Multi-Task Execution and Prioritization,” in Proceedings - IEEE International Conference on Robotics and Automation, pp. 9873–9879, 2020, doi: 10.1109/ICRA40945.2020.9196741.

S. Zhang, S. Cheng, and Z. Jin, “A Control Method of Mobile Manipulator Based on Null-Space Task Planning and Hybrid Control,” Machines, vol. 10, no. 12, p. 1222, 2022, doi: 10.3390/machines10121222.

R. S. Jamisola and R. G. Roberts, “An approach to drastically reduce the required legs DOFs for bipedal robots and lower-limb exoskeletons,” Robotica, vol. 40, no. 4, pp. 1207–1221, 2022, doi: 10.1017/S0263574721001090.

N. Wilhelm, R. Burgkart, J. Lang, C. Micheler, and C. von Deimling, “Exploiting null space potentials to control arm robots compliantly performing nonlinear tactile tasks,” International Journal of Advanced Robotic Systems, vol. 16, no. 6, p. 1729881419885473, 2019, doi: 10.1177/1729881419885473.

B. Taner and K. Subbarao, “Modeling of Cooperative Robotic Systems and Predictive Control Applied to Biped Robots and UAV-UGV Docking with Task Prioritization,” Sensors, vol. 24, no. 10, p. 3189, 2024, doi: 10.3390/s24103189.

K. Fan, Y. Liu, B. Huo, L. Yang, Z. Wu, and H. Yu, “Cascaded ESO based multi-task priority tracking and null-space compliance control for redundant robots,” Control Engineering Practice, vol. 141, p. 105710, 2023, doi: 10.1016/j.conengprac.2023.105710.

M. Khatib, K. Al Khudir, and A. De Luca, “Task Priority Matrix at the Acceleration Level: Collision Avoidance under Relaxed Constraints,” IEEE Robotics and Automation Letters, vol. 5, no. 3, pp. 4970–4977, 2020, doi: 10.1109/LRA.2020.3004771.

P. Hsu, J. Mauser, and S. Sastry, “Dynamic control of redundant manipulators,” Journal of Robotic Systems, vol. 6, no. 2, pp. 133–148, 1989, doi: 10.1002/rob.4620060203.

B. Siciliano and J.-J. E. Slotine, “A general framework for managing multiple tasks in highly redundant robotic systems,” in proceeding of 5th International Conference on Advanced Robotics, 2002, pp. 1211–1216 vol.2. doi: 10.1109/icar.1991.240390.

Y. Nakamura, H. Hanafusa, and T. Yoshikawa, “Task-Priority Based Redundancy Control of Robot Manipulators.,” International Journal of Robotics Research, vol. 6, no. 2, pp. 3–15, 1987, doi: 10.1177/027836498700600201.

J. M. Hollerbach and K. C. Suh, “Redundancy resolution of manipulators through torque optimization,” Proceedings - IEEE International Conference on Robotics and Automation, vol. 3, no. 4, pp. 1016–1021, 1985, doi: 10.1109/ROBOT.1985.1087285.

B. Stephens, “Integral control of humanoid balance,” in IEEE International Conference on Intelligent Robots and Systems, pp. 4020–4027, 2007, doi: 10.1109/IROS.2007.4399407.

O. Khatib, “Real-time obstacle avoidance for manipulators and mobile robots,” Proceedings - IEEE International Conference on Robotics and Automation, vol. 5, no. 1, pp. 500–505, 1985, doi: 10.1109/ROBOT.1985.1087247.

O. Khatib, “A Unified Approach for Motion and Force Control of Robot Manipulators: The Operational Space Formulation,” IEEE Journal on Robotics and Automation, vol. 3, no. 1, pp. 43–53, 1987, doi: 10.1109/JRA.1987.1087068.

O. KHATIB, L. SENTIS, J. PARK, and J. WARREN, “Whole-Body Dynamic Behavior and Control of Human-Like Robots,” International Journal of Humanoid Robotics, vol. 1, no. 1, pp. 29–43, 2004, doi: 10.1142/S0219843604000058.

L. Sentis and O. Khatib, “Prioritized multi-objective dynamics and control of robots in human environments,” in 2004 4th IEEE-RAS International Conference on Humanoid Robots, pp. 764–780, 2004, doi: 10.1109/ichr.2004.1442684.

J. Nakanishi, R. Cory, M. Mistry, J. Peters, and S. Schaal, “Operational space control: A theoretical and empirical comparison,” International Journal of Robotics Research, vol. 27, no. 6, pp. 737–757, 2008, doi: 10.1177/0278364908091463.




DOI: https://doi.org/10.18196/jrc.v5i5.23379

Refbacks

  • There are currently no refbacks.


Copyright (c) 2024 Ibrahim Al-Tameemi, Duc Doan, Abizer Patanwala, Mahdi Agheli

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

 


Journal of Robotics and Control (JRC)

P-ISSN: 2715-5056 || E-ISSN: 2715-5072
Organized by Peneliti Teknologi Teknik Indonesia
Published by Universitas Muhammadiyah Yogyakarta in collaboration with Peneliti Teknologi Teknik Indonesia, Indonesia and the Department of Electrical Engineering
Website: http://journal.umy.ac.id/index.php/jrc
Email: jrcofumy@gmail.com


Kuliah Teknik Elektro Terbaik