Anti-disturbance Composite Controller Design of Quadruped Robot Based on Extended State Observer and Model Predictive Control Technique

doi:10.12382/bgxb.2023.0962

Abstract

Abstract:

A novel composite control algorithm that combines the extended state observer, quadratic programming and model predictive control is proposed to improve the control performance of quadruped robot under model uncertainty and external disturbances. A model predictive controller is proposed for a quadruped robot based on the single rigid body model,and a variable bandwidth nonlinear extended state observer is developed to estimate the lumped disturbance, including the model mismatch and external forces. Based on the estimated result, a compensator is further constructed using the quadratic programming technique.The proposed control algorithm is validated through simulation. The simulated results demonstrate that the anti-disturbance composite controller is used to allow the robot to achieve the satisfactory control performance under the conditions of the changes in mass and the application of external forces. In comparison to existing studies, the proposed controller exhibits significant improvements in control accuracy and disturbance rejection capabilities.

Key words: quadruped robot, model predictive control, extended state observer, quadratic programming

CLC Number:

TJ301

XU Peng, XING Boyang, LIU Yufei, LI Yongyao, ZENG Yi, ZHENG Dongdong. Anti-disturbance Composite Controller Design of Quadruped Robot Based on Extended State Observer and Model Predictive Control Technique[J]. Acta Armamentarii, 2023, 44(S2): 12-21.

Figures/Tables 9

Fig.1 A simplified quadruped robot

Fig.2 System control framework

Fig.3 External force applied to the robot

Fig.4 Estimated results of the acceleration disturbances

Fig.5 Estimated results of the angular acceleration disturbances

Fig.6 Roll angle of robot

Fig.7 Yaw angle of robot

Fig.8 Lateral position of robot in the world frame

Fig.9 Height of robotbody

References 37

[1]	BISWAL P, MOHANTY P K. Development of quadruped walking robots: a review[J]. Ain Shams Engineering Journal, 2021, 12(2): 2017-2031. doi: 10.1016/j.asej.2020.11.005 URL
[2]	WINKLER A W, FARSHIDIAN F, PARDO D, et al. Fast trajectory optimization for legged robots using vertex-based ZMP constraints[J]. IEEE Robotics and Automation Letters, 2017, 2(4): 2201-2208. doi: 10.1109/LRA.2017.2723931 URL
[3]	CHEN H, HONG Z J, YANG S P, et al. Quadruped capturability and push recovery via a switched-systems characterization of dynamic balance[J]. IEEE Transactions on Robotics, 2023, 39(3): 2111-2130. doi: 10.1109/TRO.2023.3240622 URL
[4]	FAWCETT R T, PANDALA A, KIM J, et al. Real-time planning and nonlinear control for quadrupedal locomotion with articulated tails[J]. Journal of Dynamic Systems, Measurement, and Control, 2021, 143(7): 071004. doi: 10.1115/1.4049555 URL
[5]	LAKATOS D, PLOEGER K, LOEFFL F, et al. Dynamic locomotion gaits of a compliantly actuated quadruped with slip-like articulated legs embodied in the mechanical design[J]. IEEE Robotics and Automation Letters, 2018, 3(4): 3908-3915. doi: 10.1109/LRA.2018.2857511 URL
[6]	KOCO E, MUTKA A, KOVACIC Z. New variable passive-compliant element design for quadruped adaptation to stiffness-varying terrain[J]. International Journal of Advanced Robotic Systems, 2016, 13(3): 90. doi: 10.5772/63893 URL
[7]	HAN B, YI H Y, XU Z Y, et al. 3D-slip model based dynamic stability strategy for legged robots with impact disturbance rejection[J]. Scientific Reports, 2022, 12(1): 5892. doi: 10.1038/s41598-022-09937-9 pmid: 35393501
[8]	GONG D W, WANG P, ZHAO S Y, et al. Bionic quadruped robot dynamic gait control strategy based on twenty degrees of freedom[J]. IEEE/CAA Journal of Automatica Sinica, 2017, 5(1): 382-388. doi: 10.1109/JAS.2017.7510790 URL
[9]	WANG L, MENG L B, KANG R, et al. Design and dynamic locomotion control of quadruped robot with perception-less terrain adaptation[J]. Cyborg and Bionic Systems, 2022(2):9816495.
[10]	SHEN J J, HONG D. Convex model predictive control of single rigid body model on SO(3) for versatile dynamic legged motions[C]// Proceedings of the 39th International Conference on Robotics and Automation. Philadelphia, PA, US: IEEE, 2022: 6586-6592.
[11]	KIM D, DI CARLO J, KATZ B, et al. Highly dynamic quadruped locomotion via whole-body impulse control and model predictive control:arXiv:1909.06586[R]. Ithaca,NY, US: Cornell University, 2019:1909.06586.
[12]	YUAN S D, ZHOU Y J, LUO C. Crawling gait planning based on foot trajectory optimization for quadruped robot[C]// Proceedings of the 16th IEEE International Conference on Mechatronics and Automation. Tianjing, China: IEEE, 2019: 1490-1495.
[13]	LI X S, ZHANG X H, NIU J K, et al. A stable walking strategy of quadruped robot based on ZMP in trotting gait[C]// Proceedings of the 19th IEEE International Conference on Mechatronics and Automation (ICMA). Guilin, China: IEEE, 2022: 858-863.
[14]	王艳琴, 许威, 周川, 等. 基于质心调整的四足机器人转弯步态规划[J]. 控制工程, 2021, 28(11): 2280-2285.
	WANG Y Q, XU W, ZHOU C, et al. Turning gait strategy for quadruped robot based on adjustment of center of mass[J]. Control Engineering of China, 2021, 28(11): 2280-2285. (in Chinese)
[15]	CHEN G R, GUO S, HOU B W, et al. Virtual model control for quadruped robots[J]. IEEE Access, 2020, 8: 140736-140751. doi: 10.1109/Access.6287639 URL
[16]	谭永营, 晁智强, 金毅, 等. 基于虚拟元件的负载型四足步行平台静步态行走控制[J]. 兵工学报, 2019, 40(12): 2570-2579. doi: 10.3969/j.issn.1000-1093.2019.12.023
	TAN Y Y, CHAO Z Q, JIN Y, et al. Control of static walking gait of load carrying quadruped walking vehicle based on virtual components[J]. Acta Armamentarii, 2019, 40(12): 2570-2579. (in Chinese) doi: 10.3969/j.issn.1000-1093.2019.12.023
[17]	CUI J W, LI Z, KUANG Y Q, et al. Standing balance maintenance by virtual suspension model control for legged robot[J]. Advances in Mechanical Engineering, 2020, 12(9): 1687814020954975.
[18]	TAN Y Y, CHAO Z Q, LI H Y, et al. Control of trotting gait for load-carrying quadruped walking vehicle with eccentric torso[J]. International Journal of Advanced Robotic Systems, 2020, 17(4): 1729881420931676.
[19]	LU G L, CHEN T, RONG X W, et al. Whole-body motion planning and control of a quadruped robot for challenging terrain[J]. Journal of Field Robotics, 2023, 40(6): 1657-1677. doi: 10.1002/rob.v40.6 URL
[20]	XIE A Z, CHEN T, RONG X W, et al. A robust and compliant framework for legged mobile manipulators using virtual model control and whole-body control[J]. Robotics and Autonomous Systems, 2023, 164: 104411. doi: 10.1016/j.robot.2023.104411 URL
[21]	CUI J W, LI Z, QIU J, et al. Fault-tolerant motion planning and generation of quadruped robots synthesised by posture optimization and whole body control[J]. Complex & Intelligent Systems, 2022, 8(4): 2991-3003.
[22]	HAMED K A, KIM J, PANDALA A. Quadrupedal locomotion via event-based predictive control and QP-based virtual constraints[J]. IEEE Robotics and Automation Letters, 2020, 5(3): 4463-4470. doi: 10.1109/LSP.2016. URL
[23]	DI CARLO J, WENSING P M, KATZ B, et al. Dynamic locomotion in the MIT cheetah 3 through convex model-predictive control[C]// Proceedings of the 31st IEEE/RSJInternational Conference on Intelligent Robots and Systems. Madrid, Spain:IEEE, 2018: 7440-7447.
[24]	DING Y R, PANDALA A, PARK H W. Real-time model predictive control for versatile dynamic motions in quadrupedal robots[C]// Proceedings of the 36th International Conference on Robotics and Automation. Montreal, Canada: IEEE, 2019: 8484-8490.
[25]	DING Y R, PANDALA A, LI C Z, et al. Representation-free model predictive control for dynamic motions in quadrupeds[J]. IEEE Transactions on Robotics, 2021, 37(4): 1154-1171. doi: 10.1109/TRO.2020.3046415 URL
[26]	ZHU Q X, HUANG D H, YU B, et al. An improved method combined SMC and MLESO for impedance control of legged robots’ electro-hydraulic servo system[J]. ISA Transactions, 2022, 130: 598-609. doi: 10.1016/j.isatra.2022.03.009 URL
[27]	CHOI J, NA B, OH S, et al. A disturbance observer for robust position tracking control and ground contact detection of aCheetaroid-I leg[C]// Proceedings of the 13rd IEEE/ASME International Conference on Advanced Intelligent Mechatronics. Besacon, France: IEEE, 2014: 72-75.
[28]	朱晓璐, 万锦晓, 许威, 等. 侧向推搡下的四足机器人复合抗扰控制策略[J]. 信息与控制, 2021, 50(1): 119-128. doi: 10.13976/j.cnki.xk.2020.0158
	ZHU X L, WAN J X, XU W, et al. Composite disturbance rejection control strategy for quadruped robot under lateral disturbance[J]. Information and Control, 2021, 50(1): 119-128. (in Chinese) doi: 10.13976/j.cnki.xk.2020.0158
[29]	DINI N, MAJD V J. Sliding-mode tracking control of a walking quadruped robot with a push recovery algorithm using a nonlinear disturbance observer as a virtual force sensor[J]. Iranian Journal of Science and Technology-Transactions of Electrical Engineering, 2020, 44(3): 1033-1057. doi: 10.1007/s40998-019-00283-7
[30]	DINI N, MAJD V J, EDRISI F, et al. Estimation of external forces acting on the legs of a quadruped robot using two nonlinear disturbance observers[C]// Proceedings of the 4th International Conference on Robotics and Mechatronics. Tehran, Iran: IEEE, 2016: 72-77.
[31]	XING B Y, LIU Y F, WANG Z R, et al. Design of the anti-disturbance virtual model controller for quadruped robot[C]// Proceedings of the 33rd Chinese Control and Decision Conference. Kunming, China: IEEE, 2021: 4359-4365.
[32]	MORLANDO V, TEIMOORZADEH A, RUGGIERO F. Whole-body control with distur-bance rejection through a momentum-based observer for quadruped robots[J]. Mechanism and Machine Theory, 2021, 164: 104412. doi: 10.1016/j.mechmachtheory.2021.104412 URL
[33]	MORLANDO V, RUGGIERO F. Disturbance rejection for legged robots through a hybrid observer[C]// Proceedings of the 30th Mediterranean Conference on Control and Automation. Vouliagmeni, Greece: IEEE, 2022: 743-748.
[34]	CHENG Y, REN X M, ZHENG D D, et al. Non-linear bandwidth extended-state-observer based non-smooth funnel control for motor-drive servo systems[J]. IEEE Transactions on Industrial Electronics, 2022, 69(6): 6215-6224. doi: 10.1109/TIE.2021.3095811 URL
[35]	SLEIMAN J P, FARSHIDIAN F, MINNITI M V, et al. A unified MPC framework for whole-body dynamic locomotion and manipulation[J]. IEEE Robotics and Automation Letters, 2021, 6(3): 4688-4695.
[36]	MINNITI M V, GRANDIA R, FARSHIDIAN F, et al. Adaptive CLF-MPC with application to quadrupedal robots[J]. IEEE Robotics and Automation Letters, 2021, 7(1): 565-572.
[37]	DING Y, PANDALA A, LI C, et al. RF-MPC[CP/OL]. [2023-11-15]. https://github.com/YanranDing/RF-MPC.