Abstract：In order to realize the human-like motion control of the robotic joint system actuated by antagonistic pneumatic artificial muscles (PAMs), it is regarded as a non-linear optimal control problem with consideration of its serious non-linear properties, and the optimal performance indexes are determined according to the minimum jerk model based on the joint motion characteristics of the human arm. Firstly, the robotic joint model is linearized with the extended state observer. Then, an optimal control law is designed on the linearized standard integrator series model to realize the unconstrained human-like trajectory of the robotic joint. The simulation results show that the proposed algorithm can achieve human-like motion with a wide range (0~120°), the joint trajectories are insensitive to load variation (1 kg~5 kg), and it demonstrates good anti-disturbance performance in joint motion. The proposed approach is validated through physical experiments on an experimental platform of the robotic joint, and the design rules of the tuning parameters are discussed. Only two parameters are required to be tuned in the proposed algorithm. It is suitable for human-like motion control of the joints actuated by antagonistic PAMs, and can meet the requirements for the intrinsic safety, the motion compliance and the human-like motion patterns of collaborative robots.
 Ting C H, Yeo W H, King Y J, et al. Humanoid robot:A review of the architecture, applications and future trend[J]. Research Journal of Applied Sciences, Engineering and Technology, 2014, 7(7):1364-1369.
 Paik J K, Shin B H, Bang Y B, et al. Development of an anthropomorphic robotic arm and hand for interactive humanoids[J]. Journal of Bionic Engineering, 2012, 9(2):133-142.
 Andrikopoulos G, Nikolakopoulos G. Design, development and control of a human-inspired two-arm robot via pneumatic artificial muscles[C]//25th Mediterranean Conference on Control and Automation. Piscataway, USA:IEEE, 2017:241-246.
 Shin S Y, Kim C H. Human-like motion generation and control for humanoid's dual arm object manipulation[J]. IEEE Transactions on Industrial Electronics, 2015, 62(4):2265-2276.
 Zanchettin A M, Bascetta L, Rocco P. Achieving humanlike motion:Resolving redundancy for anthropomorphic industrial manipulators[J]. IEEE Robotics and Automation Magazine, 2013, 20(4):131-138.
 Kröger T. On-line trajectory generation in robotic systems[M]. Berlin, Germany:Springer, 2010.
 Yang N F, Zhang M, Huang C H, et al. Synergic analysis of upper limb target-reaching movements[J]. Journal of Biomechanics, 2002, 35(6):739-746.
 Flash T, Meirovitch Y, Barliya A. Models of human movement:Trajectory planning and inverse kinematics studies[J]. Robotics and Autonomous Systems, 2013, 61(4):330-339.
 Harris C M, Wolpert D M. Signal-dependent noise determines motor planning[J]. Nature, 1998, 394(6695):780-784.
 Yazdani M, Gamble G, Henderson G, et al. A simple control policy for achieving minimum jerk trajectories[J]. Neural Networks, 2012, 27:74-80.
 Ghazaei Ardakani M M, Robertsson A, Johansson R. Online minimum-jerk trajectory generation[C/OL]//IMA Conference on Mathematics of Robotics. (2015-01-01)[2018-11-20]. http://lup.lub.lu.se/search/ws/files/6156002/8053865.pdf.
 张道辉,赵新刚,韩建达,等.气动人工肌肉拮抗关节的力与刚度独立控制[J].机器人,2018,40(5):587-596.. Zhang D H, Zhao X G, Han J D, et al. Independent force and stiffness control for antagonistic joint driven by pneumatic artificial muscles[J]. Robot, 2018, 40(5):587-596.
 Andrikopoulos G, Nikolakopoulos G, Manesis S. Advanced nonlinear PID-based antagonistic control for pneumatic muscle actuators[J]. IEEE Transactions on Industrial Electronics, 2014, 61(12):6926-6937.
 于海涛,郭伟,谭宏伟,等.基于气动肌腱驱动的拮抗式仿生关节设计与控制[J].机械工程学报,2012,48(17):1-9. Yu H T, Guo W, Tan H W, et al. Design and control on antagonistic bionic joint driven by pneumatic muscles actuators[J]. Journal of Mechanical Engineering, 2012, 48(17):1-9.
 Chang M K, Liou J J, Chen M L. T-S fuzzy model-based tracking control of a one-dimensional manipulator actuated by pneumatic artificial muscles[J]. Control Engineering Practice, 2011, 19(12):1442-1449.
 Chandrapal M, Chen X Q, Wang W H, et al. Nonparametric control algorithms for a pneumatic artificial muscle[J]. Expert Systems with Applications, 2012, 39(10):8636-8644.
 朱坚民,黄春燕,雷静桃,等.气动肌腱驱动的拮抗式仿生关节位置/刚度控制[J].机械工程学报,2017,53(13):64-74. Zhu J M, Huang C Y, Lei J T, et al. Position/stiffness control of antagonistic bionic joint driven by pneumatic muscles actuators[J]. Journal of Mechanical Engineering, 2017, 53(13):64-74.
 Yang H J, Yu Y, Zhang J H. Angle tracking of a pneumatic muscle actuator mechanism under varying load conditions[J]. Control Engineering Practice, 2017, 61:1-10.
 Martens M, Boblan I. Modeling the static force of a Festo pneumatic muscle actuator:A new approach and a comparison to existing models[J]. Actuators, 2017, 6(4). DOI:10.3390/act 6040033.
 Kulic D, Venture G, Yamane K, et al. Anthropomorphic movement analysis and synthesis:A survey of methods and applications[J]. IEEE Transactions on Robotics, 2016, 32(4):776-795.
 Fligge N, McIntyre J, van der Smagt P. Minimum jerk for human catching movements in 3D[C]//IEEE RAS & EMBS International Conference on Biomedical Robotics and Biomechatronics. Piscataway, USA:IEEE, 2012:581-586.
 Kashima T, Hori K. Control of biomimetic robots based on analysis of human arm trajectories in 3D movements[J]. Artificial Life and Robotics, 2016, 21(1):24-30.
 Xie S. Advanced robotics for medical rehabilitation[M]. Cham, Switzerland:Springer, 2016.
 Li J, Qi X H, Wang H, et al. Active disturbance rejection control:Theoretical results summary and future researches[J]. Control Theory and Applications, 2017, 34(3):281-295.
 Gao Z Q. Scaling and bandwidth-parameterization based controller tuning[C]//American Control Conference. Piscataway, USA:IEEE, 2003:4989-4996.
 Kozlov A I, Muromtsev D Y. Full analysis of the triple integrator problem[J]. Automation and Remote Control, 2005, 66(1):1-9.
 Kyriakopoulos K J, Saridis G N. Minimum jerk path generation[C]//IEEE International Conference on Robotics and Automation. Piscataway, USA:IEEE, 1988:364-369.
 Naidu D S. Optimal control systems[M]. Boca Raton, USA:CRC Press, 2002.