严浙平, 杨皓宇, 张伟, 宫庆硕, 林凡太, 张雨. 基于模型预测-中枢模式发生器的六足机器人轨迹跟踪控制[J]. 机器人, 2023, 45(1): 58-69.DOI: 10.13973/j.cnki.robot.210325.
YAN Zheping, YANG Haoyu, ZHANG Wei, GONG Qingshuo, LIN Fantai, ZHANG Yu. Trajectory Tracking Control of Hexapod Robot Based on Model Prediction and Central Pattern Generator. ROBOT, 2023, 45(1): 58-69. DOI: 10.13973/j.cnki.robot.210325.
Abstract:In order to imitate animals in their excellent athletic ability and adaptability to environments, a trajectory tracking control method is proposed for the bionic hexapod robot. Firstly, the kinematics model of the robot is established, then the velocity and the angular velocity of the robot are combined with the CPG (central pattern generator) parameters by the steering parameter, and the transfer function is designed. Then the model predictive controller and the CPG network are combined through the transfer function, a CPG-based model predictive controller (MPC-CPG) is proposed, and its stability is proved. Finally, simulations and experiments are carried out for the robot to track the circular trajectory and the linear trajectory. Experiments show that under the condition of initial error, the robot can quickly eliminate the position error and the heading angle error by the MPC-CPG controller, and track the reference trajectory. The position error in trajectory tracking is always kept in -0.1~0.1 m, and the heading angle error is kept in -27°~20°. With the MPC-CPG controller, the robot not only has a high trajectory tracking accuracy, but also shows good motion smoothness and coordination, which further verifies the effectiveness of the proposed MPC-CPG controller.
[1] Sun T, Dai Z D, Manoonpong P. Distributed-force-feedbackbased reflex with online learning for adaptive quadruped motor control[J]. Neural Networks, 2021, 142:410-427. [2] Ijspeert A J. Biorobotics:Using robots to emulate and investigate agile locomotion[J]. Science, 2014, 346(6206):196-203. [3] Hutter M, Gehring C, Jud D, et al. ANYmal-A highly mobile and dynamic quadrupedal robot[C]//IEEE/RSJ International Conference on Intelligent Robots and Systems. Piscataway, USA:IEEE, 2016:38-44. [4] Bledt G, Powell M J, Katz B, et al. MIT Cheetah 3:Design and control of a robust, dynamic quadruped robot[C]//IEEE/RSJ International Conference on Intelligent Robots and Systems. Piscataway, USA:IEEE, 2018:2245-2252. [5] Semini C, Barasuol V, Goldsmith J, et al. Design of the hydraulically actuated, torque-controlled quadruped robot HyQ2Max[J]. IEEE/ASME Transactions on Mechatronics, 2017, 22(2):635-646. [6] Hutter M, Gehring C, Lauber A, et al. ANYmal-Toward legged robots for harsh environments[J]. Advanced Robotics, 2017, 31(16):918-931. [7] Kalakrishnan M, Buchli J, Pastor P, et al. Learning, planning, and control for quadruped locomotion over challenging terrain[J]. International Journal of Robotics Research, 2011, 30(2):236-258. [8] Fahmi S, Mastalli C, Focchi M, et al. Passive whole-body control for quadruped robots:Experimental validation over challenging terrain[J]. IEEE Robotics and Automation Letters, 2019, 4(3):2553-2560. [9] Delcomyn F. Neural basis of rhythmic behavior in animals[J]. Science, 1980, 210(4469):492-498. [10] Nicholls J G, Martin A R, Wallace B G, et al. From neuron to brain[M]. 4th ed. Sunderland, USA:Sinauer Associates, 2001. [11] Yu J Z, Tan M, Chen J, et al. A survey on CPG-inspired control models and system implementation[J]. IEEE Transactions on Neural Networks and Learning Systems, 2014, 25(3):441-456. [12] Zhao J X, Iwasaki T. CPG control for harmonic motion of assistive robot with human motor control identification[J]. IEEE Transactions on Control Systems Technology, 2020, 28(4):1323-1336. [13] Lu Q, Zhang Z C, Yue C. The programmable CPG model based on Matsuoka oscillator and its application to robot locomotion[J]. International Journal of Modeling, Simulation, and Scientific Computing, 2020, 11(3). DOI:10.1142/S179396232050018X. [14] Wang B R, Zhang K, Yang X F, et al. The gait planning of hexapod robot based on CPG with feedback[J]. International Journal of Advanced Robotic Systems, 2020, 17(3). DOI:10.1177/1729881420930503. [15] Liu C J, Xia L, Zhang C Z, et al. Multi-layered CPG for adaptive walking of quadruped robots[J]. Journal of Bionic Engineering, 2018, 15:341-355. [16] Sun T, Xiong X F, Dai Z D, et al. Small-sized reconfigurable quadruped robot with multiple sensory feedback for studying adaptive and versatile behaviors[J]. Frontiers in Neurorobotics, 2020. DOI:10.3389/fnbot.2020.00014. [17] Tutsoy O. CPG based RL algorithm learns to control of a humanoid robot leg[J]. International Journal of Robotics and Automation, 2015, 30(2):178-183. [18] Yang K. Dynamic model and CPG network generation of the underwater self-reconfigurable robot[J]. Advanced Robotics, 2016, 30(13):925-937. [19] Li J M, Wang J G, Yang S X, et al. Gait planning and stability control of a quadruped robot[J]. Computational Intelligence and Neuroscience, 2016. DOI:10.1155/2016/9853070. [20] Chung H Y, Hou C C, Hsu S Y. Hexapod moving in complex terrains via a new adaptive CPG gait design[J]. Industrial Robot, 2015, 42(2):129-141. [21] Chen G, Jin B, Chen Y. Accurate and robust body position trajectory tracking of six-legged walking robots with nonsingular terminal sliding mode control method[J]. Applied Mathematical Modelling, 2020, 77(2):1348-1372. [22] Yang J, Li S H, Su J Y, et al. Continuous nonsingular terminal sliding mode control for systems with mismatched disturbances[J]. Automatica, 2013, 49(7):2287-2291. [23] Feng Y, Yu X H, Man Z H. Non-singular terminal sliding mode control of rigid manipulators[J]. Automatica, 2002, 38(11):2159-2167. [24] Hu Z, Zhu D Q, Cui C C, et al. Trajectory tracking and replanning with model predictive control of autonomous underwater vehicles[J]. The Journal of Navigation, 2019, 72(2):321-341. [25] Zhou L, Wang G Q, Sun K K, et al. Trajectory tracking study of track vehicles based on model predictive control[J]. Journal of Mechanical Engineering, 2019, 65(6):329-342. [26] Mera M, Rios H, Martinez E A. A sliding-mode based controller for trajectory tracking of perturbed unicycle mobile robots[J]. Control Engineering Practice, 2020, 102. DOI:10.1016/j. conengprac.2020.104548. [27] Huang J, An H L, Yang Y, et al. Model predictive trajectory tracking control of electro-hydraulic actuator in legged robot with multi-scale online estimator[J]. IEEE Access, 2020, 8:95918-95933. [28] Liu X X, Wang W, Li X L, et al. MPC-based high-speed trajectory tracking for 4WIS robot[J]. ISA Transactions, 2021. DOI:10.1016/j.isatra.2021.05.018. [29] Bruggemann S, Possieri C. On the use of difference of log-sumexp neural networks to solve data-driven model predictive control tracking problems[J]. IEEE Control Systems Letters, 2021, 5(4):1267-1272. [30] He H W, Shi M, Li J W, et al. Design and experiential test of a model predictive path following control with adaptive preview for autonomous buses[J]. Mechanical Systems and Signal Processing, 2021, 157. DOI:10.1016/j.ymssp.2021.107701. [31] Gong P, Yan Z P, Zhang W, et al. Lyapunov-based model predictive control trajectory tracking for an autonomous underwater vehicle with external disturbances[J]. Ocean Engineering, 2021, 232. DOI:10.1016/j.oceaneng.2021.109010. [32] Tran V P, Santoso F, Garratt M A, et al. Fuzzy self-tuning of strictly negative-imaginary controllers for trajectory tracking of a quadcopter unmanned aerial vehicle[J]. IEEE Transactions on Industrial Electronics, 2021, 68(6):5036-5045. [33] Chu Z Z, Wang D, Meng F. An adaptive RBF-NMPC architecture for trajectory tracking control of underwater vehicles[J]. Machines, 2021, 9(5). DOI:10.3390/machines9050105. [34] 李升波,王建强,李克强.软约束线性模型预测控制系统的稳定性方法[J].清华大学学报(自然科学版), 2010, 50(11):1848-1852. Li S B, Wang J Q, Li K Q. Stabilization of linear predictive control systems with softening constraints[J]. Journal of Tsinghua University (Science and Technology), 2010, 50(11):1848-1852.