基于分层解耦的四轮足机器人模型预测控制

doi:10.12382/bgxb.2023.0984

摘要/Abstract

摘要：

轮足机器人是一种新型的复合机器人平台,其结合了足式机器人力伺服控制、浮动基座动力学与轮式机器人轮地接触的模型,具有轮式快速机动、足式越障机动以及轮步复合3种复合机动模式。为实现上述3种机动模式,提出了一种基于线性模型预测控制(Model Predictive Control, MPC)的轮足机器人控制方法,其采用分层控制的框架对轮子转速与四足力伺服稳定控制进行解耦,对轮子进行独立的转速控制与扭矩估计,并将轮地扭矩反馈转化为外力扰动,引入MPC控制模型中进行在线补偿;针对机体MPC稳定控制通过状态扩维的方式将控制模型转化为Ax+Bu的标准形式,通过采用重力加速度将足端力扰动进行等效转换,从而实现在不增加系统状态空间维度的同时将外力扰动引入动力学模型。通过仿真和在Panda-W轮足机器人上的实际测试,验证了所提算法可以有效补偿轮足加减速时轮地扰动力,实现机体稳定控制并进一步完成Trot轮步复合机动,在典型的平地和越野地形下有较好的控制效果。

关键词: 轮足机器人, 模型预测控制, 分层控制, 轮步复合机动

Abstract:

The wheeled-quadruped hybrid robot is an innovative composite robot platform that combines the features of legged and wheeled robots, enabling three modes of movement: fast wheel motion, legged obstacle-crossing, and wheel-leg combination. A control method for wheeled-quadruped robot based on linear model predictive control (MPC) is proposed to achieve the above three maneuvering modes. The MPC-based control method employs a hierarchical framework to separate the wheel speed control from the quadruped stability control. It independently controls the wheel speeds and estimates the torques while compensating for wheel-ground disturbances in real-time. For body stability control with MPC, the control model is converted into Ax+Bu standard form using state augmentation. Gravity acceleration is used to equivalently transform the end-effector force disturbances, allowing the external force disturbances to be integrated into the dynamic model without increasing the system’s state space dimension. In the simulation and practical test on Panda-W wheeled-quadruped robot, the proposed algorithm effectively mitigates the wheel-ground disturbances during wheel-leg acceleration and deceleration, achieving stable body control and successful Trot gait locomotion on various terrains.

Key words: wheeled-quadruped robot, model predictive control, hierarchical control, wheel-legged hybird locomotion

中图分类号:

TP242.6

邢伯阳, 许威, 李宇峰, 赵浩宇, 王康, 闫曈. 基于分层解耦的四轮足机器人模型预测控制[J]. 兵工学报, 2024, 45(12): 4272-4282.

XING Boyang, XU Wei, LI Yufeng, ZHAO Haoyu, WANG Kang, YAN Tong. Model Predictive Control for Wheeled L-quadruped Robots Based on Hierarchical Decoupling[J]. Acta Armamentarii, 2024, 45(12): 4272-4282.

图/表 16

图1 Panda-W轮足机器人

Fig.1 Panda-W wheeled-quadruped robot

图2 机器人控制系统框图

Fig.2 Block diagram of robot control system

图3 单轮控制模型

Fig.3 Single wheel control model

图4 轮足机器人受力分析图

Fig.4 Force analysis diagram of sagittal plane of wheeled-quadruped robot

图5 摆动腿落足点规划模型

Fig.5 Swing leg foothold planning model

图6 Panda-W仿真模型

Fig.6 Simulation model of Panda-W

表1 Panda-W轮足机器人参数

Table 1 Parameters of Panda-W wheeled-quadruped robot

参数	数值	参数	数值
m/kg	55	w_b/m	0.44
I_xx/(kg·m²)	0.163	h_b/m	0.49
I_yy/(kg·m²)	1.21	l₁/m	0.34
I_zz/(kg·m²)	1.36	l₂/m	0.338
l_b/m	0.66	R_wheel/m	0.187

表2 控制器参数

Table 2 Parameters of controller

参数	数值	参数	数值
R	1×10^-4	$Q w x, w y, w z$	[150,150,200]
Q_x_,_y_,_z	[200,200,1500]	K₁	3
Q_ψ_,_θ_,_φ	[50,50,50]	K₂	0.3
$Q x ·, y ·, z ·$	[500,500,500]

表2 控制器参数

Table 2 Parameters of controller

参数	数值	参数	数值
R	1×10^-4	$Q w x, w y, w z$	[150,150,200]
Q_x_,_y_,_z	[200,200,1500]	K₁	3
Q_ψ_,_θ_,_φ	[50,50,50]	K₂	0.3
$Q x ·, y ·, z ·$	[500,500,500]

图7 Webots仿真结果

Fig.7 Webots simulated results

图8 补偿轮毂电机牵引力前后控制效果对比

Fig.8 Comparison of control effects before and after compensating for wheel hub motor traction

图9 补偿轮毂电机牵引力后实验数据

Fig.9 Experimental data diagram after compensating for the traction force of hub motor

图10 足端力与电机仿真结果

Fig.10 Ground-reaction force and motor simulation data graph

图11 机器人质心状态仿真数据

Fig.11 Simulation data of robot centroid state

图12 对角小跑步态机动测试

Fig.12 Trotting gait experiment

图13 轮式机动实验

Fig.13 Wheel driving gait experiment

图14 轮步复合机动模式测试

Fig.14 Wheel-legged hybrid locomotion mode experiment

参考文献 20

[1]	CARLO J D, WENSING P M, KATZ B, et al. Dynamic locomotion in the MIT Cheetah 3 through convex model-predictive control[C]// Proceedings of the 31th International Conference on Intelligent Robots and Systems (IROS). Madrid, Spain:IEEE, 2018: 1-9.
[2]	KIM D, CARLO J D, KATZ B, et al. Highly dynamic quadruped locomotion via whole-body impulse control and model predictive control: arXiv:1909.06586[R/OL]. NY, US: Cornell University, 2019(2019-09-14)[2023-10-07]. https://arxiv.org/abs/1909.06586.
[3]	CHIGNOLI M, KIM S. Online trajectory optimization for dynamic aerial motions of a quadruped robot[C]// Proceedings of the 2021 IEEE International Conference on Robotics and Automation (ICRA). Xi’an, China: IEEE, 2021: 7693-7699.
[4]	NGUYEN C H, BAO L F, NGUYEN Q. Continuous jumping for legged robots on stepping stones via trajectory optimization and model predictive control[C]// Proceedings of the 2022 IEEE 61st Conference on Decision and Control (CDC). Cancun, Mexico: IEEE, 2022: 93-99.
[5]	BJELONIC M, SANKAR P K, BELLICOSO D, et al. Rolling in the deep-hybrid locomotion for wheeled-legged robots using online trajectory optimization[J]. IEEE Robotics and Automation Letters, 2020, 5(2): 3626-3633.
[6]	KLEMM V, MORRA A, GULICH L, et al. LQR-assisted whole-body control of a wheeled bipedal robot with kinematic loops[J]. IEEE Robotics and Automation Letters, 2020, 5(2): 3745-3752.
[7]	HOSSEINI M, RODRIGUEZ D A, BEHNKE S. State estimation for hybrid locomotion of Driving-Stepping quadrupeds[C]// Proceedings of the 2022 6th IEEE International Conference on Robotic Computing (IRC). Italy: IEEE, 2022: 103-110.
[8]	de VIRAGH Y, BJELONIC M, BELLICOSO C D, et al. Trajectory optimization for wheeled-legged quadrupedal robots using linearized ZMP constraints[J]. IEEE Robotics and Automation Letters, 2019, 4(2): 1633-1640.
[9]	ZHOU S Y, LIU S X, LIN Z X, et al. Cascade trajectory optimization with phase duration adaption and control for wheel-legged robots overcoming high obstacles[C]// Proceedings of the 2023 8th International Conference on Advanced Robotics and Mechatronics (ICARM). Sanya, China: IEEE, 2023: 832-839.
[10]	SEMINI C, BARASUOL V, CUNHA T B, et al. Towards versatile legged robots through active impedance control[J]. International Journal of Robotics Research, 2015, 34(7): 1003-1020.
[11]	ZHAO F Z, GAO J Y. Anti-slip gait planning for a humanoid robot in fast walking[J]. Applied Sciences, 2019, 9(13):2657.
[12]	CARON S, PHAM Q, NAKAMURA Y. ZMP support areas for multicontact mobility under frictional constraints[J]. IEEE Transactions on Robotics, 2017, 33(1): 67-80.
[13]	SUGIHARA T, YAMAMOTO T. Foot-guided agile control of a biped robot through ZMP manipulation[C]// Proceedings of the 2017 30th IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). Vancouver, BC, Canada: IEEE, 2017: 4546-4551.
[14]	HU J J, PRATT J E, CHEW C, et al. Virtual model control of a biped walking robot[D]. Cambridge, MA, US: Massachusetts Institute of Technology, 1995.
[15]	辛亚先. 基于分布式模型的双轮腿—臂机器人运动与作业协调控制研究[D]. 济南: 山东大学, 2021.
	XIN Y X. Research on motion and task coordination control ofbiped-armed robot based on distributed model[D]. Jinan: Shandong University, 2021. (in Chinese)
[16]	ZHANG G T, RONG X W, HUI C, et al. Torso motion control and toe trajectory generation of a trotting quadruped robot based on virtual model control[J]. Advanced Robotics, 2016, 30(4): 284-297.
[17]	de VIRAGH Y, BJELONIC M, BELLICOSO C D, et al. Trajectory optimization for wheeled legged quadrupedal robots using linearized ZMP constraints[J]. IEEE Robotics and Automation Letters, 2019, 4(2): 1633-1640.
[18]	BJELONIC M, GRANDIA R, HARLEY O, et al. Whole-body MPC and online gait sequence generation for wheeled-legged robots[C]// Proceedings of the 2021 34th IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). Prague, Czech Republic: IEEE, 2021: 8388-8395.
[19]	LI J, MA J B, NGUYEN, et al. Balancing control and pose optimization for wheel-legged robots navigating uneven terrains: arXiv:2109.09934v2[R/OL]. Ithaca, NY, US: Cornell University, 2021(2021-09-21)[2023-10-07]. https://arxiv.org/abs/2109.09934.
[20]	BJELONIC M, BELLICOSO D, VIRAGH Y D, et al. Keep Rollin’ whole-body motion control and planning for wheeled quadrupedal robots[J]. IEEE Robotics and Automation Letters, 2019, 4(2): 2116-2123.