Novel Multi-gait Strategy for Stable and Efficient Quadruped Robot Locomotion

doi:10.16182/j.issn1004731x.joss.24-0917

Abstract

Abstract:

Inspired by the natural gait transition mechanism of quadruped animals, a multi-gait motion strategy is proposed to realize the stable and efficient motion of quadruped robots on different terrains in response to the trade-off between motion energy efficiency and motion stability. The gait is defined based on the duty cycle parameters and phase bias to form the switching basis. Secondly, the affine transformation of gait parameters and the finite state machine are introduced to establish the switching sequence, which realizes the timely gait switching. The speed-gait mapping is designed based on the cost of transport (CoT) and the stability index, which determines the suitable gait selection under different terrains. The gait selection strategy and transition mechanism are combined to realize the real-time selection and switching of the multi-terrain gait under different speeds. Both the simulated and experimental results show that the proposed multi-gait strategy can realize the efficient and stable motion of the quadruped robot under different terrains.

Key words: quadruped robot, motion strategy, cost of transport, gait selection, gait transition

CLC Number:

TP242

Zhang Daoxun, Chen Xieyuanli, Zhong Zhengyu, Xu Ming, Zheng Zhiqiang, Lu Huimin. Novel Multi-gait Strategy for Stable and Efficient Quadruped Robot Locomotion[J]. Journal of System Simulation, 2025, 37(1): 13-24.

Figures/Tables 17

Fig. 1

Fig. 2

Fig. 3

Table 1

Gaits transition event

States	Events
States	E₀	E₁	E₂	E₃	E₄
Walk	$a 00$	$a 01$	$a 01, a 12$	$a 01, a 12, a 23$	$a 01, a 14$
Trot	$a 10$	$a 11$	$a 12$	$a 12, a 23$	$a 14$
Bound	$a 21, a 10$	$a 21$	$a 22$	$a 23$	$a 21, a 14$
Bound-run	$a 32, a 21, a 10$	$a 32, a 21$	$a 32$	$a 33$	$a 32, a 21, a 14$
Trot-run	$a 41, a 10$	$a 41$	$a 41, a 12$	$a 41, a 12, a 23$	$a 44$

Table 1

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Table 2

All the parameters that are used in simulation tests

参数名	数值	参数名	数值
仿真步长dt/s	0.002	N	5
切换时间T_s/s	0.5	迈步周期 $t f$ /s	0.5
运动速度v/(m/s)	0.3~2.7	权衡参数c	0.1~0.9

Table 2

Fig. 8

Fig. 9

Fig. 10

Table 3

Fig. 11

Fig. 12

Fig. 13

Fig. 14

References 28

1	Sheng Jiapeng, Chen Yanyun, Fang Xing, et al. Bio-inspired Rhythmic Locomotion for Quadruped Robots[J]. IEEE Robotics and Automation Letters, 2022, 7(3): 6782-6789.
2	Bledt G, Powell M J, Katz B, et al. MIT Cheetah 3: Design and Control of a Robust, Dynamic Quadruped Robot[C]//2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). Piscataway: IEEE, 2018: 2245-2252.
3	Jin Yongbin, Liu Xianwei, Shao Yecheng, et al. High-speed Quadrupedal Locomotion by Imitation-relaxation Reinforcement Learning[J]. Nature Machine Intelligence, 2022, 4(12): 1198-1208.
4	Norby J, Johnson A M. Fast Global Motion Planning for Dynamic Legged Robots[C]//2020 IEEE/RSJ Interna-tional Conference on Intelligent Robots and Systems (IROS). Piscataway: IEEE, 2020: 3829-3836.
5	Miki Takahiro, Lee Joonho, Hwangbo Jemin, et al. Learning Robust Perceptive Locomotion for Quadrupedal Robots in the Wild[J]. Science Robotics, 2022, 7(62): eabk2822.
6	Urbain Gabriel, Barasuol Victor, Semini Claudio, et al. Stance Control Inspired by Cerebellum Stabilizes Reflex-based Locomotion on HyQ Robot[C]//2020 IEEE International Conference on Robotics and Automation (ICRA). Piscataway: IEEE, 2020: 6127-6133.
7	Umberger B R, Martin P E. Mechanical Power and Efficiency of Level Walking with Different Stride Rates[J]. Journal of Experimental Biology, 2007, 210(18): 3255-3265.
8	Muraro A, Chevallereau C, Aoustin Y. Optimal Trajectories for a Quadruped Robot with Trot, Amble and Curvet Gaits for Two Energetic Criteria[J]. Multibody System Dynamics, 2003, 9(1): 39-62.
9	Srinivasan M, Ruina A. Computer Optimization of a Minimal Biped Model Discovers Walking and Running[J]. Nature, 2006, 439(7072): 72-75.
10	di Prampero P E. The Energy Cost of Human Locomotion on Land and in Water[J]. International Journal of Sports Medicine, 1986, 7(2): 55-72.
11	Hoyt D F, Taylor C R. Gait and the Energetics of Locomotion in Horses[J]. Nature, 1981, 292(5820): 239-240.
12	Li Qi, Qian Letian, Wang Shuhan, et al. Towards Generation and Transition of Diverse Gaits for Quadrupedal Robots Based on Trajectory Optimization and Whole-body Impedance Control[J]. IEEE Robotics and Automation Letters, 2023, 8(4): 2389-2396.
13	Koo I M, Tran Duc Trong, Haeng Lee Yoon, et al. Biologically Inspired Gait Transition Control for a Quadruped Walking Robot[J]. Autonomous Robots, 2015, 39(2): 169-182.
14	Saraf Prathamesh, Sarkar Abhishek, Javed Arshad. Terrain Adaptive Gait Transitioning for a Quadruped Robot Using Model Predictive Control[C]//2021 26th International Conference on Automation and Computing (ICAC). Piscataway: IEEE, 2021: 1-6.
15	Shang Linlin, Li Zhaosheng, Wang Wei, et al. Smooth Gait Transition Based on CPG Network for A Quadruped Robot[C]//2019 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM). Piscataway: IEEE, 2019: 358-363.
16	Fukui Takahiro, Fujisawa Hisamu, Otaka Kotaro, et al. Autonomous Gait Transition and Galloping over Unperceived Obstacles of a Quadruped Robot with CPG Modulated by Vestibular Feedback[J]. Robotics and Autonomous Systems, 2019, 111: 1-19.
17	Santos Cristina P, Matos Vítor. Gait Transition and Modulation in a Quadruped Robot: A Brainstem-like Modulation Approach[J]. Robotics and Autonomous Systems, 2011, 59(9): 620-634.
18	Dai Owaki, Ishiguro Akio. A Quadruped Robot Exhibiting Spontaneous Gait Transitions from Walking to Trotting to Galloping[J]. Scientific Reports, 2017, 7(1): 277.
19	陈久朋, 陈治帆, 伞红军, 等. 中枢模式发生器与足端轨迹的非线性映射[J]. 仪器仪表学报, 2024, 45(4): 258-271.
	Chen Jiupeng, Chen Zhifan, Hongjun San, et al. Nonlinear Mapping Between Central Pattern Generator and Foot Trajectory[J]. Chinese Journal of Scientific Instrument, 2024, 45(4): 258-271.
20	陈久朋, 李春磊, 伞红军, 等. 基于模型的四足机器人步态转换控制研究[J]. 农业机械学报, 2024, 55(3): 431-440, 451.
	Chen Jiupeng, Li Chunlei, Hongjun San, et al. Model Based Gait Transition Control for Quadruped Robots[J]. Transactions of the Chinese Society for Agricultural Machinery, 2024, 55(3): 431-440, 451.
21	张秀丽, 王琪, 黄森威, 等. 一种多模型融合的仿猎豹四足机器人复杂运动控制方法[J]. 机器人, 2022, 44(6): 682-693, 707.
	Zhang Xiuli, Wang Qi, Huang Senwei, et al. A Multi-model Fusion Based Complex Motion Control Approach for a Cheetah-mimicking Quadruped Robot[J]. Robot, 2022, 44(6): 682-693, 707.
22	Wang Jiayi, Chatzinikolaidis I, Mastalli C, et al. Automatic Gait Pattern Selection for Legged Robots[C]//2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). [S.l.]: IEEE, 2020: 3990-3997.
23	王琪, 张秀丽, 江磊, 等. 具有2DOF铰接式躯干的仿猎豹四足奔跑机器人[J]. 机器人, 2022, 44(3): 257-266.
	Wang Qi, Zhang Xiuli, Jiang Lei, et al. A Cheetah-mimicking Quadruped Running Robot with 2DOF Articulated Trunk[J]. Robot, 2022, 44(3): 257-266.
24	钱伟, 王志瑞, 苏波, 等. 变刚度四足机器人的连续型仿生脊柱设计[J]. 中南大学学报(自然科学版), 2023, 54(8): 3112-3121.
	Qian Wei, Wang Zhirui, Su Bo, et al. Mechanical Design of a Variable Stiffness Continuous Bionic Spine for a Quadruped Robot[J]. Journal of Central South University(Science and Technology), 2023, 54(8): 3112-3121.
25	Xi Weitao, Yesilevskiy Y, Remy C D. Selecting Gaits for Economical Locomotion of Legged Robots[J]. The International Journal of Robotics Research, 2016, 35(9): 1140-1154.
26	Smit-Anseeuw N, Gleason R, Vasudevan R, et al. The Energetic Benefit of Robotic Gait Selection——A Case Study on the Robot RAMone[J]. IEEE Robotics and Automation Letters, 2017, 2(2): 1124-1131.
27	Griffin T M, Kram R, Wickler S J, et al. Biomechanical and Energetic Determinants of the Walk-trot Transition in Horses[J]. Journal of Experimental Biology, 2004, 207(24): 4215-4223.
28	Norby J, Yang Y, Tajbakhsh A, et al. Quad-SDK: Full Stack Software Framework for Agile Quadrupedal Locomotion[C]//ICRA Workshop on Legged Robots. [S.l. : s.n.], 2022.

运动策略	CoT	STB	成功率
固定步态Trot	0.383	0.145	29/30
固定步态Trot-run	0.532	0.512	23/30
文献[22]策略	0.331	0.320	29/30
策略c1	0.299	0.355	29/30
策略c3	0.316	0.283	29/30
策略c5	0.330	0.118	30/30
策略c7	0.340	0.117	30/30
策略c9	0.344	0.109	30/30

[1]	Chikun Gong, Xunwei Wu, Lipeng Yuan. Control of Quadruped Robot Based on Impedance and Virtual Model [J]. Journal of System Simulation, 2022, 34(10): 2152-2161.
[2]	Xu Haidong, Gan Su, Ren Jie, Wang Binrui, Jin Yinglian. Gait CPG Adjustment for a Quadruped Robot Based on Hopf Oscillator [J]. Journal of System Simulation, 2017, 29(12): 3092-3099.
[3]	Hu Nan, Li Shaoyuan, Huang Dan, Gao Feng. Gait Planning and Control of Quadruped Robot with High Payload [J]. Journal of System Simulation, 2015, 27(3): 529-533.