Untethered quadrupedal hopping and bounding on a trampoline

doi:10.1007/s11465-019-0559-5

Frontiers of Mechanical Engineering

2020, Vol. 15

Issue (2): 181-192 https://doi.org/10.1007/s11465-019-0559-5

本期目录

Untethered quadrupedal hopping and bounding on a trampoline

Boxing WANG¹, Chunlin ZHOU¹(

), Ziheng DUAN¹, Qichao ZHU¹, Jun WU^1,², Rong XIONG¹

¹. State Key Laboratory of Industrial Control Technology, College of Control Science and Engineering, Zhejiang University, Hangzhou 310027, China
². Binhai Industrial Technology Research Institute of Zhejiang University, Tianjin 300301, China

全文: PDF(1621 KB) HTML

Abstract：

For quadruped robots with springy legs, a successful jump usually requires both suitable elastic parts and well-designed control algorithms. However, these two problems are mutually restricted and hard to solve at the same time. In this study, we attempt to solve the problem of controller design with the help of a robot without any elastic mounted parts, in which the untethered robot is made to jump on a trampoline. The differences between jumping on hard surfaces with springy legs and jumping on springy surfaces with rigid legs are briefly discussed. An intuitive control law is proposed to balance foot contact forces; in this manner, excessive pitch oscillation during hopping or bounding can be avoided. Hopping height is controlled by tuning the time delay of the leg stretch. Together with other motion generators based on kinematic law, the robot can perform translational and rotational movements while hopping or bounding on the trampoline. Experiments are conducted to validate the effectiveness of the proposed control framework.

Key words： hopping and bounding gait compliant mechanism compliant contact balance control strategy legged locomotion control quadruped robot

收稿日期: 2019-04-28 出版日期: 2020-05-25

Corresponding Author(s): Chunlin ZHOU

引用本文:

. [J]. Frontiers of Mechanical Engineering, 2020, 15(2): 181-192.
Boxing WANG, Chunlin ZHOU, Ziheng DUAN, Qichao ZHU, Jun WU, Rong XIONG. Untethered quadrupedal hopping and bounding on a trampoline. Front. Mech. Eng., 2020, 15(2): 181-192.

链接本文:

https://academic.hep.com.cn/fme/CN/10.1007/s11465-019-0559-5
https://academic.hep.com.cn/fme/CN/Y2020/V15/I2/181

Fig.1

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

$T$ /s	$φ co$	$φ st$	$φ off$	$l A$ /mm	$k p y$ /(mm?(° )^–1)	$k yaw$
2	$0.08 π$	$0.035 π$	$0.025 π$	30	5	0.08

Tab.1

Fig.10

Fig.11

Fig.12

$T$ /s	$φ co$	$φ st$	$l A$ /mm	$k b y$ /(m?s^–1?(° )^–1?s)	$k b x$ /(m?s^–1?(° )^–1?s)	$θ ˙ l$ /((° )?s^–1)	$θ ˙ u$ /((° )?s^–1)	$k yaw$
2	$0.08 π$	$0.035 π$	30	0.04	0.04	-30	-10	0.08

Tab.2

Fig.13

Fig.14

Fig.15

1	H W Park, P M Wensing, S Kim. High-speed bounding with the MIT Cheetah 2: Control design and experiments. International Journal of Robotics Research, 2017, 36(2): 167–192 https://doi.org/10.1177/0278364917694244
2	H W Park, S Park, S Kim. Variable-speed quadrupedal bounding using impulse planning: Untethered high-speed 3D running of MIT Cheetah 2. In: Proceedings of 2015 IEEE International Conference on Robotics and Automation (ICRA). Seattle: IEEE, 2015, 5163–5170 https://doi.org/10.1109/ICRA.2015.7139918
3	H W Park, P M Wensing, S Kim. Online planning for autonomous running jumps over obstacles in high-speed quadrupeds. In: Proceedings of Robotics: Science and System Conference. Rome, 2015
4	C Gehring, S Coros, M Hutter, et al. Towards automatic discovery of agile gaits for quadrupedal robots. In: Proceedings of 2014 IEEE International Conference on Robotics and Automation (ICRA). Hong Kong: IEEE, 2014, 4243–4248 https://doi.org/10.1109/ICRA.2014.6907476
5	M Hutter, C Gehring, A Lauber, et al. ANYmal-toward legged robots for harsh environments. Advanced Robotics, 2017, 31(17): 918–931 https://doi.org/10.1080/01691864.2017.1378591
6	R Blickhan. The spring-mass model for running and hopping. Journal of Biomechanics, 1989, 22(11–12): 1217–1227 https://doi.org/10.1016/0021-9290(89)90224-8
7	M D Berkemeier. Modeling the dynamics of quadrupedal running. International Journal of Robotics Research, 1998, 17(9): 971–985 https://doi.org/10.1177/027836499801700905
8	M Ahmadi, H Michalska, M Buehler. Control and stability analysis of limit cycles in a hopping robot. IEEE Transactions on Robotics, 2007, 23(3): 553–563 https://doi.org/10.1109/TRO.2007.898956
9	M Zabihi, A Alasty. Modeling and fuzzy control of one-legged somersaulting robot. In: Proceedings of 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). Madrid: IEEE, 2018, 2701–2706 https://doi.org/10.1109/IROS.2018.8593897
10	M F Hale, J L Du Bois, P Iravani. Agile and adaptive hopping height control for a pneumatic robot. In: Proceedings of 2018 IEEE International Conference on Robotics and Automation (ICRA). Brisbane: IEEE, 2018, 1–6 https://doi.org/10.1109/ICRA.2018.8460557
11	Q Liu, X Chen, B Han, et al. Virtual constraint based control of bounding gait of quadruped robots. Journal of Bionics Engineering, 2017, 14(2): 218–231 https://doi.org/10.1016/S1672-6529(16)60393-1
12	M Khoramshahi, R Nasiri, M Shushtari, et al. Adaptive natural oscillator to exploit natural dynamics for energy efficiency. Robotics and Autonomous Systems, 2017, 97: 51–60 https://doi.org/10.1016/j.robot.2017.07.017
13	R Nasiri, M Khoramshahi, M N Ahmadabadi. Design of a nonlinear adaptive natural oscillator: Towards natural dynamics exploitation in cyclic tasks. In: Proceedings of 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). Daejeon: IEEE, 2016, 3653–3658 https://doi.org/10.1109/IROS.2016.7759538
14	J Buchli, F Iida, A J Ijspeert. Finding resonance: Adaptive frequency oscillators for dynamic legged locomotion. In: Proceedings of 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). Beijing: IEEE, 2006, 3903–3909 https://doi.org/10.1109/IROS.2006.281802
15	J Buchli, A J Ijspeert. Self-organized adaptive legged locomotion in a compliant quadruped robot. Autonomous Robots, 2008, 25(4): 331–347 https://doi.org/10.1007/s10514-008-9099-2
16	G A Pratt, M M Williamson. Series elastic actuators. In: Proceedings of 1995 IEEE/RSJ International Conference on Intelligent Robots and Systems. Human Robot Interaction and Cooperative Robots. Pittsburgh: IEEE, 1995, 399–406 https://doi.org/10.1109/IROS.1995.525827
17	J E Pratt, B T Krupp. Series elastic actuators for legged robots. Unmanned Ground Vehicle Technology VI, 2004, 5422: 135–145 https://doi.org/10.1117/12.548000
18	A G L Junior, R M de Andrade, A Bento Filho. Series elastic actuator: Design, analysis and comparison. In: Wang G, ed. Recent Advances in Robotic Systems. London: IntechOpen, 2016, 203–234 https://doi.org/10.5772/63573
19	A Spröwitz, A Tuleu, M Vespignani, et al. Towards dynamic trot gait locomotion: Design, control, and experiments with Cheetah-cub, a compliant quadruped robot. International Journal of Robotics Research, 2013, 32(8): 932–950 https://doi.org/10.1177/0278364913489205
20	M Azad, M N Mistry. Balance control strategy for legged robots with compliant contacts. In: Proceedings of 2015 IEEE International Conference on Robotics and Automation (ICRA). Seattle: IEEE, 2015: 4391–4396 https://doi.org/10.1109/ICRA.2015.7139806
21	C Canudas, L Roussel, A Goswami. Periodic stabilization of a 1-DOF hopping robot on nonlinear compliant surface. IFAC Proceedings Volumes, 1997, 30(20): 385–390 https://doi.org/10.1016/S1474-6670(17)44293-5
22	K N Murphy, M H Raibert. Trotting and bounding in a planar two-legged mode. In: Morecki A, Bianchi G, Kȩdzior K, eds. Theory and Practice of Robots and Manipulators. Boston: Springer, 1985, 411–420 https://doi.org/10.1007/978-1-4615-9882-4_43
23	M H Raibert. Trotting, pacing and bounding by a quadruped robot. Journal of Biomechanics, 1990, 23: 79–98 https://doi.org/10.1016/0021-9290(90)90043-3
24	I Poulakakis, E Papadopoulos, M Buehler. On the stability of the passive dynamics of quadrupedal running with a bounding gait. International Journal of Robotics Research, 2006, 25(7): 669–687 https://doi.org/10.1177/0278364906066768
25	C Zhou, B Wang, Q Zhu, et al. An online gait generator for quadruped walking using motor primitives. International Journal of Advanced Robotic Systems, 2016, 13(6): 1729881416657960 https://doi.org/10.1177/1729881416657960
26	B Wang, Z Wan, C Zhou, et al. A multi-module controller for walking quadruped robots. Journal of Bionics Engineering, 2019, 16(2): 253–263 https://doi.org/10.1007/s42235-019-0021-8
27	A J Ijspeert, J Nakanishi, H Hoffmann, et al. Dynamical movement primitives: Learning attractor models for motor behaviors. Neural Computation, 2013, 25(2): 328–373 https://doi.org/10.1162/NECO_a_00393
28	M Ajallooeian, J van den Kieboom, A Mukovskiy, et al. A general family of morphed nonlinear phase oscillators with arbitrary limit cycle shape. Physica D: Nonlinear Phenomena, 2013, 263: 41–56 https://doi.org/10.1016/j.physd.2013.07.016

[1]

FME-19023-OF-WB_suppl_1

Video

Viewed

Full text

Abstract

Cited

Shared

Discussed