Abstract
Most legged animals use their flexible body and supporting muscles to produce power for their locomotion, resulting in superior mobility and fast motions. In reality, an animal body consists of multiple bones and joints as well as legs having two or three segments with mass and inertia. In this paper, we study the bounding locomotion of a quadruped robot with a model closer to a real animal, i.e., a model that has one spinal joint, multiple two-segmented prismatic legs with masses and series elastic actuators, to obtain an insight into the robot’s dynamic behaviors. The models with passive mechanical properties are optimized with open-loop control to achieve the periodic bounding gait. The effects of spine flexibility in a segmented body are investigated on quadrupedal bounding gait by changing dynamic properties and hardware parameters. Comparisons of models reveal that body flexibility affects energy consumption and increases leg recirculation and stride length. The cost of transport of the articulated spine models is smaller than that of the rigid body one at low speed (\(< 0.45\sqrt{gl_0}\)) and bigger at high speed (\(>0.45\sqrt{gl_0}\)). The stride length increases 25%. Furthermore, the study on location of spinal joint reveals that the asymmetric segmented body possesses bigger spine oscillation; up to 370% higher actuator force/torque in the rear leg but 36.1% smaller in the front leg; shorter stride period; and smaller cost of transport which helps the robot to run more efficiently. The study also shows that the asymmetric mass distribution of the body caused the torque/force increase at the rear leg, especially at hip joint, and the decrease at the front leg.
Similar content being viewed by others
References
Raibert MH (1986) Legged robots that balance. MIT Press, Cambridge
Poulakakis I (2006) On the stability of the passive dynamics of quadrupedal running with a bounding gait. Int J Robot Res 25(7):669–687
Fukuoka Y, Kimura H, Cohen AH (2003) Adaptive running of a quadruped robot on irregular terrain based on biological concepts. Int J Robot Res 2(3):187–202
BostonDynamics, BigDog Overview (2010)
Boston Dynamics, Introducing Spot (2015). https://www.youtube.com/watch?v=M8YjvHYbZ9w
Lee YH, Lee YH, Lee H, Phan LT, Kang H et al (2017) Trajectory design and control of quadruped robot for trotting over obstacles. In: IEEE/RSJ international conference on intelligent robots and systems, pp 4897–4902
Boszczyk BM, Boszczyk AA, Putz R (2001) Comparative and functional anatomy of the mammalian lumbar spine. Anat Rec 264(2):157–168
Heglund NC, Taylor CR (1988) Speed, stride frequency and energy cost per stride: how do they change with body size and gait? J Exp Biol 138(1):301–318
Hildebrand M (1959) Motions of the running cheetah and horse. J Mammal 40(4):481–495
Schilling N, Hackert R (2006) Sagittal spine movements of small therian mammals during asymmetrical gaits. J Exp Biol 209(Pt 19):3925–3939
Alexander RM (1984) The gaits of bipedal and quadrupedal animals. Int J Robot Res 3(2):49–59
Leeser KF, Raibert M (1996) Locomotion experiments on a planar quadruped robot with articulated spine by locomotion experiments on a planar quadruped robot with. Master’s Thesis, Massachusetts Institute of Technology
Seok S, Wang A, Otten D, Lang J, Kim S (2013) Design principles for highly efficient quadrupeds and implementation on the MIT Cheetah robot. In: IEEE international conference on robotics and automation, pp 3307–3312
Boston Dynamics, Cheetah-Fastest Legged Robot (2012). http://www.bostondynamics.com/
Boston Dynamics, Introducing Wildcat (2013). https://youtu.be/wE3fmFTtP9g
Duperret JM, Pusey GDKJL, Koditschek DE (2014) Towards a comparative measure of legged agility. In: International symposium on experimental robotics
Nanua P (1992) Dynamics of a galloping quadruped. Ph.D. dissertation, Ohio State University
Culha U, Saranli U (2011) Quadrupedal bounding with an actuated spinal joint. In: IEEE international conference on robotics and automation, pp 1392–1397
Pouya S, Khodabakhsh M, Moeckel R, Ijspeert AJ (2012) Role of spine compliance and actuation in the bounding performance of quadruped robots. In: Proceedings of the dynamic walking conference
Cao Q, Poulakakis I (2013) Passive stability and control of quadrupedal bounding with a flexible torso. In: IEEE/RSJ international conference on intelligent robots and systems, pp 6037–6043
Deng Q, Wang S, Xu W, Mo J, Liang Q (2012) Quasi passive bounding of a quadruped model with articulated spine. Mech Mach Theory 52:232–242
Yamasaki R, Ambe Y, Aoi S, Matsuno F (2013) Quadrupedal bounding with spring-damper body joint. In: IEEE/RSJ international conference on intelligent robots and systems, pp 2345–2350
Cao Q, Poulakakis I (2015) On the energetics of quadrupedal running: predicting the metabolic cost of transport via a flexible-torso model. Bioinspiration Biomim 5:232–242
Rummel J, Seyfarth A (2008) Stable running with segmented legs. Int J Robot Res 27(8):919–934
Koutsoukis K, Papadopoulos E (2016) On passive quadrupedal bounding with translational spinal joint. In: IEEE/RSJ international conference on intelligent robots and systems, pp 3406–3411
Fisher C, Shield S, Patel A (2017) The effect of spine morphology on rapid acceleration in quadruped robots. In: IEEE/RSJ international conference on intelligent robots and systems, pp 2121–2127
Alexander RM, Jayes AS, Ker RF (1980) Estimates of energy cost for quadruped running gaits. J Zool Lond 190:155–192
Schmiedeler JP, Waldron KJ (1999) The mechanics of quadrupedal galloping and the future of legged vehicles. Int J Robot Res 18(12):1224–1234
Zou H, Schmiedeler JP (2006) The effect of asymmetrical body-mass distribution on the stability and dynamics of quadruped bounding. IEEE Trans Robot 22(4):711–723
Phan LT, Lee YH, Kim DY, Lee H, Choi HR (2016) Hybrid Quadruped Bounding with a passive compliant spine and asymmetric segmented body. In: IEEE/RSJ international conference on intelligent robots and systems, pp 3387–3392
Phan LT, Lee YH, Lee YH, Lee H, Choi HR (2017) Study on quadruped bounding with a passive compliant spine. In: IEEE/RSJ international conference on intelligent robots and systems, pp 3387–3392
Remy CD, Buffinton K, Siegwart R (2011) A MATLAB framework for efficient gait creation. In: IEEE/RSJ international conference on intelligent robots and systems, pp 190–196
Alexander RM (1990) Three uses for springs in legged locomotion. Int J Robot Res 9(2):53–61
Pratt Gill A, Williamson Matthew M (1995) Series elastic actuators. In: Proceedings 1995 IEEE/RSJ international workshop on intelligent robots and systems (IROS), pp 399–406
Brown TG (1911) Studies in the physiology of the nervous system. VIII. Neural balance and reflex reversal, with a note on progression in the decerebrate Guine-Pig. Exp Physiol 4:273–288
Cao Q, Poulakakis I (2014) On the energetics of quadrupedal bounding with and without torso compliance. In: IEEE international conference on intelligent robots and systems, Chicago, USA, pp 4901–4906
Mares MA (1999) Encyclopedia of deserts. University of Oklahoma Press, Norman, p 111
Hoyt DF, Taylor CR (1981) Gait and the energetics of locomotion in horses. Nature 292(5820):239–240
Xi W, Yesilevskiy Y, Remy CD (2015) Selecting gaits for economical locomotion of legged robots. Int J Robot Res 35(9):1140–1154
Acknowledgements
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No.2014R1A2A2A01005241).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Phan, L.T., Lee, Y.H., Lee, Y.H. et al. Study on effects of spinal joint for running quadruped robots. Intel Serv Robotics 13, 29–46 (2020). https://doi.org/10.1007/s11370-019-00297-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11370-019-00297-4