ATRIAS is a human-scale 3D-capable bipedal robot designed to mechanically embody the spring-mass model for dynamic walking and running. To help bring the extensive work on this theoretical model further into practice, we present the design and validation of a spring-mass robot that can operate in real-world settings (i.e. off-tether and without planarizing restraints). We outline the mechanisms and design choices necessary to meet these specifications, particularly ATRIAS’ four-bar series-elastic leg design. We experimentally demonstrate the following robot capabilities, which are characteristics of the target model. 1) We present the robot’s physical capability for both grounded and aerial gaits, including planar walking and sustained hopping, while being more efficient than similarly gait-versatile bipeds. 2) The robot can be controlled by enforcing quantities derived from the simpler spring-mass model, such as leg angles and leg forces. 3) ATRIAS replicates the center-of-mass dynamics of human hopping and (novelly) walking, a key spring-mass model feature. Lastly, we present dynamically stable stepping in 3D without external support, demonstrating that this theoretical model has practical potential for real-world locomotion.
AbateAHattonRLHurstJW (2015) Passive-dynamic leg design for agile robots. In: 2015 IEEE international conference on robotics and automation (ICRA), Seattle, WA, 26–30 May 2015, pp.4519–4524. IEEE.
2.
AhmadiMBuehlerM (1999) The ARL monopod II running robot: Control and energetics. In: IEEE international conference on robotics and automation (ICRA), Detroit, MI, 10–15 May 1999, pp.1689–1694. IEEE.
AmesAD (2014) Human-inspired control of bipedal walking robots. Automatic Control, IEEE Transactions on59(5): 1115–1130.
5.
AndradaENyakaturaJMüllerR. (2012) Grounded running: An overlooked strategy for robots. In: Autonomous Mobile Systems, Springer, Heidelberg, 2012, pp. 79–87.
6.
AndrewsB. (2011) Running over unknown rough terrain with a one-legged planar robot. Bioinspiration & Biomimetics6(2): 026009.
7.
BhounsulePACortellJGrewal. (2014) Low-bandwidth reflex-based control for lower power walking: 65 km on a single battery charge. The International Journal of Robotics Research33(10): 1305–1321.
8.
Birn-JefferyAHubickiCMBlumY. (2014) Don’t break a leg: Running birds from quail to ostrich prioritise leg safety and economy on uneven terrain. Journal of Experimental Biology217(21): 3786–3796.
9.
BlickhanR (1989) The spring mass model for running and hopping. Journal of Biomechanics22(11–12): 1217–1227.
10.
BlickhanRFullRJ (1993) Similarity in multilegged locomotion: Bouncing like a monopode. Journal of Comparative Physiology173(5): 509–517.
11.
BlumYLipfertSWRummelJ. (2010) Swing leg control in human running. Bioinspiration & Biomimetics5(2): 026006.
12.
BoaventuraTSeminiSBuchiJ. (2012) Dynamic torque control of a hydraulic quadruped robot. In: 2012 IEEE international conference on robotics and automation (ICRA), Saint Paul, MN, 14–18 May 2012, pp.1889–1894. IEEE.
13.
BussBGHamedKAGriffinBA. (2016) Experimental results for 3D bipedal robot walking based on systematic optimization of virtual constraints. American control conference In review.
14.
BylKBylMRutschmannM. (2012) Series-elastic actuation prototype for rough terrain hopping. In: 2012 IEEE international conference on technologies for practical robot applications (TePRA). Woburn, MA, 23–24 April 2012, pp. 103–110. IEEE.
15.
ChangYHRoizRAAuyangAG (2008) Intralimb compensation strategy depends on the nature of joint perturbation in human hopping. Journal of Biomechanics41(9): 1832–9.
16.
ChoBkParkSsOhJh (2010) Stabilization of a hopping humanoid robot for a push. In: 2010 10th IEEE-RAS international conference on humanoid robots, Nashville, TN, 6–8 December 2010, pp.60–65. IEEE.
17.
ColettJSHurstJW (2011) Artificial restraint systems for walking and running robots: An overview. International Journal of Humanoid Robotics9(1): 1250001.
18.
CollinsSH. (2005) Efficient bipedal robots based on passive-dynamic walkers. Science307(5712): 1082–1085.
19.
DaleyMABiewenerAA (2006) Running over rough terrain reveals limb control for intrinsic stability. Proceedings of the National Academy of Sciences103(42): 15681–15686.
20.
DalleauGBelliABourdinM. (1998) The spring-mass model and the energy cost of treadmill running. European Journal of Applied Physiology and Occupational physiology77(3): 257–63.
21.
ErezTLowreyKTassaY. (2013) An integrated system for real-time model predictive control of humanoid robots. In: IEEE/RAS international conference on humanoid robots, Atlanta, GA, 15–17 October 2013, pp.292–299. IEEE.
22.
ErnstMGeyerHBlickhanR (2012) Extension and customization of self-stability control in compliant legged systems. Bioinspiration & Biomimetics7(4): 046002.
23.
FarleyCTGlasheenJMcMahonTA (1993) Running springs: Speed and animal size. Journal of Experimental Biology185(1): 71–86.
24.
FerrisDPLouieMFarleyCT (1998) Running in the real world: Adjusting leg stiffness for different surfaces. Proceedings of the Royal Society of London B: Biological Sciences265(1400): 989–993.
25.
FullRJKoditschekDE (1999) Templates and anchors: Neuromechanical hypotheses of legged locomotion on land. Journal of Experimental Biology202(23): 3325–3332.
26.
FullRJKubowTSchmittJ. (2002) Quantifying dynamic stability and maneuverability in legged locomotion. Integrative and Comparative Biology42(1): 149–157.
27.
GeyerHSeyfarthABlickhanR (2005) Spring-mass running: Simple approximate solution and application to gait stability. Journal of Theoretical Biology232(3): 315–328.
28.
GeyerHSeyfarthABlickhanR (2006) Compliant leg behaviour explains basic dynamics of walking and running. Proceedings of the Royal Society of London B: Biological Sciences273(1603): 2861–2867.
29.
GhigliazzaRMAltendorferRHolmesP. (2003) A simply stabilized running model. SIAM Journal of Applied Dynamical Systems2(2): 187–218.
30.
GrimesJAHurstJW (2012) The design of ATRIAS 1.0: a unique monopod, hopping robot. In: Proceedings of the 15th International Conference on Climbing and Walking Robots and the Support Technologies for Mobile Machines (CLAWAR), Baltimore, MD, 23–26 July 2012, pp.548–554. World Scientific Publishing.
31.
GrizzleJWHurstJMorrisB. (2009) Mabel, a new robotic bipedal walker and runner. In: American control conference, St. Louis, Missouri, 10–12 June 2009, pp.2030–2036. IEEE.
32.
HamedKAGrizzleJW (2014) Event-based stabilization of periodic orbits for underactuated 3D bipedal robots with left-right symmetry. IEEE Transactions on Robotics30(2): 365–381.
33.
HereidAKolathayaSJonesMS. (2014) Dynamic multi-domain bipedal walking with ATRIAS through SLIP based human-inspired control. In: Proceedings of the 17th international conference on hybrid systems: Computation and control, Zurich, Switzerland, 15–17 April 2014, pp.263–272. New York, NY: ACM.
34.
HiroseMOgawaK (2007) Honda humanoid robots development. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences365(1850): 11–19.
35.
HobbelenDde BoerTWisseM (2008) System overview of bipedal robots Flame and TUlip: Tailor-made for limit cycle walking. In: 2008 IEEE/RSJ international conference on intelligent robots and systems (IROS), Nice, France, 22–26 September 2008, pp.2486–2491. IEEE.
36.
HoganN (1985) Impedance control: An approach to manipulation: Part III – Applications. Journal of dynamic systems, measurement, and control107(2): 17–24.
37.
HubickiCMHurstJW (2012) Running on soft ground: Simple, energy-optimal disturbance rejection. In: Proceedings of the 15th international conference on climbing and walking robots (CLAWAR), Baltimore, MD, 23–26 July 2012, pp.543–548. World Scientific Publishing.
38.
HyonSHEmuraT (2005) Symmetric walking control: Invariance and global stability. In: IEEE/RSJ international conference on robotics and automation (ICRA), Barcelona, Spain, 18–22 April 2005, pp.1443–1450. IEEE.
39.
HyonSHMitaT (2002) Development of a biologically inspired hopping robot –“Kenken”. In: Proceedings of the 2002 IEEE international converence on robotics and automation (ICRA), Washington DC, 11–15 May 2002, vol. 4, pp. 3984–3991. IEEE.
40.
KanekoKKanehiroFMorisawaM. (2011) Humanoid robot HRP-4-humanoid robotics platform with lightweight and slim body. In: 2011 IEEE/RSJ international conference on intelligent robots and systems (IROS), San Francisco, CA, 25–30 September 2011, pp. 4400–4407. IEEE.
41.
KemperKKoeplDHurstJW (2010) Optimal passive dynamics for torque/force control. In: International conference on robotics and automation (ICRA), pp.2149–2154.
42.
KoeplDHurstJW (2013) Impulse control for planar spring-mass running. Journal of Intelligent & Robotic Systems2: 1–15.
43.
LeeDVIsaacsMRHigginsTE. (2014) Scaling of the spring in the leg during bouncing gaits of mammals. Integrative and Comparative Biology54(6): 1099–1108.
44.
LipfertSWGüntherMRenjewskiD. (2012) A model-experiment comparison of system dynamics for human walking and running. Journal of Theoretical Biology292: 11–17.
45.
McGeerT (1990) Passive dynamic walking. International Journal of Robotics Research9(2): 62–82.
46.
ManchesterIRMettinUIidaF. (2011) Stable dynamic walking over uneven terrain. The International Journal of Robotics Research30(3): 265–279.
47.
MartinWCWuAGeyerH (2015) Robust spring mass model running for a physical bipedal robot. In: International conference on robotics and automation (ICRA), Seattle, WA, 26–30 May 2015, pp. 6307–6312. IEEE.
48.
MausHMSeyfarthA (2014) Walking in circles: A modelling approach. Journal of The Royal Society Interface11(99): 20140594.
49.
MausHM. (2010) Upright human gait did not provide a major mechanical challenge for our ancestors. Nature Communications1(6): 70.
50.
ParkIWKimJYLeeJ. (2007) Mechanical design of the humanoid robot platform, HUBO. Advanced Robotics21(11): 1305–1322.
51.
PeekemaARenjewskiDHurstJW (2013) Open-source real-time robot operation and control system for highly dynamic, modular machines. In: ASME International Design Engineering Technical (IDET), Portland, OR, 4–7 August 2013, pp.V07AT10A063. New York, NY: ASME.
52.
PeukerFMaufroyCSeyfarthA (2012) Leg-adjustment strategies for stable running in three dimensions. Bioinspiration & Biomimetics7(3): 036002.
53.
PiovanGBylK (2013) Two-element control for the active SLIP model. In: 2013 IEEE international conference on robotics and automation (ICRA), Karlsruhe, Germany, 6–10 May 2013, pp.5656–5662. IEEE.
54.
PoulakakisIGrizzleJW (2009) The spring loaded inverted pendulum as the hybrid zero dynamics of an asymmetric hopper. IEEE Transactions on Automatic Control54(8): 1779–1793.
55.
PrattJChewC-MTorres Ann. (2001) Virtual model control: an intuitive approach for bipedal locomotion. The International Journal of Robotics Research20(2): 129–143.
56.
PrattJKoolenTde BoerT. (2012) Capturability-based analysis and control of legged locomotion, part 2: Application to M2V2, a lower-body humanoid. The International Journal of Robotics Research31(10): 1117–1133.
57.
RaibertMH (1986) Legged robots that balance, volume 29. MA: MIT Press. City: Cambridge.
58.
RamezaniAHurstJWHamedKA. (2013) Performance analysis and feedback control of ATRIAS, a 3D bipedal robot. Journal of Dynamic Systems, Measurement, and Control136(2): 021012.
59.
RenjewskiD (2012) An engineering contribution to human gait biomechanics. Phd dissertation, TU Ilmenau.
60.
RezazadehSHubickiCMJonesMS. (2015) Spring-mass walking with ATRIAS in 3D: Robust gait control spanning zero to 4.3 kph on a heavily underactuated bipedal robot. In: Proceedings of the ASME 2015 dynamic systems and control conference ASME/DSCC 2015, Columbus OH, 28–30 October 2015, pp. V001T04A003. New York, NY: ASME.
61.
RobinsonDWPrattJEPaluskaDJ. (1999) Series elastic actuator development for a biomimetic walking robot. In:IEEE/ASME international conference on advanced intelligent mechatronics, pp.561–568.
62.
RoosFJohanssonHWikanderJ (2006) Optimal selection of motor and gearhead in mechatronic applications. Mechatronics16(1): 63–72.
63.
SeipelJEHolmesP (2005) Running in three dimensions: Analysis of a point-mass sprung-leg model. International Journal of Robotics Research24(8): 657–674.
64.
SeokSWangAChuahMY. (2013) Design principles for highly efficient quadrupeds and implementation on the MIT Cheetah robot. In: 2013 IEEE international conference on robotics and automation (ICRA), Karlsruhe, Germany, 6–10 May 2013, pp.3307–3312. IEEE.
65.
SeyfarthAGeyerH (2002) Natural control of spring-like running: Optimised self-stabilisation. In: International conference on climbing and walking robots (CLAWAR), Paris, France, 25–27 September 2002, vol.1, pp.81–85. Suffolk UK: Professional Engineering Publishing.
66.
SeyfarthAGeyerHHerrHM (2003) Swing-leg retraction: a simple control model for stable running. The Journal of Experimental Biology206(15): 2547–2555.
67.
SinnetRWAmesAD (2009) 3D bipedal walking with knees and feet: A hybrid geometric approach. In: Proceedings of the 48th IEEE conference on decision and control, 2009 held jointly with the 2009 28th Chinese control conference. CDC/CCC 2009, Shanghai China, 15–18 December 2009, pp.3208–3213. IEEE.
68.
SpongM (1998) Underactuated mechanical systems. In: SicilianoBValavanisK (eds) Control Problems in Robotics and Automation, Lecture Notes in Control and Information Sciences, volume 230. Berlin/Heidelberg: Springer, pp.135–150.
69.
SpröwitzATuleuAVespignaniM. (2013) Towards dynamic trot gait locomotion: Design, control, and experiments with Cheetah-cub, a compliant quadruped robot. The International Journal of Robotics Research32(8): 932–950.
70.
SreenathKParkH-WPoulakakisI. (2013) Embedding active force control within the compliant hybrid zero dynamics to achieve stable, fast running on MABEL. The International Journal of Robotics Research32(3): 324–345.
71.
SrinivasanMRuinaA (2006) Computer optimization of a minimal biped model discovers walking and running. Nature439(7072): 72–75.
72.
StephensBJAtkesonCG (2010) Dynamic balance force control for compliant humanoid robots. In: 2010 IEEE/RSJ international conference on intelligent robots and systems, Taipei, Taiwan, 18–22 October 2010, pp.1248–1255. IEEE.
73.
SullivanTSeipelJ (2014) 3D dynamics of bipedal running: Effects of step width on an amputee-inspired robot. In: IEEE international conference on intelligent robots and systems (IROS), Chicago, IL, 14–18 September 2014, pp.939–944. IEEE.
74.
UrataJNakanishiYOkadaK. (2010) Design of high torque and high speed leg module for high power humanoid. In: 2010 IEEE/RSJ international conference on intelligent robots and systems (IROS), Taipei, Taiwan, 18–22 October 2010, pp.4497–4502. IEEE.
75.
VukobratovićMBorovacB (2004) Zero-moment point – thirty five years of its life. International Journal of Humanoid Robotics1(1): 157–173.
76.
WaldronKJKinzelGL (1981) The relationship between actuator geometry and mechanical efficiency in robots. In: MoreckiBianchi GKȩdziorK (eds) Fourth symposium on theory and practice of robots and manipulators, Warsaw, Poland, 8–12 September 1981, pp.366–374. Warsaw, Poland: Polish Scientific Publishers.
77.
WesterveltERGrizzleJWKoditschekDE (2003) Hybrid zero dynamics of planar biped walkers. Automatic Control, IEEE Transactions on48(1): 42–56.
78.
ZeglinG (1999) The bow leg hopping robot. PhD Thesis, Robotics Institute, Carnegie Mellon University, Pittsburgh, PA, USA.
79.
ZhangTQianFLiC. (2013) Ground fluidization promotes rapid running of a lightweight robot. The International Journal of Robotics Research32(7): 859–869.
Supplementary Material
Please find the following supplemental material available below.
For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.
For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.
