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Gait Optimization for Quadruped Rovers

Published online by Cambridge University Press:  02 October 2019

Lukas Zhornyak and
M. Reza EmamiOpen the ORCID record for M. Reza Emami[Opens in a new window]
Lukas Zhornyak
Affiliation:
Institute for Aerospace Studies, University of Toronto, Toronto, Canada, M3H 5T6 E-mail: lukas.zhornyak@mail.utoronto.ca
M. Reza Emami*
Affiliation:
Institute for Aerospace Studies, University of Toronto, Toronto, Canada, M3H 5T6 E-mail: lukas.zhornyak@mail.utoronto.caDivision of Space Engineering, Luleå University of Technology, Kiruna, Sweden, 98128
*
*Corresponding author. E-mail: emami@utias.utoronto.ca
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Summary

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This paper studies the gait characteristics of a quadruped rover that mimics domestic cats, and attempts to optimize these characteristics. The kinematics and dynamics formulation of the rover’s three-dimensional model is developed, and its gait, pose and corresponding control parameters are computed to minimize torque or maximize speed, using a genetic algorithm. The optimization model consists of a set of equality and inequality constraints that ensure the feasibility and stability of the gaits, while considering the entire gait spectrum that feline species exhibit. The optimal gaits for minimizing the torque closely resemble lateral sequence gaiting, with a trotting behaviour as speed increases. A running gait is obtained at the maximum speed. The optimization results appear to conform to the biological observations of feline species, suggesting the tendency of conserving energy in biological gaiting.

Keywords

Quadruped roverGait planningGait optimizationGenetic algorithm

Information

Type
Articles
Information
Robotica , Volume 38 , Issue 7 , July 2020, pp. 1263 - 1287
Copyright
© Cambridge University Press 2019

References

Usherwood, J., “Why not walk faster?” Biol. Lett. 1(3), 338–341 (2005).CrossRefGoogle Scholar
Silva, M. and Machado, J., “A historical perspective of legged robots,” J. Vib. Control 13(9–10), 1447–1486 (2007).CrossRefGoogle Scholar
Coros, S., Karpathy, A., Jones, B., Reveret, L. and Panne, M., “Locomotion skills for simulated quadrupeds,” ACM Trans. Graph. 30(4), 59:1–59:11 (2011).CrossRefGoogle Scholar
Bogert, A., Schamhardt, H. and Crowe, A., “Simulation of quadrupedal locomotion using a rigid dynamics model,” J. Biomech. 22(1), 33–41 (1989).CrossRefGoogle Scholar
Marhefka, D., Orin, D., Schmiedeler, J. and Waldron, K., “Intelligent control of quadruped gallops,” IEEE/ASME Trans. Mech . 8(4), 446–456 (2003).CrossRefGoogle Scholar
Herr, H. and McMohan, M., “A galloping horse model,” Int. J. Robot. Res. 20(1), 26–37 (2001).CrossRefGoogle Scholar
Tarokh, M. and Ho, H. D., “Kinematics-based simulation and animation of articulated rovers traversing uneven terrains,” Robotica 37(6), 1057–1072 (2019).CrossRefGoogle Scholar
Sarmah, A. N., Boruah, A., Kalita, D., Neog, D. and Paul, S., “A bio-inspired implementation of walking and stair climbing on a quadruped robot,” Procedia Comput. Sci . 143, 671–677 (2018).CrossRefGoogle Scholar
Vermeulen, J., Lefeber, D. and Verrelst, B., “Control of foot placement, forward velocity and body orientation of a one-legged hopping robot,” Robotica 21(1), 45–57 (2003).CrossRefGoogle Scholar
Paul, R., Robot Manipulators: Mathematics, Programming, and Control: the Computer Control of Robot Manipulators, Artificial Intelligence Series (MIT Press, Cambridge, 1981).Google Scholar
Silva, M., Barbosa, R. and Machado, T., “Ga Optimization of an Hexapod Robot Parameters for Periodic Gaits,” In: Proceedings of 1st International Symposium on Computational Intelligence for Engineering Systems, Porto, Portugal (2009).Google Scholar
Seyfarth, A., Geyer, H. and Herr, H., “Swing-leg retraction: A simple control model for stable running,” J. Exp. Biol. 206, 2547–2555 (2003).CrossRefGoogle Scholar
Wisse, M., Atkeson, C. and Kloimwieder, D., “Swing Leg Retraction Helps Biped Walking Stability,” In: Proceedings of 5th IEEE-RAS International Conference on Humanoid Robots, Tsukuba, Japan (2005), pp. 295–300.Google Scholar
Hu, L. and Zhou, C., “Eda-Based Optimization and Learning Methods for Biped Gait Generation,” Robotic Welding, Intelligence and Automation (Tarn, T.-J., Chen, S.-B. and Zhou, C., eds.), vol. 362 (2007) pp. 541–549.Google Scholar
Daoxiong, G., Yan, J. and Zuo, G., “A review of gait optimization based on evolutionary computation,” Appl. Comput. Intell. Soft Comput. 2010 (2010).CrossRefGoogle Scholar
Shrivastava, M., Dutta, A. and Saxena, A., “Trajectory generation using ga for an 8 dof biped robot with deformation at the sole of the foot,” J. Intell. Robot. Syst. Theo. Appl. 49(1), 67–84 (2006).CrossRefGoogle Scholar
Kiguchi, K., Kusumoto, Y., Watanabe, K., Izumi, K. and Fukuda, T., “Energy-optimal gait analysis of quadruped robots,” Artif Life Robot . 6(3), 120–125 (2002).CrossRefGoogle Scholar
Chernova, S. and Veloso, M., “An Evolutionary Approach to Gait Learning for Four-Legged Robots,” In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Sendai, Japan, vol. 3 (2004) pp. 2562–2567.Google Scholar
Hornby, G., Fujita, M., Takamura, S., Yamamoto, T. and Hanagata, O., “Autonomous Evolution of Gaits with the Sony Quadruped Robot,” In: Proceedings of the Genetic and Evolutionary Computation Conference, Orlando, Florida (1999) pp. 1297–1304.Google Scholar
Kim, M. and Uther, W., “Automatic Gait Optimisation for Quadruped Robots,” In: Australasian Conference on Robotics and Automation, Brisbane, Australia (2003).Google Scholar
Bi, S., Zhuang, Z., Xia, T., Mo, H.-X., Min, H.-Q. and Luo, R.-H., “Multi-Objective Optimization for a Humanoid Robot Walking on Slopes,” In: Proceedings of IEEE Conference on Machine Learning and Cybernetics, Guilin, China (2011) pp. 1261–1267.Google Scholar
Day, L. and Jayne, B., “Interspecific scaling of the morphology and posture of the limbs during locomotion of cats (felidae),” J. Exp. Biol. 210, 642–654 (2007).CrossRefGoogle ScholarPubMed
Alexander, R., “The gaits of bipedal and quadrupedal animals,” Int. J. Robot. Res. 3(2), 49–59 (1984).CrossRefGoogle Scholar
Tsujita, K., Tsuchiya, K. and Onat, A., “Locomotion Control of a Multipod Locomotion Robot with CPG Principles,” In: Proceedings of the 6th International Symposium of Artificial Life and Robotics, vol. 2 (2001) pp. 421–426.Google Scholar
Westervelt, E., Grizzle, J., Chevallereau, C., Choi, J. and Morris, B., Feedback Control of Dynamic Bipedal Robot Locomotion, Automation andControl Engineering (CRC Press, New York, 2007).Google Scholar
Craig, J. J., Introduction to Robotics: Mechanics and Control, Addison-Wesley Series in Electrical and Computer Engineering: Control Engineering. (Pearson, Prentice Hall, 2005).Google Scholar
Meghdari, A., Karimi, R., Pishkenari, H., Gaskarimahalle, A. and Mahboobi, S., “An effective approach for dynamic analysis of rovers,” Robotica 23(6), 771–780 (2005).CrossRefGoogle Scholar
Wang, Z., Ding, X., Rovetta, A. and Giusti, A., “Mobility analysis of the typical gait of a radial symmetrical six-legged robot,” Mechatronics 21(7), 1133–1146 (2011).CrossRefGoogle Scholar
Kalakrishnan, M., “Learning, planning, and control for quadruped locomotion over challenging terrain,” Int. J. Robot. Res. 30(2), 236–258 (2011).CrossRefGoogle Scholar
Denavit, J. and Hartenberg, R., “A kinematic notation for lower-pair mechanisms based on matrices,” Trans ASME J. Appl. Mech . 22, 215–221 (1955).Google Scholar
Konak, A., Coit, D. and Smith, A., “Multi-objective optimization using genetic algorithms: A tutorial,” Reliab. Eng. Syst. Saf. 91(9), 992–1007 (2006).CrossRefGoogle Scholar
Wight, D., “A foot placement strategy for robust bipedal gait control,” Ph.D. Thesis, (University of Waterloo, Canada, 2008).Google Scholar
Kang, T., Kim, H., Son, T. and Choi, H., “Design of Quadruped Walking and Climbing Robot,” In: Proceedings of IEEE Conference on Intelligent Robots and Systems, Las Vegas, NV (2003) pp. 619–624.Google Scholar
Briskin, E., Chernyshev, V. and Maloletov, A., “On Conception of Walking Machines Designing,” In: Proceedings of IEEE Conference on Advanced Robotics, Coimbra, Portugal (2003) pp. 1763–1768.Google Scholar
Silva, M. and Machado, J., “Kinematic and dynamic performance analysis of artificial legged systems,” Robotica 26(1), 19–39 (2008).CrossRefGoogle Scholar
Maufroy, C., Kimura, H. and Takase, K., “Integration of posture and rhythmic motion controls in quadrupedal dynamic walking using phase modulations based on leg loading/unloading,” Auton. Robots 28(3), 331–353 (2010).CrossRefGoogle Scholar
Roan, P., Burmeister, A., Rahimi, A. and Holz, K., “Real-World Validation of Three Tipover Algorithms for Mobile Robots,” In: IEEE International Conference on Robotics and Automation, Anchorage, Alaska (2010) pp. 4431–4436.Google Scholar
Pratt, J. and Tedrake, R., “Velocity-Based Stability Margins for Fast Bipedal Walking,” In: Fast Motions in Biomechanics and Robotics: Optimization and Feedback Control (Springer, Berlin, Heidelberg, 2007).Google Scholar
Tamaki, H., Kita, H. and Kobayashi, S., “Multi-Objective Optimizations by Genetic Algorithms: A Review,” In: Proceedings of IEEE International Conference on Evolutionary Computation, Nagoya, Japan (1996) pp. 517–522.Google Scholar
Goslow, G. E., Reinking, R. M. and Stuart, D. G., “The cat step cycle: Hind limb joint angles and muscle lengths during unrestrained locomotion,” J. Morphol. 141(1), 1–41 (1973).CrossRefGoogle Scholar
Smith, J., Chung, S. and Zernicke, R., “Gait-related motor patterns and hindlimb kinetics for the cat trot and gallop,” Exp. Brain Res. 94(2), 308–322 (1993).CrossRefGoogle Scholar
Wisleder, D., Zernicke, R. and Smith, J., “Speed-related changes in hindlimb intersegmental dynamics during the swing phase of cat locomotion,” Exp. Brain Res. 79(3), 651–660 (1990).CrossRefGoogle Scholar
Vilensky, J. A. and Patrick, M. C., “Inter and intratrial variation in cat locomotor behavior,” Physiol. Behav. 33(5), 733–743 (1984).CrossRefGoogle Scholar
Taylor, C., Heglund, N. and Maloiy, G., “Energetics and mechanics of terrestrial locomotion,” Exp. Biol. 97(1–2) (1982).CrossRefGoogle Scholar