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Energy optimal motion planning of a 14-DOF biped robot on 3D terrain using a new speed function incorporating biped dynamics and terrain geometry

Published online by Cambridge University Press:  14 May 2021

Jitendra Kumar  and
Ashish Dutta Open the ORCID record for Ashish Dutta [Opens in a new window]
Jitendra Kumar
Affiliation:
Department of Mechanical Engineering, IIT Kanpur, 208016, India
Ashish Dutta*
Affiliation:
Department of Mechanical Engineering, IIT Kanpur, 208016, India
*
*Corresponding author. Email: [email protected]
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Abstract

In this paper, a new method is proposed to find a feasible energy-efficient path between an initial point and goal point on uneven terrain and then to optimally traverse the path. The path is planned by integrating the geometric features of the uneven terrain and the biped robot dynamics. This integrated information of biped dynamics and associated cost (energy) for moving toward the goal point is used to define the value of a new speed function at each point on the discretized surface of the terrain. The value is stored as a matrix called the dynamic transport cost (DTC). The path is obtained by solving the Eikonal equation numerically by fast marching method (FMM) on an orthogonal grid, by using the information stored in the DTC matrix. One step of walk on uneven terrain is characterized by 10 footstep parameters (FSPs); these FSPs represent the position of swinging foot at the starting and ending time of the walk, orientation, and state (left or right) of support foot. A walking dataset was created for different walking conditions (FSPs), which the biped robot is likely to encounter when it has to walk on the uneven terrain. The corresponding energy optimal hip and foot trajectory parameters (HFTPs) are obtained by optimization using a genetic algorithm (GA). The created walk dataset is generalized by training a feedforward neural network (NN) using the scaled conjugate gradient (SCG) algorithm. The Foot placement planner gives a sequence of foot positions and orientations along the obtained path, which is followed by the biped robot by generating real-time optimal foot and hip trajectories using the learned NN. Simulation results on different types of uneven terrains validate the proposed method.

Keywords

Fast marching methodSpeed functionUneven terrainDynamic transport cost matrixGradient descent algorithmGenetic algorithmFootstep parametership and foot trajectory parameters
Type
Article
Information
Robotica , Volume 40 , Issue 2 , February 2022 , pp. 250 - 278
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

Latombe, J. C., Robot Motion Planning (Kluwer Academic Publishers, Norwell, MA, USA, 1991).CrossRefGoogle Scholar
Choset, H., Hutchinson, S., Lynch, K., Kantor, G., Burgard, W., Kavraki, L., Thrun, S. and Arkin, R., Principles of Robot Motion: Theory, Algorithms, and Implementation. A Bradford Book (Prentice Hall of India, Delhi, India, 2005).Google Scholar
Stentz, A., “Optimal and Efficient Path Planning for Partially-Known Environments,” Proceedings of the 1994 IEEE International Conference on Robotics and Automation, vol. 4 (1994) pp. 3310–3317. doi: 10.1109/ROBOT.1994.351061 CrossRefGoogle Scholar
Karkowski, P. and Bennewitz, M., “Real-Time Footstep Planning Using a Geometric Approach,” 2016 IEEE International Conference on Robotics and Automation (ICRA) (2016) pp. 1782–1787. doi: 10.1109/ICRA.2016.7487323 CrossRefGoogle Scholar
Hornung, A. and Bennewitz, M., “Adaptive Level-of-Detail Planning for Efficient Humanoid Navigation,” 2012 IEEE International Conference on Robotics and Automation (2012) pp. 997–1002. doi: 10.1109/ICRA.2012.6224898 CrossRefGoogle Scholar
Bessonnet, G., Seguin, P. and Sardain, P., “A parametric optimization approach to walking pattern synthesis,” Int. J. Rob. Res. 24(7), 523–536 (2005). doi: 10.1177/0278364905055377 CrossRefGoogle Scholar
Huang, Q., Yokoi, K., Kajita, S., Kaneko, K., Arai, H., Koyachi, N. and Tanie, K., “Planning walking patterns for a biped robot,” IEEE Trans. Rob. Autom. 17(3), 280–289 (2001). doi: 10.1109/70.938385 CrossRefGoogle Scholar
Tlalolini, D., Aoustin, Y. and Christine, C., “Design of a walking cyclic gait with single support phases and impacts for the locomotor system of a thirteen-link 3d biped using the parametric optimization,” Multibody Syst. Dyn. 23(1), 33–56 (2010). doi: 10.1007/s11044-009-9175-1 CrossRefGoogle Scholar
Sarkar, A. and Dutta, A., “8-DOF biped robot with compliant-links,” Rob. Auto. Syst. 63, 57–67 (2015). doi: 10.1016/j.robot.2014.09.014 CrossRefGoogle Scholar
Sarkar, A. and Dutta, A., “Optimal trajectory generation and design of an 8-DOF compliant biped robot for walk on inclined ground,” J. Intell. Robot. Syst. 94, 583–602 (2019). doi: 10.1007/s10846-018-0882-9 CrossRefGoogle Scholar
bo Zhong, Q. and Chen, F., “Trajectory planning for biped robot walking on uneven terrain – taking stepping as an example,” CAAI Trans. Intell. Technol. 1(3), 197–209 (2016). doi: 10.1016/j.trit.2016.10.009 CrossRefGoogle Scholar
Janardhan, V. and Prasanth Kumar, R., “Generating real-time trajectories for a planar biped robot crossing a wide ditch with landing uncertainties,” Robotica 37(1), 109–140 (2019). doi: 10.1017/S0263574718000887 CrossRefGoogle Scholar
Chestnutt, J., Kuffner, J., Nishiwaki, K. and Kagami, S., “Planning Biped Navigation Strategies in Complex Environments,” Proceedings of the 2003 International Conference on Humanoid Robots (2003).Google Scholar
Luo, R. C. and Lin, S. J., Impedance and Force Compliant Control for Bipedal Robot Walking on Uneven Terrain,” 2015 IEEE International Conference on Systems, Man, and Cybernetics (2015) pp. 228–233. doi: 10.1109/SMC.2015.52 CrossRefGoogle Scholar
Yi, J., Zhu, Q., Xiong, R. and Wu, J., “Walking algorithm of humanoid robot on uneven terrain with terrain estimation,” Int. J. Adv. Rob. Syst. 13(1), 35 (2016). doi: 10.5772/62245 CrossRefGoogle Scholar
Cupec, R., Aleksi, I. and Schmidt, G., “Step sequence planning for a biped robot by means of a cylindrical shape model and a high-resolution 2.5D map,” Rob. Auto. Syst. 59(2), 84–100 (2011). doi: 10.1016/j.robot.2010.10.007 CrossRefGoogle Scholar
Chestnutt, J., Lau, M., Cheung, G., Kuffner, J., Hodgins, J. and Kanade, T., “Footstep Planning for the Honda Asimo Humanoid,” Proceedings of the 2005 IEEE International Conference on Robotics and Automation (2005) pp. 629–634. doi: 10.1109/ROBOT.2005.1570188 CrossRefGoogle Scholar
Hirai, K., Hirose, M., Haikawa, Y. and Takenaka, T., “The Development of Honda Humanoid Robot,” Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146), vol. 2 (1998) pp. 1321–1326. doi: 10.1109/ROBOT.1998.677288 CrossRefGoogle Scholar
Gupta, G. and Dutta, A., “Trajectory generation and step planning of a 12 DOF biped robot on uneven surface,” Robotica 36(7), 945–970 (2018). doi: 10.1017/S0263574718000188 CrossRefGoogle Scholar
Cheng, M.-Y. and Lin, C.-S., “Dynamic biped robot locomotion on less structured surfaces,” Robotica 18(2), 163–170 (2000). doi: 10.1017/S0263574799002076 CrossRefGoogle Scholar
Seo, Y.-J. and Yoon, Y.-S., “Design of a robust dynamic gait of the biped using the concept of dynamic stability margin,” Robotica 13(5), 461–468 (1995). doi: 10.1017/S0263574700018294 CrossRefGoogle Scholar
Garrido, S., Malfaz, M. and Blanco, D., “Application of the fast marching method for outdoor motion planning in robotics,” Rob. Auto. Syst. 61(2), 106–114 (2013). doi: 10.1016/j.robot.2012.10.012 CrossRefGoogle Scholar
Garrido, S., Moreno, L., Martín, F. and Álvarez, D., “Fast marching subjected to a vector field-path planning method for mars rovers,” Expert Syst. Appl. 78, 334–346 (2017). doi: 10.1016/j.eswa.2017.02.019 CrossRefGoogle Scholar
McGeer, T., “Passive dynamic walking,” Int. J. Rob. Res. 9(2), 62–82 (1990).CrossRefGoogle Scholar
Spong, M. W., “Passivity based control of the compass gait biped,” IFAC Proc. 32(2), 506–510 (1999).CrossRefGoogle Scholar
Spong, M. W. and Bhatia, G., “Further Results on Control of the Compass Gait Biped,” Proceedings 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003) (Cat. No.03CH37453), vol. 2 (2003) pp. 1933–1938. doi: 10.1109/IROS.2003.1248927 CrossRefGoogle Scholar
Asano, F., “Stability Analysis of Passive Compass Gait Using Linearized Model,” 2011 IEEE International Conference on Robotics and Automation (2011) pp. 557–562. doi: 10.1109/ICRA.2011.5979647 CrossRefGoogle Scholar
Ochs, K., “A comprehensive analytical solution of the nonlinear pendulum,” Eur. J. Phys. 32(2), 479–490 (2011). doi: 10.1088/0143-0807/32/2/019 CrossRefGoogle Scholar
Olivares, M. and Albertos, P., “Linear control of the flywheel inverted pendulum,” ISA Trans. 53(5), 1396–1403 (2014), iCCA 2013. doi: https://doi.org/10.1016/j.isatra.2013.12.030 URL http://www.sciencedirect.com/science/article/pii/S0019057813002401Google Scholar
Kasaei, M., Lau, N. and Pereira, A., “An Optimal Closed-Loop Framework to Develop Stable Walking for Humanoid Robot,” 2018 IEEE International Conference on Autonomous Robot Systems and Competitions (ICARSC) (2018) pp. 30–35. doi: 10.1109/ICARSC.2018.8374156 CrossRefGoogle Scholar
Crews, S. and Travers, M., “Energy management through footstep selection for bipedal robots,” IEEE Rob. Autom. Lett. 5(4), 5485–5493 (2020). doi: 10.1109/LRA.2020.3003235 CrossRefGoogle Scholar
Pratt, J., Carff, J., Drakunov, S. and Goswami, A., “Capture Point: A Step Toward Humanoid Push Recovery,” 2006 6th IEEE-RAS International Conference on Humanoid Robots (2006) pp. 200–207. doi: 10.1109/ICHR.2006.321385 CrossRefGoogle Scholar
Ramos, O. E. and Hauser, K., “Generalizations of the Capture Point to Nonlinear Center of Mass Paths and Uneven Terrain,” 2015 IEEE-RAS 15th International Conference on Humanoid Robots (Humanoids) (2015) pp. 851–858. doi: 10.1109/HUMANOIDS.2015.7363461 CrossRefGoogle Scholar
Nguyen, Q., Da, X., Grizzle, J. and Sreenath, K., Dynamic Walking on Stepping Stones with Gait Library and Control Barrier Functions (2020) pp. 384–399. doi: 10.1007/978-3-030-43089-4_25 CrossRefGoogle Scholar
Da, X., Harib, O., Hartley, R., Griffin, B. and Grizzle, J. W., “From 2D design of underactuated bipedal gaits to 3D implementation: Walking with speed tracking,” IEEE Access 4, 3469–3478 (2016). doi: 10.1109/ACCESS.2016.2582731 CrossRefGoogle Scholar
Craig, J., Introduction to Robotics: Mechanics and Control, Addison-Wesley Series in Electrical and Computer Engineering: Control Engineering (Pearson Education, Inc. Pearson Prentice Hall Pearson Education, Inc. Upper Saddle River, NJ, 2005).Google Scholar
Fu, K. S., Gonzalez, R. C. and Lee, C. S. G., Robotics: Control, Sensing, Vision, and Intelligence (McGraw-Hill, Inc., New York, NY, USA, 1987).Google Scholar
Vukobratović, M. and Borovac, B., “Zero-moment point – thirty five years of its life,” Int. J. Hum. Rob. 01(01), 157–173 (2004). doi: 10.1142/S0219843604000083 CrossRefGoogle Scholar
Sardain, P. and Bessonnet, G., “Forces acting on a biped robot. center of pressure-zero moment point,” Trans. Sys. Man Cyber. Part A 34(8), 630–637 (2004). doi: 10.1109/TSMCA.2004.832811 CrossRefGoogle Scholar
Holland, J. H., Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology. Control and Artificial Intelligence (MIT Press, Cambridge, MA, USA, 1992).Google Scholar
Goldberg, D. E., Genetic Algorithms in Search, Optimization and Machine Learning, 1st edn. (Addison-Wesley Longman Publishing Co., Inc., Boston, MA, USA, 1989).Google Scholar
Srinivas, M. and Patnaik, L. M., “Genetic algorithms: A survey,” Computer 27(6), 17–26 (1994). doi: 10.1109/2.294849 CrossRefGoogle Scholar
MATLAB, Optimization Toolbox, Version 7.4 (R2016a), The MathWorks Inc. (Natick, MA, 2016).Google Scholar
Carbone, G., Ceccarelli, M., Oliveira, P. J., Saramago, S. F. P. and Carvalho, J. C. M., “An optimum path planning for cassino parallel manipulator by using inverse dynamics,” Robotica 26(2), 229–239 (2008). doi: 10.1017/S0263574707003839 CrossRefGoogle Scholar
Hornik, K., “Approximation capabilities of multilayer feedforward networks,” Neural Networks 4(2), 251–257 (1991). doi: 10.1016/0893-6080(91)90009-T CrossRefGoogle Scholar
MATLAB, Neural Network Toolbox, Version 9.0 (R2016a), The MathWorks Inc. (Natick, MA, 2016).Google Scholar
Sethian, J., “Fast marching methods,” SIAM Rev. 41(2), 199–235 (1999). doi: 10.1137/S0036144598347059 CrossRefGoogle Scholar
Kimmel, R. and Sethian, J. A., Computing geodesic paths on manifolds,” Proc. Natl. Acad. Sci. USA 95(15), 8431–8435 (1998).CrossRefGoogle Scholar
Sethian, J. A. and Vladimirsky, A., “Fast methods for the Eikonal and related Hamilton–Jacobi equations on unstructured meshes,” Proc. Natl. Acad. Sci. USA 97(11), 5699–5703 (2000). doi: 10.1073/pnas.090060097 CrossRefGoogle Scholar
Castejón, C., Boada, B. L., Blanco, D. and Moreno, L., “Traversable region modeling for outdoor navigation,” J. Intell. Rob. Syst. 43(2), 175–216 (2005). doi: 10.1007/s10846-005-9005-5 CrossRefGoogle Scholar