Surrogate Model Based Optimization for Omni-directional Walking Parameters of Humanoids
ZHANG Jiwen1,2,3, LIU Li1,2,3, LI Changshuo1, CHEN Ken1,2,3
1. Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China;
2. Beijing Key Lab of Precision/Ultra-precision Manufacturing Equipments and Control, Tsinghua University, Beijing 100084, China;
3. The State Key Laboratory of Tribology, Beijing 100084, China
张继文, 刘莉, 李昌硕, 陈恳. 仿人机器人全方位步行参数的代理模型优化[J]. 机器人, 2016, 38(1): 56-63,74.DOI: 10.13973/j.cnki.robot.2016.0056.
ZHANG Jiwen, LIU Li, LI Changshuo, CHEN Ken. Surrogate Model Based Optimization for Omni-directional Walking Parameters of Humanoids. ROBOT, 2016, 38(1): 56-63,74. DOI: 10.13973/j.cnki.robot.2016.0056.
摘要
仿人机器人的全方位步行参数对其行走稳定性、灵活性、快速性具有较大影响，然而物理机器人与描述其前后步幅连接约束的简化动力学模型间的数学关系却难于建立，因而难于获得优化目标表达式和相应的优化方法．本文从步幅跟随规划算法中提取出 7 个关键影响参数，并将标准实验工况下的步幅跟随性能指定为优化目标，从而将问题转化为一个黑盒优化过程．基于动力学仿真建立 Kriging 代理模型，通过 Latin 超立方初始实验和 EGO（effective global optimization）迭代建模优化求解该问题．动力学仿真结果表明，在较少的实验代价下，该方法实现了全方位步行参数的优化，该方法能够实现步行速度和步幅跟随能力的综合提升．
Omni-directional walking parameters of a humanoid robot have great impacts on its walking stability, flexibility and rapidity. However, it is difficult to establish the mathematical relationship between the physical robot and the simplified dynamics model which describes its inter-pace connectivity constraints. Therefore, it is hard to obtain the expression of the optimization objective as well as the optimization method. In this paper, seven key effective parameters are extracted from the stride tracking planning algorithm, and the tracking quality of a standard walking experiment is designated as the optimization objective. The problem is thus transferred into a black-box optimization process. Kriging surrogate model is established by dynamics simulation, and the initial experiments designed with Latin Hypercube as well as the EGO (effective global optimization) iterative modeling and optimization are adopted to solve this problem. Dynamics simulation results show that the omni-directional walking parameters are optimized via the proposed approach with quite a little experiment cost. The approach is also able to promote remarkably the walking speed and stride tracking ability simultaneously.
[1] Hengst B, Ibbotson D, Pham S B, et al. Omnidirectional locomotion for quadruped robots[M]//Lecture Notes in Artificial Intelligence, vol.2377. Berlin, Germany: Springer-Verlag, 2002: 368-373.[2] Kamikawa K, Arai T, Inoue K, et al. Omni-directional gait of multi-legged rescue robot[C]//IEEE International Conference on Robotics and Automation. Piscataway, USA: IEEE, 2004: 2171-2176.[3] Behnke S. Online trajectory generation for omnidirectional biped walking[C]//IEEE International Conference on Roboticsand Automation. Piscataway, USA: IEEE, 2006: 1597-1603.[4] Kajita S, Kanehiro F, Kaneko K, et al. Biped walking pattern generation by using preview control of zero-moment point [C]//IEEE International Conference on Robotics and Automation. Piscataway, USA: IEEE, 2003: 1620-1626.[5] Colin G, Hartl E, Thomas R, et al. A robust closed-loop gait for the standard platform league humanoid[C]//Proceedings of the Fourth Workshop on Humanoid Soccer Robots in conjunction with the 2009 IEEE-RAS International Conference on Humanoid Robots. http://www.ais.uni-bonn.de/humanoidsoccer/ ws09/program.html.[6] Gouaillier D, Collette C, Kilner C. Omni-directional closed-loop walk for NAO[C]//IEEE/RAS International Conference on Humanoid Robots. Piscataway, USA: IEEE, 2010: 448-454.[7] Strom J, George S, Eric C. Omnidirectional walking using ZMP and preview control for the NAO humanoid robot[M]//Lecture Notes in Computer Science, vol.5949. Berlin, Germany: Springer-Verlag, 2010: 378-389.[8] Shafii N, Abdolmaleki A, Ferreira R, et al. Omnidirectional walking and active balance for soccer humanoid robot [C]//Progress in Artificial Intelligence. Berlin, Germany: Springer-Verlag, 2013: 283-294.[9] Alcaraz-Jimenez J J, Herrero-Perez D, Martinez-Barbera H. Motion planning for omnidirectional dynamic gait in humanoid soccer robots[J]. Journal of Physical Agents, 2011, 5(1): 25-34.[10] 薛峰,陈小平.一种提高双足机器人机动性的步行模式规划方法[J].小型微型计算机系统,2012,33(9): 1928-1933. ewline Xue F, Chen X P. Novel gait pattern planning method for increasing flexibility of biped robot[J]. Journal of Chinese Computer Systems, 2012, 33(9): 1928-1933.[11] Harada K, Kajita S, Kaneko K, et al. An analytical method on real-time gait planning for a humanoid robot[J]. International Journal of Humanoid Robotics, 2006, 3(1): 1-19.[12] 张继文,刘莉,李昌硕,等.仿人机器人参数化全方位步态规划方法[J].机器人,2014,36(2):210-217. ewline Zhang J W, Liu L, Li C S, et al. Parametric omni-directional gait planning of humanoid robots[J]. Robot, 2014, 36(2): 210-217.[13] Hemker T, Stelzer M, Stryk O V. Efficient walking speed optimization of a humanoid robot[J]. International Journal of Robotics Research, 2009, 28(2): 303-314. [14] Wang G G, Shan S. Review of metamodeling techniques in support of engineering design optimization[J]. Journal of Mechanical Design, 2007, 129(4): 370-380. [15] Picheny V, Ginsbourger D, Richet Y, et al. Quantile-based optimization of noisy computer experiments with tunable precision[J]. Technometrics, 2013, 55(1): 2-13. [16] Simpson T W, Mauery T M, Korte J J, et al. Kriging models for global approximation in simulation-based multidisciplinary design optimization[J]. AIAA Journal, 2001, 39(12): 2233-2241. [17] Sacks J, Welch W J, Mitchell T J, et al. Design and analysis of computer experiments[J]. Statistical Science, 1989, 4(4): 409-423.[18] Santner T J, Williams B J, Notz W. The design and analysis of computer experiments[M]//Springer Series in Statistics. Berlin, Germany: Springer-Verlag, 2003.[19] 邹林君.基于Kriging 模型的全局优化方法研究[D].武汉:华中科技大学,2011.Zou L J. Research on global optimization method based on Kriging model[D]. Wuhan: Huazhong University of Science and Technology, 2011. [20] Svanberg K. A class of globally convergent optimization methods based on conservative convex separable approximations[J]. SIAM Journal on Optimization, 2002, 12(2): 555-573. [21] Jones D R, Schonlau M, Welch W J. Efficient global optimization of expensive black-box functions[J]. Journal of Global Optimization, 1998, 13(4): 455-492. [22] Kanehiro F, Hirukawa H, Kajita S. OpenHRP: Open architecture humanoid robotics platform[J]. International Journal of Robotics Research, 2004,23(2): 155-165. [23] OpenHRP Team, Humanoid Research Group. OpenHRP users manual sample humanoid robot[DB/OL]. (2012-10-15) [2015-11-17].http://fkanehiro.github.io/openhrp3-doc/en/sample_ model.html.[24] Roustant O, Ginsbourger D, Deville Y. DiceKriging, DiceOptim: Two R packages for the analysis of computer experiments by Kriging-based metamodeling and optimization[J]. Journal of Statistical Software, 2013,51(1): 1-55.[25] Viana F A. SURROGATES toolboxes[DB/OL]. (2011-11-1) [2015-11-17].https://sites.google.com/site/felipeacviana/surrogatestoolbox.
