| Robot Modeling and Contro |
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| On-line optimal gait generation for biped walking robot by using double generating functions method |
| CHEN Di-jian, XU Yi-zhan, WANG Bin-rui |
| College of Mechanical and Electrical Engineering, China Jiliang University, Hangzhou 310018, China |
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Abstract The double generating functions method from optimal control theory was applied to the on-line optimal gait generation of the biped walking robot.A linear quadratic optimal control problem was designed for the linearized robot model by taking the joint angle and torque as state and input variables respectively and considering its energy consumption.The solution of the problem was derived based on a couple of generating functions,and can be parametrized as the off-line calculated coefficients and boundary conditions. The evaluation correspondingly consisted of the off-line numerical integration part and on-line algebraic computation part.A multi-step example illustrated that the method promoted the efficiency of the on-line trajectory generation.Then a PD controller was designed. When the robot walks with reasonable step lengths and time periods,the error induced by the linearization can be controlled within a small range that the trajectory of the nonlinear model can well follow the reference trajectory of the linearized model.
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Received: 13 February 2018
Published: 26 June 2018
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基于双生成函数的步行机器人最优步态生成
将最优控制理论中的双生成函数方法应用到双足步行机器人的在线最优步态生成中.针对线性化的机器人模型，分别以关节角度和力矩为状态和输入变量，考虑能量消耗，构造线性二次型最优控制问题.基于一对生成函数推导得到该问题的解，可以参数化为线下计算系数和边界条件，相对应的求解过程由线下数值积分部分和线上代数运算部分组成.通过设置多步仿真实例进行计算.结果表明，利用该方法可以显著地提高机器人步态的在线生成效率.设计比例微分控制器，当机器人以合理的步长和适当的时间段行走时，由线性化引起的建模误差可以被控制在较小范围之内，非线性模型的轨迹可以很好地跟踪线性化模型的轨迹.
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| [1] SHIN H K,KIM B K.Energy-efficient gait planning and control for biped robots utilizing the allowable ZMP region[J].IEEE Transactions on Robotics,2014,30(4):986-993.
[2] 张博,杜志江,孙立宁,等.双足步行机器人步态规划方法研究[J].机械与电子,2008(4):52-55. ZHANG Bo,DU Zhi-jiang,SUN Li-ning,et al.Research on gait planning of biped walking robot[J].Machinery and Electronics,2008(4):52-55.
[3] 李攀,魏洪兴.双足机器人步态规划方法研究[J].机械工程与自动化,2017(4):22-24. LI Pan,WEI Hong-xing.Method of gait planning for biped robot[J].Mechanical Engineering and Automation,2017(4):22-24.
[4] ROSTAMI M,BESSONNET G. Sagittal gait of a biped robot during the single support phase.part 2:optimal motion[J].Robotica,2001,19(3):241-245.
[5] SAIDOUNI T,BESSONNET G.Generating globally optimised sagittal gait cycles of a biped robot[J].Robotica, 2003, 21(2):199-210.
[6] MCGEER T.Passive dynamic walking[J].International Journal of Robotics Research,1990,9(2):62-82.
[7] LEE J H,OKAMOTO S,KOIKE H,et al.Development and motion control of a biped walking robot based on passive walking theory[J].Artificial Life and Robotics,2014,19(1):68-75.
[8] SAFA A,NARAGHI M.The role of walking surface in enhancing the stability of the simplest passive dynamic biped[J].Robotica,2015,33(1):195-207.
[9] GRITLI H,BELGHITH H,KHRAIEF N.OGY-based control of chaos in semi-passive dynamic walking of a torso-driven biped robot[J].Nonlinear Dynamics,2015,79(2):1363-1384.
[10] CAO Y,SUZUKI S,HOSHINO Y.Uphill and level walking of a three-dimensional biped quasi-passive walking robot by torso control[J].Robotica,2016,34(3):483-496.
[11] ZHU H,LUO H,MEI T,et al.Energy-efficient bio-inspired gait planning and control for biped robot based on human locomotion analysis[J].Journal of Bionic Engineering,2016,13(2):271-282.
[12] WANG L,LIU Z,CHEN C,et al.Energy-efficient svm learning control system for biped walking robots[J].IEEE Transactions on Neural Networks and Learning Systems,2013,24(5):831-837.
[13] ASANO F,YAMAKITA M,KAMAMICHI N,et al.A novel gait generation for biped walking robots based on mechanical energy constraint[J].IEEE Transactions on Robotics and Automation,2004,20(3):565-573.
[14] COLLINS S,RUINA A,TEDRAKE R,et al.Efficient bipedal robots based on passive-dynamic walkers[J].Science,2005,307(5712):1082-1085.
[15] SATOH S,FUJIMOTO K,HYON S.A framework for optimal gait generation via learning optimal control using virtual constraint[C]//Proceedings of the 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems.Nice:IEEE,2008:3426-3432.
[16] FUJIMOTO K,SUGIE T.Iterative learning control of hamiltonian systems:I/O based optimal control approach[J].IEEE Transactions on Automatic Control,2003,48(10):1756-1761.
[17] SHIN H K,KIM B K.Energy-efficient gait planning and control for biped robots utilizing vertical body motion and allowable ZMP region[J].IEEE Transactions on Industrial Electronics,2015,62(4):2277-2286.
[18] MCENEANEY W,DOWER P.The principle of least action and fundamental solutions of mass-spring and n-body two-point boundary value problems[J].SIAM Journal on Control and Optimization,2015,53(5):2898-2933.
[19] CRISTIANI E,MARTINON P.Initialization of the shooting method via the Hamilton-Jacobi-bellman approach[J].Journal of Optimization Theory and Applications,2010,146(2):321-346.
[20] GUIBOUT V,SCHEERES D J.Solving relative two point boundary value problems:spacecraft formation flight transfers application[J].Journal of Guidance, Control, and Dynamics,2004,27(4):693-704.
[21] PARK C,SCHEERES D J.Determination of optimal feedback terminal controllers for general boundary conditions using generating functions[J].Automatica, 2006,42(5):869-875.
[22] HAO Z,FUJIMOTO K.Approximate solutions to the Hamilton-Jacobi equations for generating functions with a quadratic cost function with respect to the input[C]//Proceedings of the 4th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control. Bertinoro:Elsevier, 2012:194-199.
[23] HAO Z,FUJIMOTO K,HAYAKAWA Y.Optimal trajectory generation for linear systems based on double generating functions[J].SICE Journal of Control,Measurement,and System Integration, 2012, 6(3):194-201.
[24] GEERING H P.Optimal control with engineering applications[M]. 1st ed. Berlin:Springer,2007:24-35.
[25] HURMUZLU Y,CHANG T H.Rigid body collisions of a special class of planar kinematic chains[J].IEEE Transactions on Systems, Man, and Cybernetics,1992,22(5):964-971. |
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