以角为支点平衡的立方体机器人动力学建模
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摘要
针对立方体机器人的平衡控制问题,建立其以角为支点平衡的动力学模型.以所设计的物理样机为具体研究对象,在分析其运动学原理的基础上,定义了表达系统运动属性所需的最少变量,基于拉格朗日方法,对系统的能量函数和广义力进行计算,建立了立方体机器人以其角为支点平衡的动力学模型.通过数值仿真,对所建立模型的正确性进行了理论分析,并将模型与虚拟样机的零输入响应进行对比,响应曲线基本一致,验证了模型的准确性.将基于所建立动力学模型设计的平衡控制器应用于虚拟样机的控制,实验表明,该控制器可有效实现立方体机器人的平衡控制,进一步完成了对模型有效性的验证.建立的动力学模型为后期继续研究立方体机器人平衡控制问题提供了基础.
Aiming at the balancing control problem of a cubical robot,a system balancing on its corner was modeled by taking the physical prototype as research object,and least system variables were defined for expressing system movement attributes. The energy function and generalized forces of the system were calculated,and the dynamic model of the cubical robot balancing on its corner was derived based on Lagrange method. The correctness of the model was analyzed in theory by numerical simulation,and the model precision was verified with basically indetical response results about zero-input experiment in comparision betweeen the model and virtual prototype. A balancing controller designed based on the dynamic model was applied in balancing control of the virtual prototype. The experiment results show that the cubical robot can balance effectively by the controller,then the effectiveness of the model is verified further. The dynamic model provides an important foundation for the further research on balancing control of the cubical robot.
Aiming at the balancing control problem of a cubical robot,a system balancing on its corner was modeled by taking the physical prototype as research object,and least system variables were defined for expressing system movement attributes. The energy function and generalized forces of the system were calculated,and the dynamic model of the cubical robot balancing on its corner was derived based on Lagrange method. The correctness of the model was analyzed in theory by numerical simulation,and the model precision was verified with basically indetical response results about zero-input experiment in comparision betweeen the model and virtual prototype. A balancing controller designed based on the dynamic model was applied in balancing control of the virtual prototype. The experiment results show that the cubical robot can balance effectively by the controller,then the effectiveness of the model is verified further. The dynamic model provides an important foundation for the further research on balancing control of the cubical robot.
引文
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[2]张永立.空间多级倒立摆非线性控制方法研究[D].大连:大连理工大学,2011.ZHANG Y L.Research on nonlinear control technique for spherical multi-rod inverted pendulum system[D].Dalian:Dalian University of Technology,2011.(in Chinese)
[3]BRISILLA R M,SANKARANARAYANAN V.Nonlinear control of mobile inverted pendulum[J].Robotics&Autonomous Systems,2015,70:145-155.
[4]阮晓钢,王旭,陈志刚.独轮机器人的建模与自抗扰控制算法[J].控制与决策,2015,30(12):2253-2258.RUAN X G,WANG X,CHEN Z G.Modeling and active disturbance rejection algorithm of single wheel robot[J].Control and Decision,2015,30(12):2253-2258.(in Chinese)
[5]PAULOS J,ECKENSTEIN N,TOSUN T,et al.Automated self-assembly of large maritime structures by a team of robotic boats[J].IEEE Transactions on Automation Science&Engineering,2015,12(3):958-968.
[6]The Ohio State University.Syllabus[EB/OL].[2018-03-01].http:∥www2.ece.ohio-state.edu/~passino/ee758.html.
[7]田莉.立方体系统的模糊控制算法研究[D].南京:南京理工大学,2006.TIAN L.Research on fuzzy control algorithm of cube system[D].Nanjing:Nanjing University of Science and Technology,2006.(in Chinese)
[8]邱振彬.基于观测器的立方体系统控制研究[D].南京:南京理工大学,2009.QIU Z B.Research on control of cube system based on observer[D].Nanjing:Nanjing University of Science and Technology,2009.(in Chinese)
[9]TRIMPE S,D'ANDREA R.The balancing cube:a dynamic sculpture as test bed for distributed estimation and control[J].IEEE Control Systems,2012,32(6):48-75.
[10]GAJAMOHAN M,MERZ M,THOMMEN I,et al.The cubli:a cube that can jump up and balance[C]∥IEEE/RS International Conference on Intelligent Robots and Systems.Piscataway:IEEE,2012:3722-3727.
[11]MUEHLEBACH M,D’ANDREA R.Nonlinear analysis and control of a reaction-wheel-based 3-D inverted pendulum[J].IEEE Transactions on Control System Technology,2017,25(1):235-246.
[12]KIM S,KWON S J.Dynamic modeling of a two-wheeled inverted pendulum balancing mobile robot[J].International Journal of Control,Automation and Systems,2015,13(4):926-933.
[13]MUEHLEBACH M,GAJAMOHAN M,D’ANDREA R.Nonlinear analysis and control of a reaction wheel-based3D inverted pendulum[C]∥52nd IEEE Conference on Decision and Control.Piscataway:IEEE,2013:1283-1288.
[14]GAJAMOHAN M,MUEHLEBACH M,WIDMER T,et al.The cubli:a reaction wheel based 3D inverted pendulum[C]∥European Control Conference.Piscataway:IEEE,2013:268-274.
[15]陈志刚,阮晓钢,李元.自平衡立方体机器人动力学建模[J].北京工业大学学报,2018,44(3):95-100.CHEN Z G,RUAN X G,LI Y.Dynamic modeling of a self-balancing cubical robot[J].Journal of Beijing University of Technology,2018,44(3):95-100.(in Chinese)
[16]叶敏,肖龙翔.分析力学[M].天津:天津大学出版社,2001:140-158.
[17]OLIVARES M,ALBERTOS P.Linear control of the flywheel inverted pendulum[J].Isa Transactions,2014,53(5):1396-1403.
[18]BLOCK D J,ASTROM K J,SPONG M W.The reaction wheel pendulum[M].Williston:Morgan&Claypool Publishers,2007:1-105.
[19]杜孝平,赵凯琪.基于PID的移动机器人运动控制系统设计与实现[J].通信学报,2016,37(增刊1):43-49.DU X P,ZHAO K Q.Design and implementation of the motion control system of the mobile robot based on PID[J].Journal of Communications,2016,37(Suppl 1):43-49.(in Chinese)
[20]王启源,阮晓钢.独轮自平衡机器人双闭环非线性PID控制[J].控制与决策,2012,27(4):593-597.WANG Q Y,RUAN X G.Dual loop nonlinear PIDcontrol of single-wheeled robot[J].Control and Decision,2012,27(4):593-597.(in Chinese)
[21]YUAN X F,XIANG Y Z,WANG Y,et al.Neural networks based PID control of bidirectional inductive power transfer system[J].Neural Processing Letters,2016,43(3):837-847.