自平衡立方体机器人动力学建模

Dynamic Modeling of a Self-balancing Cubical Robot

针对立方体机器人自平衡控制问题,对其以棱边为支点的动力学建模问题进行了研究.以所设计的立方体机器人样机为具体研究对象,分别采用拉格朗日方法和凯恩方法建立起相应的动力学模型,通过比较2种方法的建模结果和数值仿真分析,从理论上验证了所建立模型的正确性.基于建立的模型设计了平衡控制器,并将其应用于立方体机器人样机控制,取得了预期的效果,再次验证所建立模型的正确性.所建立的动力学模型,为进一步研究立方体机器人的平衡控制奠定了基础.

Aiming at the problem of self-balancing control of a cubical robot,this paper researched the dynamic modeling of the cubical robot balancing on its edge. Using the prototype of cubical robot built as the subject,the dynamic model was derived with Lagrange method and Kane method. The correctness of the model was verified in theory by comparison of the two methods and numerical simulation. The controller designed based on the mathematical model was used in balance control of the physical cubical robot prototype. The correctness of the model was verified again with the expected effect. This dynamic model can provide a base for further study of balance control of a cubical robot balancing on its corner.