以角为支点平衡的立方体机器人动力学建模

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.