中文摘要：

提出了一种柔性双轮平衡机器人，其机身具有以一段弹簧作为弹性阻尼的被动俯仰旋转关节．运用拉格朗日方法建立了此机器人在平面运动的动力学模型．基于此模型，首先证明了柔性双轮平衡机器人在直立平衡点不稳定和局部可控．其次，分析了关节刚度对线性二次型最优姿态平衡控制系统的影响．结果显示，关节刚度减小在理论上能够加强系统的鲁棒性，却使得控制系统动态性能下降．本文提出的模型及相关分析为柔性双轮平衡机器人的设计和控制提供了一定理论依据．

英文摘要：

This paper presents a kind of FTWBR （flexible two-wheeled balancing robot）. Its main body has a passive pitch-joint which contains a spring as elastic damping. The Lagrange approach is used to formulate the dynamic model of the robot moving in plane. Based on the model, it is proved firstly that FTWBR is unstable and locally controllable at upright equilibrium state. Secondly, the impact of joint-stiffness on the linear quadratic optimal posture balancing control system is analyzed. The result demonstrates that the decrease of the joint-stiffness will improve the robustness of the control system theoretically, but it degrades the dynamic performance of the control system. The proposed dynamic model and the analysis provide some theoretical basis for designing and controlling FTWBR.