中文摘要：

弹簧负载倒立摆（spring loaded inverted pendulum，SLIP）模型动力学分析缺乏有效解析化处理手段，为此提出一种基于摄动理论的SLIP模型支撑相动力学近似解求解方法．建立了飞行相顶点高度的Poincare映射，从而获得了SLIP模型动力学完整的解析化描述，通过误差分析验证了基于近似解析解的顶点高度预测值具有良好的数值逼近精度．在此基础上针对SLIP弹跳系统的运动控制，设计了基于Poincare逆映射的SLIP系统顶点高度无差拍控制器，并进行了阶跃期望轨迹跟踪实验．实验结果表明：本文所提出的算法具有快速跟踪期望轨迹的控制效果，同时可以有效抑制系统超调．此外，对质心水平速率实验曲线的分析证明算法在控制弹跳速率与高度间具有等效性，扩展了算法的应用范围．

英文摘要：

An approximate analytical solution of SLIP （spring loaded inverted pendulum） model dynamics in stance phase is proposed based on perturbation theory, aiming at resolving the lack of analytical method to deal with SLIP model dynamics. The Poincare map of apex height in flight phase is established through which the entire dynamics of SLIP model is derived analytically. The error analysis results indicate that the prediction of apex height with approximate solution possesses high approximation precision. Aiming at the locomotion control of SLIP hopper, the deadbeat controller for apex height of SLIP system is designed based on the inverse Poincare map. The tracking simulation of desired step signal is implemented to show that the algorithm proposed in this paper not only can track the desired trajectory but also inhibits overshoot effectively. Furthermore, the equivalence of apex velocity control and height control is verified through analyzing the experiment curve of horizontal velocity of the center of mass, which extends the application range of the algorithm.