Abstract In this paper the effect of different parameters on the periodic orbits of an under-actuated passive biped is studied. The system is designed to follow a periodic orbit in the phase plane, starting from an initial condition and walking down a slope. The dynamic motion of the system is cast as an optimization problem under constraints that impose the periodicity with optimal behavior. The effect of dynamics and kinematics factors such as inertia and length characteristics of the biped and slope angle on the stability and bifurcation phenomena is extensively studied. In the following, it is shown how an under-actuated arm can perfectly synchronize its stabilizing motion with walking. The effect of dynamics parameters of the arm on the locomotion of the biped, stability criteria and the robustness of the whole system is extensively investigated. The results of the paper clearly illustrate the effects of dynamics parameters as well as the stabilizing arm on the stability, energy, and step characteristics of locomotion.

中文翻译：

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被动动态两足动物的轨道分析；模型参数和稳定臂的影响

摘要 本文研究了不同参数对欠驱动被动双足动物周期轨道的影响。该系统设计为遵循相平面中的周期性轨道，从初始条件开始并沿着斜坡走下。系统的动态运动被转换为约束条件下的优化问题，这些约束强加了具有最佳行为的周期性。广泛研究了动力学和运动学因素，例如双足动物的惯性和长度特性以及倾斜角对稳定性和分叉现象的影响。下面将展示欠驱动臂如何将其稳定运动与步行完美同步。手臂动力学参数对两足动物运动的影响，对整个系统的稳定性标准和稳健性进行了广泛的研究。论文的结果清楚地说明了动力学参数以及稳定臂对运动稳定性、能量和步进特性的影响。