Karagoz O K, Secer G, Ankarali M M, Saranli U
Electrical and Electronics Engineering Department, Middle East Technical University, Ankara, Turkey.
Robotics and Artificial Intelligence Technologies Application and Research Center (ROMER), Middle East Technical University, Ankara, Turkey.
Bioinspir Biomim. 2022 May 26;17(4). doi: 10.1088/1748-3190/ac6d97.
The spring-loaded inverted pendulum model has been one of the most studied conceptual models in the locomotion community. Even though it can adequately explain the center of mass trajectories of numerous legged animals, it remains insufficient in template-based control of complex robot platforms, being unable to capture additional dynamic characteristics of locomotion exhibited in additional degrees of freedom such as trunk pitch oscillations. In fact, analysis of trunk behavior during locomotion has been one of the motivations behind studying the virtual pivot point (VPP) concept, with biological inspiration and basis for both natural and synthetic systems with non-negligible trunk dynamics. This study first presents a comprehensive analysis of the VPP concept for planar running behaviors, followed by a systematic study of the existence and characteristics of periodic solutions. In particular, we investigate how periodic solutions depend on model control parameters and compare them based on stability and energetic cost. We then develop a feedback controller that can stabilize system dynamics around its periodic solutions and evaluate performance as compared to a previously introduced controller from the literature. We demonstrate the effectiveness of both controllers and find that the proposed control scheme creates larger basins of attraction with minor degradation in convergence speed. In conclusion, this study shows that the VPP concept, in conjunction with the proposed controller, could be beneficial in designing and controlling legged robots capable of running with non-trivial upper body dynamics. Our systematic analysis of periodic solutions arising from the use of the VPP concept is also an important step towards a more formal basis for comparisons of the VPP concept with bio-locomotion.
弹簧加载倒立摆模型一直是运动学界研究最多的概念模型之一。尽管它能够充分解释众多有腿动物的质心轨迹，但在基于模板的复杂机器人平台控制方面仍显不足，无法捕捉诸如躯干俯仰振荡等额外自由度所展现的运动的其他动态特性。事实上，对运动过程中躯干行为的分析一直是研究虚拟枢轴点（VPP）概念的动机之一，它为具有不可忽略的躯干动力学的自然和合成系统提供了生物学灵感及基础。本研究首先对平面跑步行为的VPP概念进行了全面分析，随后对周期解的存在性和特性进行了系统研究。特别是，我们研究了周期解如何依赖于模型控制参数，并基于稳定性和能量消耗对它们进行比较。然后，我们开发了一种反馈控制器，该控制器能够围绕其周期解稳定系统动力学，并与文献中先前引入的控制器相比评估性能。我们证明了这两种控制器的有效性，并发现所提出的控制方案在收敛速度略有下降的情况下创建了更大的吸引域。总之，本研究表明，VPP概念与所提出的控制器相结合，可能有助于设计和控制能够在具有复杂上身动力学的情况下奔跑的有腿机器人。我们对使用VPP概念产生的周期解进行的系统分析，也是朝着为VPP概念与生物运动的比较建立更正式基础迈出的重要一步。
