Analysis and control of a running spring-mass model with a trunk based on virtual pendulum concept

Karagoz, O K
Secer, G
Ankaralı, Mustafa Mert
Saranli, U
© 2022 IOP Publishing Ltd.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.
Bioinspiration & biomimetics


Sever Gökmen, İzel; Ankaralı, Mustafa Mert; Saranlı, Uluç; Department of Electrical and Electronics Engineering (2022-2-10)
One of the benchmark models for analyzing legged systems in biology and robotics is the Spring-Loaded Inverted Pendulum (SLIP) template and its extensions. The basic SLIP model consists of a single point mass with an ideal spring connecting it to the ground during the stance phase. After its introduction, this model has received numerous extensions to handle physical constraints that exist in practical configurations, such as the upper body's effect on the system dynamics. Although the SLIP template can des...
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© 2020 IEEE.The Spring-Loaded Inverted Pendulum (SLIP) template and its extensions have long been used as benchmark models for analyzing the dynamics of legged systems in biology and robotics. The fundamental SLIP model is composed of single point mass attached to the ground (during stance phase) via an ideal lossless spring. Many researchers introduced various extensions to this fundamental model, such as damping torque actuation, to handle critical physical phenomena that are unavoidable in real systems. ...
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Citation Formats
O. K. Karagoz, G. Secer, M. M. Ankaralı, and U. Saranli, “Analysis and control of a running spring-mass model with a trunk based on virtual pendulum concept,” Bioinspiration & biomimetics, vol. 17, no. 4, pp. 0–0, 2022, Accessed: 00, 2022. [Online]. Available: