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Summer Report 2009

Anirudha Majumdar

The Spring Loaded Inverted Pendulum (SLIP) template, illustrated in Figure 1, has been used with a large degree of success to describe the COM dynamics of several animals [1]. It has been hypothesized that the anchoring of SLIP in animals results in locomotion that is energy efficient [1]. Over the last few months, I have worked with Dr. Haldun Komsuoglu and Yasemin Ozkan Aydin to test this hypothesis using the EduBot, a R-Hex-like robot that has six actively driven C-shaped compliant legs. It has been our goal to find a correlation between specific resistance [2] (a standard measure of locomotion efficiency) and the SLIP-ness of a gait. Specific resistance is defined as follows:

where P_av is the average power consumed and v_av is the average speed. m and g are the mass of the robot and acceleration due to gravity respectively. The SLIP-ness of a gait is characterized by the fitting error of the SLIP model fitted to the COM trajectory of the robot.

The Vicon system was used to track the geometric center (assumed to be the same as the COM) of the robot. The raw data from the Vicon system is passed through a post-processing pipeline that first performs a homogeneous transformation to allow us to consider the COM trajectory in the co-ordinate frame attached to the ground (instead of the Vicon’s co-ordinate system). Then, the co-ordinate system is re-oriented in order to obtain the COM trajectory in the sagittal plane. Finally, a non-linear regression is performed to fit the SLIP template to the robot’s COM trajectory during each stance of a run.

Four gaits, with different specific resistances were chosen and their respective fits to the SLIP model were compared. Our results provide evidence for a strong correlation between SLIP-ness and specific resistance. Figure 2 shows specific resistance (SR) vs normalized SLIP model fit error (nerr).The data points are color-coded according to the associated gaits. As the plot illustrates, there appears to be a monotonic relationship between SR and nerr.


[1] P. Holmes, R. J. Full, D. Koditschek, and J. Guckenheimer, dynamics of legged locomotion: Models, analyses, and challenges, SIAM Review, vol. 48, no. 2, May 2006.

[2] Gabrielli, G. and von Karman, Th., What price speed?, Mechanical Engineering, Vol 72, 1950.

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