Ground Reference Points in Legged Locomotion: Definitions, Biological Trajectories and Control Implications

By Marko B. Popovic, Ambarish Goswami, Hugh M. Herr. Int. J. Robotics Res., 2005

360 citations recorded by the source corpus.

The zero moment point (ZMP), foot rotation indicator (FRI) and centroidal moment pivot (CMP) are important ground reference points used for motion identification and control in biomechanics and legged robotics. In this paper, we study these reference points for normal human walking, and discuss their applicability in legged machine control. Since the FRI was proposed as an indicator of foot rotation, we hypothesize that the FRI will closely track the ZMP in early single support when the foot remains flat on the ground, but will then significantly diverge from the ZMP in late single support as the foot rolls during heel-off. Additionally, since spin angular momentum has been shown to remain small throughout the walking cycle, we hypothesize that the CMP will never leave the ground support base throughout the entire gait cycle, closely tracking the ZMP. We test these hypotheses using a morphologically realistic human model and kinetic and kinematic gait data measured from ten human subjects walking at self-selected speeds. We find that the mean separation distance between the FRI and ZMP during heel-off is within the accuracy of their measurement (0.1% of foot length). Thus, the FRI point is determined not to be an adequate measure of foot rotational acceleration and a modified FRI point is proposed. Finally, we find that the CMP never leaves the ground support base, and the mean separation distance between the CMP and ZMP is small (14% of foot length), highlighting how closely the human body regulates spin angular momentum in level ground walking.

Subfields: Biomedical Engineering

View Paper: https://www.semanticscholar.org/paper/2558f2943310f250aa339d74619de082c35e1789

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In Biomedical Engineering

Citations in the corpus

Capturability-based analysis and control of legged locomotion, Part 1: Theory and application to three simple gait models (2011, methodology): “(30b) The point rCMP is the centroidal moment pivot (CMP) as defined in Popovic et al. (2005).”
Centroidal dynamics of a humanoid robot (2013, background): “However, it was much later before its importance for balance maintenance for humans and humanoid robots started to be seriously explored (Nishiwaki et al. 2002; Goswami and Kallem 2004; Naksuk et al. 2004, 2005; Komura et al. 2005; Abdallah and Goswami 2005; Popovic et al. 2004, 2005).”
Models, feedback control, and open problems of 3D bipedal robotic walking (2014, background): “Additional information on ZMP-based methods and related ground reference points is given in [53, 205, 207, 145].”
Feedback Control of Dynamic Bipedal Robot Locomotion (2007, background): “The reader seeking further information on the ZMP and other ground reference points, such as the FRI, is referred to [177,234] and references therein.”
Three-Dimensional Bipedal Walking Control Based on Divergent Component of Motion (2015, background): “The eCMP is closely related to the CMP [27] but not restricted to the foot plane or ground surface.”
Lower Extremity Exoskeletons and Active Orthoses: Challenges and State-of-the-Art (2008, methodology): “Details of the experimental methods used to capture these data can be found in [5].”
Humanoid push recovery (2007, background): “In fact, there have been numerous attempts to identify important “points” in humanoid balancing and locomotion [8].”
Capturability-based analysis and control of legged locomotion, Part 2: Application to M2V2, a lower-body humanoid (2012, methodology): “Here we have used the fact that the CoP is equal to the Zero Moment Point when the ground is flat and horizontal [20].”
Heuristic Planning for Rough Terrain Locomotion in Presence of External Disturbances and Variable Perception Quality (2018, neutral): “(38) in an explicit form28, we get [51]: { ∆xcomx = 1 fextz−mg [ fextx(xcomz − xzmpz) + τexty ]”