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biomechanik:modellierung:mm4:em

Extended models (Model zoo)


Module-Icon TMIP IP Extended models
Event none
Author Maziar A. Sharbafi
Requirements Module TM, TMSLIP and TMIP
teaching time 45 min
Last modified 11.7.2017

This part and also the next two parts EMSLIP and EMIP are basically a summarized version of subchapter 3.6 of a book chapter recently published which is edited by Maziar Sharbafi and Andre Seyfarth titled: Bioinspired legged locomotion. The book can be found here and a complete description of these models can be found in the last subchapter of the third chapter of this book.

Template models usually have limitations in describing different features of locomotion. For example, SLIP model cannot describe posture control. Therefore, these model should be minimally extended that can describe the required features. In this section, we will describe how simplified models can be subsequently extended in order to increase the level of more detail of the simulation models.

Whereas complex simulation models are often directly related to the structure of the human body (body segments corresponding to bones, muscles, tendons and other soft tissues) the design of !!simplified models highly depend on mechanical intuition like in the inverted pendulum (IP) model (Cavagna et al. 1963), the lateral leg spring (LLS) model (Schmitt and Holmes, 2000) or the spring-loaded inverted pendulum (SLIP) model (Blickhan, 1989; McMahon and Cheng, 1990). These models are focusing on describing the axial leg function as a simple telescopic leg spring, with either a constant leg length during stance (IP model) or a leg force proportional to the amount of leg compression (LLS or SLIP model). The assumption of spring-like leg function can be found in approximation experimentally both in animals (Blickhan and Full, 1993) and humans (Lipfert 2009) during steady state locomotion. However, there are also clear deviations in the locomotion dynamics that are not well described by these simple models.

The key limitations of both the IP model and the SLIP model as the most common template models for legged locomotion are summarized in Table 1. Corresponding model extensions that are suitable to overcome these limitations are also presented. It is important to note that we only select elementary extensions of the model, however, also combinations of the model extensions are possible to consider, like XT-SLIP (Sharbafi et al. 2013a) which is an extended SLIP model with trunk (T-SLIP), and added leg mass (M-SLIP) or the ballistic walking model presented of Mochon and McMahon (1980). Model extensions can address either mechanics or control of the system. Another class of model extensions comprises muscles (e.g. single-joint and two-joint muscles with muscle fiber-tendon dynamics) and neural circuits (e.g. sensory feedback pathways) describing muscle stimulation and integration of sensory signals. A sophisticated extension of the SLIP model including muscles, reflex pathways and segmented legs is the gait model of Geyer and Herr (Geyer and Herr, 2010), which originates on the neuro-muscular model introduced by Geyer et al., (2003).


The extensions of IP and SLIP models described in this subchapter (Table 1) are shown in Fig. 1 and Fig. 2, respectively. The reasoning of the different extensions in both templates is often similar. In the following we will describe selected model extensions in more detail. We will start with model extensions regarding the leg structure, followed with model describing the dynamics of the trunk and finally models including lateral leg placements and locomotion in 3D.


Fig.1.Extensions of the sagittal SLIP model with selected added model features: foot segment (F-SLIP); number of legs (bipedal B-SLIP, quadrupedal Q-SLIP etc); leg masses (M-SLIP); segmented legs, 2 and 3 leg segments; swing leg dynamics as pendulum, spring loaded pendulum SLP or two-segmented swing leg; control for varying leg spring properties during stance (VLS-SLIP), at mid-stance (E-SLIP) or continuous control during step (CT-SLIP); added trunk (T-SLIP); muscle-like leg function (leg muscle) and different reflex pathways (force, length and velocity feedback) and lateral movements (3D SLIP). Each of these model extensions can be considered as a separate or in combination with others e.g., BT-SLIP. Gray color indicates control features of SLIP based models.


Fig. 2. Extensions of the sagittal inverted pendulum (2D IP) model with selected added model features: hip spring between both legs, foot (flat or curved) attached to the lower end of the IP, swing leg dynamics by adding leg masses, segmented swing leg or rimless wheel model, linear inverted pendulum (LIP) with leg force law, including lateral movements (3D IP), and adding trunk. Different control policies can be applied to each of these model extensions, e.g. the capture point concept for LIP model (Pratt et al., 2006).

Exercise:

  1. How can you categorize extensions on SLIP model regarding the locomotor subfunctions?
  2. How can you categorize extensions on IP model regarding the locomotor subfunctions?

References:

Blickhan, R. (1989). The spring-mass model for running and hopping. Journal of biomechanics, 22(11-12), 1217-1227.

Blickhan, R., & Full, R. J. (1993). Similarity in multilegged locomotion: bouncing like a monopode. Journal of Comparative Physiology A, 173(5), 509-517.

Cavagna, G., Saibene, F., & Margaria, R. (1963). External work in walking. Journal of Applied Physiology, 18, 1–9.

Geyer, H., Seyfarth, A., & Blickhan, R. (2003). Positive force feedback in bouncing gaits?. Proceedings of the Royal Society of London B: Biological Sciences, 270(1529), 2173-2183.

Geyer, H., & Herr, H. (2010). A muscle-reflex model that encodes principles of legged mechanics produces human walking dynamics and muscle activities. IEEE Transactions on neural systems and rehabilitation engineering, 18(3), 263-273.

McMahon, T. A., & Cheng, G. C. (1990). The mechanics of running: how does stiffness couple with speed?. Journal of biomechanics, 23, 65-78.

Mochon, S., & McMahon, T. A. (1980). Ballistic walking. Journal of biomechanics, 13(1), 49-57.

Pratt, J., Carff, J., Drakunov, S., & Goswami, A. (2006). Capture point: A step toward humanoid push recovery. In 2006 6th IEEE-RAS international conference on humanoid robots (pp. 200-207). IEEE.

Schmitt, J., & Holmes, P. (2000). Mechanical models for insect locomotion: dynamics and stability in the horizontal plane I. Theory. Biological cybernetics, 83(6), 501-515.

Sharbafi, M. A., Maufroy, C., Ahmadabadi, M. N., Yazdanpanah, M. J., & Seyfarth, A. (2013a). Robust hopping based on virtual pendulum posture control. Bioinspiration & biomimetics, 8(3), 036002.

Sharbafi, M. A., Ahmadabadi, M. N., Yazdanpanah, M. J., Mohammadinejad, A., & Seyfarth, A., (2013b) “Compliant hip function simplifies control for hopping and running,” in IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

biomechanik/modellierung/mm4/em.txt · Zuletzt geändert: 28.11.2022 00:58 von 127.0.0.1


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