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biomechanik:modellierung:mm4:tmslip

# SLIP model and locomotor subfunctions

Module-Icon TMSLIP SLIP model and locomotor subfunctions none Maziar A. Sharbafi Module TBM and TM 45 min 11.7.2017

In this section, we discuss the properties of the SLIP model. Based on the locomotor subfunction concept, we divide this section to three subsections and explain the abilities and limitations of the SLIP model in addressing each subfunction. Then some solutions to extend this model are presented.

#### Stance locomotor subfunction in SLIP

Stance as the first locomotor subfunction is defined as the axial function of the stance leg in interaction with the ground. In Fig. 1, the leg force-length relationship is illustrated for human walking nad running at different speeds. It can be seen that in running the curves can be acceptably approximated by straight lines, while in walking they are more nonlinear. This means that the spring in SLIP model can predict human running sufficiently precise. However, for walking, we need to adapt the stiffness and rest length. In [Sharbafi 2017], two springs are used to approximate leg force-length relationship in single support at different speeds (see Fig. 2). These results show that although SLIP can predict GRF and CoM motion, it needs to extend to better represent stance leg function in walking

Figure 1. Leg force-length relationship for walking and running at different speeds ((from Lipfert 2010]).

There are extended models of SLIP concentrating on changing the leg spring stiffness and rest lengths to better predict human gaits even for hopping and running (e.g., ESLIP [Ludwig 2010] and VLS [Riese 2013]). We discuss more about these models in Extended models (Model zoo).

Figure 2. Leg force-length relation in single support of walking and its approximation by two lines (variable stiffness and rest length).

#### Swing locomotor subfunction in SLIP

In the basic SLIP model, the swing leg just determines the angle of attack (the configuration of the swing leg at the moment of touchdown). As the legs are massless in this model, not controller is used to adjust the swing leg motion. However, studies on models and human gaits show the way of reaching this target angle at touchdown is important in increasing the stability of the gait. In [Seyfarth 2003], swing leg retraction (SLR) was implemented on the SLIP model in a simple way (see Fig. 3). SLR is defined by the downward movement of the swing leg just before touchdown. In this paper, the swing leg angle is set to an initial value at apex and starts to decrease with a constant angular speed. As can be seen in Fig. 3, the region of stability is increased by growing the angular speed ($\omega_R$).

Figure 3. Swing leg retraction and its effects on stability.

In [Poggensee2014], human walking and running are investigated regarding the occurrence and variation patterns of SLR in human walking and running. As can be seen in Fig. 4, not only the existence, but also the linear relation between the motion speed and the swing leg retraction speed can be realized in human walking and running.

Figure 4. Swing leg retraction and gait speed relation for walking and running.

There are many methods for swing leg adjustment. In contrast to steady state gaits, fixed angle of attack does not work on uncertain (e.g. on rough terrain) and perturbed gaits. In order to adapt the leg angle during leg swinging to increase robustness against perturbations, state feedback can be used [Raibert 1986]. In most of such control strategies, the foot landing position is adjusted based on the horizontal velocity [Poulakakis 2009] [Sato 2004]. In [Sharbafi 2016, three control approaches for swing leg adjustment were compared through their abilities in predicting human swing leg adjustment strategy and also their robustness against perturbation at different gaits using SLIP-based simulation models. Fig. 5 shows these three methods(VBLA (Velocity based leg adjustment), Peuker and Raiert approaches) schematically.

Figure 5. Three different swing leg adjustment approaches compared in Shrabfi et al. 2016.

It was shown that VBLA is the best in mimicking human leg adjustment in walking perturbed hopping, achieve the largest range of running velocities by a fixed controller and provide a robust walking in simulation model with BSLIP model. From analytical point of view the main advantage of this approach is that it uses both elements of the velocity vector, the magnitude and the angle (or horizontal and vertical elements). This provides an ability to react properly to any perturbations and increase the region of stability. This was tested by SLIP and BSLIP model for running and walking, respectively. As an important task in locomotion, it can be merged with other control techniques for stance phase like balancing and leg length adjustment for more complex models, e.g., with extended trunk TSLIP for running and hopping (see Extended models (Model zoo)) and BTSLIP for walking (see Extended models (Model zoo)).

From the experimental side of view, VBLA can unify the human-like swing leg adjustment control at a certain speed, for human subjects with different body parameters in walking and perturbed hopping. This model was also implemented on a simulation model of BioBiped robot as one of the locomotion sub-function controllers resulting in stable forward hopping [Sharbafi 2014]. In addition to control of bipedal robots, this method can be easily implemented on exoskeleton to assist (impaired) humans in foot placement.

#### Balance locomotor subfunction in SLIP

In SLIP model, leg force is assumed to be proportional to the amount of leg compression, i.e. the shortening of the leg length measured between CoM and the contacting point at the ground. Therefore, this model assumes that leg forces are directed towards the CoM. However, experimental data indicate that measured leg forces do not point exactly to the CoM but sometimes intersect at a point above it, called virtual pivot point (VPP, [Maus 2010]) or divergent point (DP, [Gruben 2012]). In order to represent this observation in the model, the SLIP must be extended to include a model of the upper body. It is modeled by addition of a rigid trunk to SLIP. Then, hip torques can be calculated to deviate forces generated by the leg spring to intersect at the VPP and stabilization of the upright posture (or posture control ) can be achieved. In this model, the hip torque depends on the amount of the leg force and the angular orientation of the leg with respect to the trunk. This means that traditional SLIP cannot address balancing subfunction and it needs to be extended to describe this third locomotor subfunction.

In Extended models (Model zoo), we present the TSLIP (Trunk+SLIP) model and further extensions which are required for explaining posture control. Most of the posture control methods sitting on top of such models rely on the feedback control of the trunk orientation with respect to an absolute referential frame. In contrary, this VPP-based control scheme was shown to be capable of supporting upright trunk posture during locomotion without the need to explicitly measure the trunk orientation with respect to the gravity direction. Similar to adjustment of leg parameters (e.g. leg stiffness/rest length) for stance control in the SLIP model, the position of the VPP can be considered as a control target. This approach was validated in simulations, where it yielded stable upright walking and running patterns [Sharbafi 2013].

### Exercise:

1. Based on the force-length curves in Fig. 1, could you suggest an appropriate template model (for stance subfunction) in running?
2. Is your suggested template in the previous exercise appropriate for walking as well?If not, what modifications do you suggest to make it useful for walking?
3. If the angle of attack is the same in the model with fixed angle of attack and with swing leg retraction (SLR), how SLR can increase the stability range of the model?
4. Can you find a relation the swing leg retraction and impact at touchdown? IS SLR useful for reducing impacts? Then what do you predict for relation between SLR speed and the motion speed?
5. There are studies showing the advantages of VBLA compared to Peuker or Raibert approaches for swing leg adjustment. How do you justify that?
6. How does SLIP model confront balance subfunction of locomotion?

### References

[Gruben 2012] K. G. Gruben and W. L. Boehm, „Force direction pattern stabilizes sagittal plane mechanics of human walking,“ Human Movement Science, vol. 31, no. 3, pp. 649-659, 2012.

[Maus 2010] H. M. Maus, S. Lipfert, M. Gross, J. Rummel, and A. Seyfarth, „Upright human gait did not provide a major mechanical challenge for our ancestors,“ Nature Communications, vol. 1, no. 6, pp. 1-6, 2010.

[Poulakakis 2009] I. Poulakakis and J. W. Grizzle, “The spring loaded inverted pendulum as the hybrid zero dynamics of an asymmetric hopper,” IEEE Transaction on Automatic Contro, vol. 54, no. 8, pp. 1779–1793, 2009.

[Raibert 1986] M. H. Raibert, Legged Robots that Balance. MIT Press, Cambridge MA, 1986.

[Sato 2004] A. Sato, “A planar hopping robot with one actuator: design, simulation, and experimental results,” in IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2004.

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

[Sharbafi 2014] M. A. Sharbafi, K. Radkhah, O. von Stryk, and A. Seyfarth, “Hopping control for the musculoskeletal bipedal robot: Biobiped,” in 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems. IEEE, 2014, pp. 4868–4875.

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

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