A model-based strategy for quadruped running with differentiated fore- and hind leg morphologies

2021 ◽  
Author(s):  
Kuan-Yu Tseng ◽  
Pei-Chun Lin
Keyword(s):  
Ground Reaction Force ◽  
Reaction Force ◽  
Basins Of Attraction ◽  
Quadruped Robot ◽  
Model Based ◽  
Proposed Model ◽  
Point Motion ◽  
Leg Motion ◽  
Natural Dynamics ◽  
Leg Morphology

Abstract This article introduces a model-based strategy for a quadruped robot with differentiated fore- and hind-leg ground reaction-force patterns to generate animal-like running behavior. The proposed model comprises a rigid body and two eSLIP legs with dampers. The eccentric-SLIP (eSLIP) model extends the traditional spring-loaded inverted pendulum (SLIP) model by adding a bar to offset the spring direction. The proposed two-leg eSLIP (TL-eSLIP) model’s fore- and hind legs were designed to have the same offset magnitude but in opposite offset directions, producing different braking and thrusting force patterns. The TL-eSLIP model’s reference leg trajectories were designed based on the fixed-point motion of the eSLIP model. Additionally, the legs were clock torque-controlled to modulate leg motion and stabilize the model to follow its natural dynamics. The model’s equations for motion were derived, and the model’s dynamic behavior was simulated and analyzed. The simulation results indicate that the model with leg offsets and in either trotting or pronking has differentiated leg force patterns, and it is more stable and has larger basins of attraction than the model without leg offsets. A quadruped robot was built for experimental validation. The experimental results demonstrate that the robot with differentiated legs ran with differentiated ground reaction force patterns and ran more stably than another robot with the same leg morphology.

A Modified Dugoff Tire Model for Combined-slip Forces

2010 ◽  
Vol 38 (3) ◽  
pp. 228-244 ◽  
Author(s):  
Nenggen Ding ◽  
Saied Taheri
Keyword(s):  
Vehicle Dynamics ◽  
Tire Model ◽  
Magic Formula ◽  
Model Based ◽  
Proposed Model ◽  
Road Friction ◽  
On Line ◽  
Double Lane Change ◽  
Tire Forces ◽  
Tire Models

Abstract Easy-to-use tire models for vehicle dynamics have been persistently studied for such applications as control design and model-based on-line estimation. This paper proposes a modified combined-slip tire model based on Dugoff tire. The proposed model takes emphasis on less time consumption for calculation and uses a minimum set of parameters to express tire forces. Modification of Dugoff tire model is made on two aspects: one is taking different tire/road friction coefficients for different magnitudes of slip and the other is employing the concept of friction ellipse. The proposed model is evaluated by comparison with the LuGre tire model. Although there are some discrepancies between the two models, the proposed combined-slip model is generally acceptable due to its simplicity and easiness to use. Extracting parameters from the coefficients of a Magic Formula tire model based on measured tire data, the proposed model is further evaluated by conducting a double lane change maneuver, and simulation results show that the trajectory using the proposed tire model is closer to that using the Magic Formula tire model than Dugoff tire model.

scholarly journals Running ground reaction forces across footwear conditions are predicted from the motion of two body mass components

2019 ◽  
Vol 126 (5) ◽  
pp. 1315-1325 ◽  
Author(s):  
Andrew B. Udofa ◽  
Kenneth P. Clark ◽  
Laurence J. Ryan ◽  
Peter G. Weyand
Keyword(s):  
Ground Reaction Force ◽  
Lower Limb ◽  
Reaction Force ◽  
Ground Reaction Forces ◽  
Vertical Ground Reaction Force ◽  
Time Patterns ◽  
Foot Strike ◽  
Reaction Forces ◽  
Vertical Ground ◽  
Force Time

Although running shoes alter foot-ground reaction forces, particularly during impact, how they do so is incompletely understood. Here, we hypothesized that footwear effects on running ground reaction force-time patterns can be accurately predicted from the motion of two components of the body’s mass (mb): the contacting lower-limb (m1 = 0.08mb) and the remainder (m2 = 0.92mb). Simultaneous motion and vertical ground reaction force-time data were acquired at 1,000 Hz from eight uninstructed subjects running on a force-instrumented treadmill at 4.0 and 7.0 m/s under four footwear conditions: barefoot, minimal sole, thin sole, and thick sole. Vertical ground reaction force-time patterns were generated from the two-mass model using body mass and footfall-specific measures of contact time, aerial time, and lower-limb impact deceleration. Model force-time patterns generated using the empirical inputs acquired for each footfall matched the measured patterns closely across the four footwear conditions at both protocol speeds ( r2 = 0.96 ± 0.004; root mean squared error  = 0.17 ± 0.01 body-weight units; n = 275 total footfalls). Foot landing angles (θF) were inversely related to footwear thickness; more positive or plantar-flexed landing angles coincided with longer-impact durations and force-time patterns lacking distinct rising-edge force peaks. Our results support three conclusions: 1) running ground reaction force-time patterns across footwear conditions can be accurately predicted using our two-mass, two-impulse model, 2) impact forces, regardless of foot strike mechanics, can be accurately quantified from lower-limb motion and a fixed anatomical mass (0.08mb), and 3) runners maintain similar loading rates (ΔFvertical/Δtime) across footwear conditions by altering foot strike angle to regulate the duration of impact. NEW & NOTEWORTHY Here, we validate a two-mass, two-impulse model of running vertical ground reaction forces across four footwear thickness conditions (barefoot, minimal, thin, thick). Our model allows the impact portion of the impulse to be extracted from measured total ground reaction force-time patterns using motion data from the ankle. The gait adjustments observed across footwear conditions revealed that runners maintained similar loading rates across footwear conditions by altering foot strike angles to regulate the duration of impact.

A new path loss model based on the volumetric occupancy rate for the pine forests at 5G frequency band

2020 ◽  
pp. 1-10
Author(s):  
Abdullah Genc
Keyword(s):  
Path Loss ◽  
Forest Area ◽  
Occupancy Rate ◽  
Loss Model ◽  
Path Loss Model ◽  
Model Based ◽  
Proposed Model ◽  
Pine Trees ◽  
Foliage Density ◽  
Reference Measurements

Abstract In this paper, a new empirical path loss model based on frequency, distance, and volumetric occupancy rate is generated at the 3.5 and 4.2 GHz in the scope of 5G frequency bands. This study aims to determine the effect of the volumetric occupancy rate on path loss depending on the foliage density of the trees in the pine forest area. Using 4.2 GHz and the effect of the volumetric occupancy rate contributes to the literature in terms of novelty. Both the reference measurements to generate a model and verification measurements to verify the proposed models are conducted in three different regions of the forest area with double ridged horn antennas. These regions of the artificial forest area consist of regularly sorted and identical pine trees. Root mean square error (RMSE) and R-squared values are calculated to evaluate the performance of the proposed model. For 3.5 and 4.2 GHz, while the RMSEs are 3.983 and 3.883, the values of R-squared are 0.967 and 0.963, respectively. Additionally, the results are compared with four path loss models which are commonly used in the forest area. The proposed one has the best performance among the other models with values 3.98 and 3.88 dB for 3.5 and 4.2 GHz.

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