10 Paper discussion + terradynamics 4/25/2018

Transcription

1 10 Paper discussion + terradynamics 4/25/2018

2 Paper discussion

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4 Paper for next Wednesday Next Wednesday we will discuss this paper out in Science last week

5 Terradynamics

6 Lack of Locomotor-Environment Interaction Models for Complex Terrain Biology Physics Engineering Aerodynamics Hydrodynamics Need Terradynamics! Body Leg Spring Spring-Mass Model for Running

7 Terramechanics for off-road vehicle mobility Bekker (1960) Wong (2010) Sand Soil Mud Snow Horizontal plate approximation Vehicle weight Meirion-Griffith (2012) Pressure Depth Lift Sinkage NASA Glenn Research Center Pressure vs. depth Lift Sinkage

8 Limitation of classical terramechanics Inaccurate for highly curved interface e.g., small wheels w/ large sinkage Bekker (1960) Wong (2010) $400M project JPL Lift Sinkage -Over-predict lift -Under-predict sinkage e.g., Mars rover on Martian soil Not expected to work for legs

9 Terramechanics tests focus on controlling vehicle Karl Iagnemma, MIT Control/variation of wheel parameters Oravec Doctoral Dissertation Ground is not precisely prepared 10 steps NASA Glenn Research Center

10 Granular media as model for flowable ground Dry granular media e.g., sand, gravel -Discrete particles -Dissipative, repulsive contact forces Solid- and fluid- like properties Flow Re-solidify Compared to soil, mud, snow: -Relatively uniform -No cohesion Jaeger et al. (1996)

11 Control of granular media by a fluidized bed Uneven, sloped, variable compaction Loosely packed Compaction Closely packed Normalized yield force Flat, level, uniform, adjustable compaction 50 cm 250 cm Flow distributor Li et al (2009), PNAS Increase 5 Air flow Loosely packed Compaction Closely packed

12 Bio-inspired legged robot RHex 2 kg, 30 cm long (KodLab, UPenn) Slowed 20 KodLab Tuned for solid ground fast Low frequency High frequency slow

13 Initial test of robot on granular media Tuned for solid ground fast Li et al. (2009), PNAS Li et al. (2010), Exp. Mech. Ground matters! Tuned for granular media fast slow slow Failure to move (~0 BL/s) Movement (~1 BL/s) Closely packed Closely packed

14 Movement is sensitive to ground compaction and leg frequency Legs rotate faster or Ground becomes less compact Li et al. (2009), PNAS Li et al. (2010), Exp. Mech. Tuned for granular media Legs rotate slower or fast Ground becomes more compact slow Failure to move (~0 BL/s) Movement (~1 BL/s) Closely packed Closely packed

15 Measuring yield force during forced leg rotation Yield criterion for granular media: Applied force > Yield force! Fluidize (yield) Applied force < Yield force! Re-solidify Robot arm w/force sensor Li et al. (2009), PNAS Li et al. (2010), Exp. Mech. Yield force Fixed axle π/2 π/2 Fluidized bed Vertical force Yield force 0 π/2 Leg angle π/2

16 Movement occurs on re-solidified granular media Yield criterion for granular media: Applied force > Yield force! Fluidize (yield) Applied force < Yield force! Re-solidify Li et al. (2009), PNAS Li et al. (2010), Exp. Mech. Yield force Free axle π/2 π/2 Applied force (Weight + inertial force) Re-solidify Slowed 20 Vertical force Yield Yield Yield force Applied force 0 π/2 Leg angle π/2

17 Forces are affected by ground and leg kinematics Li et al. (2009), PNAS Li et al. (2010), Exp. Mech. Normalized yield force (pressure/depth) Increase 5 Ground becomes less compact! Yield force Legs rotate faster or in fast phase! Applied force (weight + inertial force) Loosely packed Compaction Closely packed Vertical force Yield Applied force force Yield Applied force force 0 π/2 Leg angle π/2

18 No re-solidification results in failure to move Yield criterion for granular media: Applied force > Yield force! Fluidize (yield) Applied force < Yield force! Re-solidify Li et al. (2009), PNAS Li et al. (2010), Exp. Mech. Yield force Free axle π/2 π/2 Applied force Slowed 20 Vertical force Continuously yielding Applied force Yield force 0 π/2 Leg angle π/2

19 A common feature in cursorial (rapid running) animals Zebra-tailed lizard (Callisaurus draconoides) Coombs, (1978) Hildebrand (1985) Sengi SVL: 6-10 cm mass: ~10 g 1 cm Elongate distal elements (foot) Kangaroo rat Impala Cheetah Kangaroo

20 Zebra-tailed lizard Foot elongation to the extreme leg foot femur tibia metatarsus fourth toe 19% SVL 18% 13% 24% 38 BL/s 18% SVL 21% 14% 21% 43 BL/s 25% SVL 28% 17% 25% 55 BL/s 21% SVL 21% 14% 16% 49 BL/s Irschick & Jayne (1999) Hind leg length Running speed 22% SVL 20% 11% 14% 27 BL/s 100% BL 50 BL/s Correlations between hind leg length and running speed

21 Real time Youtube Better performance in biology Desert generalist Field observations of 50 BL/s on both solid and granular surfaces Irschick & Jayne (1999) Possible advantages: Increase stride length & contact area Mosaer (1932) Hildebrand (1985) Mechanisms not well understood

22 Foot kinematics on solid ground Li et al. (2012) J. Exp. Biol. Foot touch ground at and pivot about toe tips Top view, slowed 40 Side view, slowed 40

23 Foot function on solid ground: Energy-saving spring Li et al. (2012) J. Exp. Biol. Foot dissection Normalized oot curvature Tendon spring length change (mm) Foot model Time (% period) Foot spring extends then recoils Stores then releases elastic energy

24 Foot function on solid ground: Energy-saving spring Li et al. (2012) J. Exp. Biol. Foot model Normalized mechanical energy Torque (N m) Work loop experiments Touch down Mid stance Take off Elastic energy storage Elastic energy release Displacement (º) Foot resilience = 44 ± 12 % Foot saves 40% mechanical work needed per step

25 Foot kinematics on granular media Li et al. (2012) J. Exp. Biol. Entire foot contact ground; Long toes rotate deep into ground X-ray, slowed 30 Top view, slowed N.S. Speed (BL/s) Side view, slowed 40

26 Foot function on granular media: Force-generating paddle Li et al. (2012) J. Exp. Biol. F = α Area Depth Time (% period) Left Right CoM dynamics Vertical speed (cm/s) Time (% period) Experiment Model Vertical force balance over a stride:

27 Foot function on granular media: Force-generating paddle Li et al. (2012) J. Exp. Biol. Solid Granular Knee angle (º) Time (% Period) Normalizedm echanical energy Knee extends more during stance (Leg does more muscle work) Energy loss to ground: Touch down Mid stance Take off Energy loss to ground Legs must do 2 more mechanical work than on solid ground

28 How can we predict forces? Resistive Force Theory Robot leg Total lift Total drag Li et al. (2009), PNAS Li et al. (2010), Exp. Mech. Animal foot Li et al. (2010), J. Exp. Biol. For each element: (1) Depth Li, Zhang, and Goldman (2013), Science (2) Orientation (3) Direction -are different Orientation Direction Vertical stress Plate element -change with time Depth Horizontal stress Test on robotic physical model (precise & easy to control)

29 Measuring stresses using a plate element Li, Zhang, and Goldman (2013), Science Total force Vertical stress σ z Orientation β Direction γ Plate element Depth z Horizontal stress σ x 4 3 Fully immersed and far from boundary Vertical Stress/depth (slope) Stress σ z,x (N/cm 2 ) Intrusion Horizontal Extraction Fluidization Stress Depth z (cm)

30 Force is sensitive to intruder orientation and direction Vertical stress / depth Li, Zhang, and Goldman (2013), Science Vertical stress σ z Orientation β Depth z Orientation angle Direction γ Plate element Horizontal stress σ x Pressure Depth Direction angle

31 Resistive force theory accurately predicts forces Vertical stress / depth Li, Zhang, and Goldman (2013), Science Total lift Fixed axle Total drag Orientation angle Total force (N) Direction angle No model fitting parameters Leg angle

32 Using resistive force theory to predict movement Li, Zhang, and Goldman (2013), Science Movement is primarily in vertical plane 3D printed legs Measure -Dimensions -Mass m -Moment of inertia I Divide body/legs into 30 elements MBDyn software Ghiringhelli et al. (1999)

33 Resistive force theory accurately predicts robot movement C-leg Experiment Li, Zhang, and Goldman (2013), Science Speed (cm/s) Experiment Model Time (s) Simulation using Resistive Force Theory slowed 5

34 Resistive force theory accurately predicts robot movement C-leg reversed Li, Zhang, and Goldman (2013), Science Experiment Experiment Model Speed (cm/s) Time (s) Simulation using Resistive Force Theory First model capable of predicting multi-legged movement on flowable ground

35 Resistive force theory enables rapid design prediction Li, Zhang, and Goldman (2013), Science Average speed (cm/s) Experiment Resistive Force Theory (No model fitting parameters) Highest speed Time for each trial: RFT Simulation 10 seconds Experiments 10 minutes Leg curvature (normalized) Optimal curvature DEM Simulation 1 week Reversed c-leg C-leg

36 Resistive force theory is general for level, uniform, dry granular media Different particle size, shape, friction, compaction, polydispersity (particle size variation) 1 mm poppy seeds Loosely packed Li, Zhang, and Goldman (2013), Science General stress profile Closely packed 0.3 mm glass spheres Loosely packed 3 mm glass spheres Closely packed Closely packed Pressure Depth Single measurement can be used!