Limbless locomotion 5/9/2018

Transcription

1 Limbless locomotion 5/9/2018

2 Limbless locomotion Biological inspiration Modes of movement Physics of interaction with the ground Robot examples Actuation Control

3 Limbless locomotion

4 Limbless locomotion

5 Snakes A vertebrate with the largest number of vertebrae ( ) of any animal The vertebrae of the snake form ball-and-socket joints with additional projections that eliminate torsional motion to protect the spinal cord. Limbless locomotion They work in environments where traditional machines are precluded due to size or shape and where appendages such as wheels or legs cause entrapment or failure Tight spaces Long narrow interior traverses Travel over loose materials and terrains,

6 Pros and Cons of Snake Locomotion Pro Con + Stability (large contact area) + Traverse rough and sandy terrain + Passing through limited space + Redundant (failed parts don t stop the motion) + Sealing (skin) against hostile environments - Energy efficiency (energy loss due to friction and lateral acceleration) - Difficult thermal control - Wear problem - Limited speed

7 Snake Locomotion Gaits a) Concertina: Folding and unfolding. Gray (1946) JEB, Jayne et al. (1991) JEB, Marvi et al. (2012) JRSI b) Lateral undulation: A two-dimensional traveling wave from head to tail. Jayne (1988) JEB, Hu et al. (2009) PNAS c) Sidewinding: A three-dimensional helical wave from head to tail. Secor et al. (1992) JEB, Hatton et al. (2010) ICRA, Marvi et al. (2014) Science d) Rectilinear: all of the points on snake body moving on a straight line. Lissman (1950) JEB, Marvi et al. (2013) JRSI

8 Snake Locomotion Gaits Concertina (accordion-like motion) Used in confined areas such as tunnels Can be used for climbing inside vertical tree trunks A form of two-anchor crawling Slower and less energy efficient than lateral undulation Serpentine locomotion (lateral undulation) All parts of the body move simultaneously, experiencing continuous sliding contact with the ground (all parts moving at the same speed that occurs through the propagation of waves from the front to rear of the snake).

9 Snake Locomotion Gaits Sidewinding On low shear surfaces such as loose sand Contacting body parts do not slide Slower but more efficient (no work against friction) than lateral undulation Rectilinear A one-dimensional traveling contraction wave moving in the posterior direction Used by larger snakes, e.g. Boa, Python Slow, but useful for moving in limited space

10 Contact mechanics of snake locomotion

11 Snake Scales Snakes utilize functional surfaces to modify their frictional properties.

12 Role of Scales in Locomotion Snakes cannot move forward without friction anisotropy

13 Friction Coefficients 0.9 Static friction coefficients Asleep Awake Forward N Backward 0 Forward Backward F app F fric Friction Coefficient µ = F fric /N Corn snakes, N = 2, m = 42 ± 5 g, L = 61 ± 4 cm

14 Passive Friction Anisotropy Geometry Gray (1946), JEB Hu, et al. (2009), PNAS Boa Corn Snake Green Snake Sidewinder Micro-scale properties Hazel, et al. (1999), J. of Biomechanics 3 mm 2 µm

15 Active Friction Anisotropy

16 Scalybot

17 Optimal Angles of Attack * * θ * * θ ( o ) θ ( o ) Scales angle of attack: 30 o : min forward dynamic friction, 50 o : max backward static friction

18 Concertina locomotion Mini-scale W Styrofoam Wood θ Plexiglass Change channel width and inclination Measure kinematic parameters and transverse force

19 Concertina Motion t t

20 Transverse Force T i T i X Transverse force varies: 1) along the body and 2) within one period of motion. X

21 Effect of Width on Body Shape Different body shape and speed in channels of different width Transition to lateral undulation in wide channels

22 Rectilinear movement Snakes use optimal wave frequencies: higher values increase Froude number causing the snake to slip; smaller values decrease thrust and so body speed.

23 Three Species of Snakes Boa Constrictor Studied 10 cm Gaboon Viper 10 cm Dumeril s Boa 10 cm ax climbing Max stationary µ b =0.89 Max stationary µ b =0.32 Max stationary µ b =0.05 θ=42 o θ=15 o Max climbing θ=18 o θ=7 o Max climbing θ=3 o θ=2 o 3 Juvenile Red-tailed Boa (Boa Constrictor) Length = 53.3 ± 1.5 cm 1 Gaboon Viper (Bitis gabonica) Length = 122 cm 2 Dumeril s Boas (Boa Dumerili) Length = ± 10.6 cm

24 Time 0 s 2 cm 1.3 s 2.6 s 4 s i = 25 i = 22 x 22 (cm) i = 1 t (sec)

25 Best Fit for Displacement Function Wave propagation direction s = 0 s = L x θ U R 2 =0.98 R 2 =0.98 R 2 =0.99 x' (t,s) = A sin(ωt + ks) + s

26 Sidewinding BBC

27 BBC

28 Increasing contact length: Costantino et al., (2011) Phys. Rev. E

29 Two Orthogonal Waves Z Wave direction Y X Direction of motion

30 Sidewinders control their contact length with sand V 0 deg V 20 deg

31 Drag experiments

32 Sand Stiffness vs Inclination Angle

33 Biorobotics Lab, CMU Biorobotics Lab, CMU Biorobotics Lab, CMU

34 Different Failure Regimes

35 Different Failure Regimes

36 Take Home Messages

37 Snake-like robots Chosett, CMU Ijspeert, EPFL Borenstein Burdick, Caltech Liljeback, NTNU Hirose, Tokyo Inst. Tech

38 Modeling serpentine locomotion If we assume no sliding then there is a constraint on the wheel movement In a continuum model the tangential and normal forces at each element are related to the joint torque and curvature

39 Controlling serpentine locomotion: a geometric approach

40 Controlling serpentine locomotion: a geometric approach

41 Controlling serpentine locomotion: a geometric approach

42 Controlling serpentine locomotion: a CPG approach

43 Controlling serpentine locomotion: a CPG approach

44 Controlling serpentine locomotion: traveling wave modulation

45 Actuation of snake robots

46 For next week Monday meetings Wednesday new paper