Scansorial Landing and Perching
Alexis Lussier-Desbiens, Alan Asbeck and Mark R. Cutkosky
ISRR 2009, Aug 31 - Sep 3, Lucerne CH
Biomimetics and Dextrous
Manipulation Laboratory
Stanford University
http://bdml.stanford.edu
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2
Advantages of Perching
• Greatly extend mission time
• Stable vantage point while perched
• Possibility of landing and physically interacting with a surface.
• Perching combines the best of climbing and flying: – Agile and fast while flying
– Can cover long distances
– Low energy consumption while perched
– Wait for better weather conditions
– Quiet (no motor noise)
3RiSE platform climbing library at
SwRI, San Antonio, TX
3
Why vertical surfaces?• Common in urban environments
• Easy to detect
• Often provide a large surface to simplify landing
• After an explosion, earthquake, etc. walls may be comparatively safe, clean and uncluttered
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4
Related Work
• On agile flight: – How et al. (MIT) on indoor flying and hovering
– Oh et al. (Drexel) on autonomous hovering
• On perching aerodynamics & control:
– Wickenheiser et al. (Cornell) on vehicle morphing for perching
– Tedrake et al. (MIT) on controllability of fixed-wing plane for perching on a wire
• Hybrid aerial/terrestrial vehicle (Quinn)
• No detailed consideration of the landing system
• Slow maneuvers sensitive to disturbances
• Use of highly accurate motion capture system/sensors to enable control
[Cory & Tedrake, 2008]
[Wickenheiser, 2007]
[Green & Oh, 2006] 5
5
6
Approach:
• Conventional plane
• Quick maneuver to minimize
disturbance effects
• Focus on suspension and spines
to simplify sensing and control
• Everything onboard
Sonar
Spines
Paparazzi Autopilot & sensors
2) Wall detection
5) Rest
1) Approach
3) Pitch up
4) Touchdown
Elevator
Modified FlatanaAirplane
Suspension
6
Perching Strategy
1. Fly toward wall ~ 9 m/s
2. Detect wall with ultrasonic sensor
• 20 Hz, 6 m range
3. Pitch up to slow down (takes about 2-3m)
4. Touchdown possible for about 1.5 m before impact
5. Touchdown at 1-3 m/s. Let suspension absorb impact
7
Pitching up Successful landingWaiting for wall detection
!6 !5 !4 !3 !2 !1 0
!0.8
!0.6
!0.4
!0.2
0
x (m)
y (
m)
Simulated trajectory of the perching maneuver
(inspired by [Cory & Tedrake 2008])
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8
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Clinging with spines
• Used on Spinybot and RiSE to climb brick, stucco, concrete rock...
• Spine mechanisms take advantage of
robot's control over foot trajectories
and forces.
• With UAVs, the challenge is to
provide desired trajectory and forces
using momentum of the plane.
9
Why spines?– require no power
– work on a range of outdoor surfaces
– relatively unaffected by films of dirt and moisture
– leave no trace of their passage
– provide many loading cycles
9
Spine suspensions
• Small spines (10-15 µm tip radius) catch and hang on asperities
• Individual spine suspensions distribute the load
• Loading trajectory required
10
1
2
34 5
Approach volume
Loading ForcesVolume
y
x
Loading cycle
1. Normal force
2. P
ull d
ow
n3. P
ull a
way
10
Spine/surface interaction
11
mg
11
Spine limit curve -- 1 foot, 10 spines
(for roofing paper -- similar to stucco or composite roof shingles)
12
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12
overload
limits
friction
limit
Limit on
Fn/Ftan
safe region
Fn
Ftan
gravitypull-in
Revisit spine constraints, from standpoint of the plane
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13
mg
Fpull-in
Fstatic
F0
Fmax
Spine constraints, from the standpoint of the plane
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The actual picture is a bit messier...
15
Fn
Ftan
Fmax
Fstatic
measuredsimulated
• Loading trajectory is important
• Low damping ratio: – Ratio Fn/Ftan too high
– Rebound
• High damping ratio: – High peak force
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Leg suspension requirements
Early tests revealed that vertical rebound was the main failure
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Solution: design suspension (links, springs, dampers, nonlinear elements) to absorb kinetic energy and direct forces toward spines with:
– moderate peak landing force
– moderate suspension travel(no knee contact)
– no negative tangential forces (vertical rebound, detachment)
– small negative normal forces (no horizontal bounce-off)
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Pseudo-elasticlink model accountsfor bending.
Suspension model
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Hip damping is large and nonlinear
Toe suspension(new)
(dynamic equations via Autolev; simulations in Matlab)
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Leg Structure
Foam
hip
Balsa/Carbon
femur
Sorbothane
knee
Carbon
tibia
Foam
ankle
Spines
Attachment
points
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Nonlinear elements
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Scansorial Landing and Perching 9
100 105 110 115 120 125 130 135 1400
0.1
0.2
0.3
0.4
Hip angle (deg)
Mo
me
nt (N
m)
100 105 110 115 120 125 130 135 1400
0.01
0.02
0.03
0.04
0.05
0.06
Hip angle (deg)
Stiff
ne
ss (
Nm
/deg
)k = 0.0041 + 0.05/(! ! 100)
Fit
Data
Fig. 6 Hip joint stiffness as a function of the hip angle. The non-linearity prevents excessive com-pression for high landing forces.
4.2 Planar landing model
In order to predict and tune the forces during landing, a simple planar model of theairplane and suspension was created as shown in fig. 7. In this model we ignore rolland yaw motions and lump the two legs together as a single mechanism. The planeis modeled as a rigid body subject to gravity. We ignore aerodynamic forces as wehave determined that they do not contribute significantly to the motion of our planeafter contact.
We introduce four right-handed reference frames: The wall frame W is definedwith the unit vector wx oriented toward the wall and wy upward along the surface;the airplane frame A is rotated by ! from W around wz, with its origin at the airplanecenter of mass; the femur frame F is rotated by qH from A with its origin at the hipjoint; and the tibia frame T , is rotated by qK from F with its origin at the knee.
Intermittent contact forces, N, with the wall are modeled at the knee and the tailby the use of a spring and damper:
N =
!"
#
0 if xc < 0kgxcwx if xc > 0 and xc < 0
(kgxc +bgxc)wx if xc > 0 and xc > 0(2)
where kg and bg are the properties of the ground and xc = xtail ! xwall for the tailpoint.
Friction at the contact points is modeled using the continuous model from (Mit-iguy and Banerjee, 1999):
F f =!µk |N| v|v|+ "v
(3)
Where µk is the coefficient of kinetic friction, |N| is the magnitude of the normalforce, v is the velocity of the point in contact and "v is a small positive number.
Because of its light weight, the suspension is modeled as two massless links,ignoring the ankle joint and the spine suspension because of their small motions in
Hip stiffness versus hip angle
(damping follows similar trend)
• Material properties +
kinematics to create roughly constant force
• Damping scaled w.r.t position and velocity
• Urethane foam exhibits reduced damping at high velocity
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Comparing model & force plate data
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spine dragging effects
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Touchdownpossible
Pitch upmaneuver
Elevatorup
Walldetection
9 m/s
2 m/s
xy
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30/40 successful landings (10 autonomous, 20 in manual control)
• Pitch = 65 to 110 deg
• Pitch rate = 0 to 200 deg/s• vx = 1 - 2.7 m/s (forward)
• vy = up to 1 m/s (downward)
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Improvements and future work
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• Land on other surfaces (horizontal, inverted)
– > use opposed spines
• Real conditions (windy, etc.)
• Maneuver on the wall(hybrid scansorial robotics)
• Take off from the wall!
Spiny Gripper
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• Grips to rough surfaces – concrete,
stucco, tar paper
• Multiple uses per mission
• Leaves no trace
• Spines engage bumps/pits on the
surface
• Spines undergo hundreds of
attach/detach cycles before dulling
• Current linkage material (the hard part)
deforms in heat (140°F)
– Heat-resistant polyurethanes are
available, will be used in future versions
Spine –
steel
fishhook
140°F 32°F
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Improvements and future work
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Limits for directional adhesion(e.g. Stickybot)
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pulloff
limits
-10 0 10 20
-10
0
10
20
Tangential Force (mN/stalk)
Normal Force (mN/stalk)
500µm
-10 0 10 20
-10
0
10
20
Tangential Force (mN/stalk)
Normal Force (mN/stalk)
500µm
600µm
-10 0 10 20
-10
0
10
20
Tangential Force (mN/stalk)
Normal Force (mN/stalk)
500µm
600µm
700µm
FN
Ftan
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Spine limit curve -- 1 foot, 10 spines
(for roofing paper -- similar to stucco or composite roof shingles)
26
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Onboard Sensors
• Simple wall detection using the LV-Maxsonar:
– Range of 6 m
– Update rate of 20 Hz
• Onboard accelerometer and gyro are used for data analysis
• Combined using a second order complementary filter:
• Need something better!!!
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65 70 75 80 85 90
!20
0
20
40
60
80
Pit
ch
(d
eg
)
time (sec)
Different techniques for measuring pitch
Complementary Filter
Rate Gyro Integration
Gravity measurement
Sensitive to vibrations
Drifting
!!s + 1!s + 1
"2
"(s) =!2s
(!s + 1)2"(s) +
2!s + 1(!s + 1)2
"(s)
Hgravity =0.03292z ! 0.03265z2 ! 1.967z + 0.9672
Hgyro =0.01639z ! 0.01639z2 ! 1.967z + 0.9672
Cyaw = 2000" 0.6426z!1 ! 0.5861z!2
1! 0.8508z!1 + 0.1337z!2
Croll = 150" 0.189z!1
1! 0.8511z!1
1
27
CL = 2 sin(!) cos(!)CD = 2 sin2(!)
L =12!v2ACL
D =12!v2ACD
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Aero Model(inspired by [Cory & Tedrake 2008])
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