Transcript Terrain Rendering and Level of Detail Lecture 5

Walking Robots
Lecture 9 - Week 5
Advanced Programming for 3D Applications
CE00383-3
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Types of Locomotion in Nature
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Real Robots
Sneak (Epson, Japan)
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Rollerwalker (University of Tokyo, Japan)
U-BOT (University of Massachusetts, USA)
Real Robots (cont.)
The Self Deploying Microglider
(EPFL, France)
Aiko
(SINTEF Applied Cybernetics, Japan)
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Real Robots (cont.)
Battlefield Extraction-assist Robot
(Vecna Technologies, USA)
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Asimo
(Honda, Japan)
Why Legs?
• Potentially less weight
• Better handling of rough terrains
– Only about a half of the world’s land mass is accessible by current manbuilt vehicles
• Do less damage to terrains (environmentally conscious)
• More energy-efficient
• More maneuverability
– Use of isolated footholds that optimize support and traction
(i.e. ladder)
• Active suspension
– Decouples the path of body from the path of feet
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Why Legs? (cont.)
• Aren’t wheels and caterpillars good enough?
– Wheels and caterpillars always need “continuous” support from the
ground. Legs can enable a robot to make use of “discreet” footholds.
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Why Bipeds?
• Why 2 legs? 4 or 6 legs give more stability, don’t they?
– A biped robot body can be made shorter along the walking direction
and can turn around in small areas
– Light weight
– More efficient due to less number of actuators needed
• Everything around us is built to be comfortable for use by human
form
• Social interaction with robots and our perception (HRI perspective)
– Form will become as important as functionality in the future
• Our instinctive desire to create a replica of ourselves (maybe?)
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Joints in a Leg
• At least 2 DOF (degrees of freedom) needed to move a leg
– A lift motion + a swing motion
• A human leg has 30 DOF
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–
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Hip joint = 3 DOF
Knee joint = 1 ~ 2 DOF (almost a hinge)
Ankle joint = 1 DOF (hinge)
24 DOF for the foot!
• In many cases, a robot leg has 3 DOF
– Control becomes increasingly complex with added DOF
• With 4 DOF, ankle joint can be added
• Reasonably walking biped robots have been built with as few as 4
DOF
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Joints in a Leg (cont.)
• Picture of a joint model
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Stability
• Stability means the capability to maintain the body posture given
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the control patterns
Statically stable walking implies that the posture can be achieved
even if the legs are frozen / the motion is stopped at any time,
without loss of stability
Dynamic stability implies that stability can only be achieved
through active control of the leg motion
Statically stable systems can be controlled using kinematic models
Dynamic walking requires use of dynamical models
Gaits
• Gaits determine the sequence of configurations of the legs
– A sequence of lift and release events of individual legs
• Gaits can be divided into 2 main classes
– Periodic gaits  repeat the same sequence of movements
– Non-periodic or free gaits  no periodicity in the control and could be controlled
by the layout of environment
• The number of possible events N for a walking machine with k legs
is:
N = (2k – 1)!
• For a biped robot (k = 2), there are 3! = 6 possible events
– Lift left leg, lift right leg, release left leg, release right leg, lift both legs, release
both legs
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Gaits (cont.)
• An example of a static gait with 6 legs
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Gaits and Stability
• People, and humanoid robots, are not statically stable
• Standing up and walking appear effortless to us, but we are actually
using active control of our balance
– We use muscles and tendons
– Robots use motors
• In order to remain stable, the robot’s Center of Gravity must fall
under its polygon of support
– The polygon is basically the projection between all of its support points onto the
surface
– In a biped robot, the polygon is really a line
• The center of gravity cannot be aligned in a stable way with a point on that line to keep
the robot upright
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Gaits and Stability (cont.)
• Each vertex = support foot
• Quadruped Robot – Gait Motion
Dot = center of gravity
(http://www.youtube.com/watch?v=lxIy3jYuQCo)
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Control of a Walking Robot
• 3 things that control must consider for walking:
– Gait: the sequence of leg movements
– Foot placement
– Body movement for supporting legs
• Leg control patterns
– Legs have 2 major states:
• Stance: On the ground
• Fly: In the air moving to a new position
– Fly state has 3 major components:
• Lift phase: leaving the ground
• Transfer: moving to a new position
• Landing: smooth placement on the ground
• More DOF for the legs means
– Smoother movement, but
– Increasingly complex controls
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Walking vs Running
• Motion of a legged system is called walking if in all instances at least
one leg is supporting the body
- Honda Asimo walking
(http://www.youtube.com/watch?v=IMR553sg3-Q)
- First Asimo version is E0 in 1986. It took 20-25 seconds for 1 complete step
• If there are instances where no legs are on the ground, it is called
running
- Honda Asimo running
(http://www.youtube.com/watch?v=DZscwdXF920)
- Honda Asimo running (close-up)
(http://www.youtube.com/watch?v=TVSOCb6O-4A)
• Walking can be statically or dynamically stable
- With 2 legs, almost always dynamically stable
• Running is always dynamically stable
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Biped Walking = Rolling
• Rolling is quite efficient
• Biped walking is similar to rolling
a polygon
– Polygon side length = step length
– As step length gets shorter, more
like rolling a circle
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Walking State Methodology
• Walking algorithm for biped robots often derived from classical
control theory
– Uses a reference trajectory for the robot to follow
– Reference trajectories can rarely be defined to work in the real world
• Irregular terrains and encountering different obstacles, etc.
• Uses static balance poses to define points of tending to balance
during a gait
• The point that a biped robot tends to balance is called a state
• The walking states are chosen as the maximum and minimum
tending to balance stance equilibrium positions where little or no
torque needs to be applied to maintain the state
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Walking State Methodology
(cont.)
• Marching gait example
• 5 states where the robots tends to either balance or tend to topple
• The center of gravity tends to shift as shown by the cube on top of
the robot
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Walking State Methodology
(cont.)
• While advancing to new
states during the actual
walking locomotion, an
autonomous robot’s
software should ideally
extrapolate the gait from
balanced state to the next.
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Walking State Methodology
(cont.)
• In states 2 and 4, we can interpret the robot as tending to an out of
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balance point. If the leg that is bent continues in the same direction, then
the robot will topple.
The control algorithm should not counter the tending to topple position by
bending the other knee on the other leg or shifting the original leg back to
its initial position.
The control algorithm should continue with the balance control state,
expecting that to prevent a fall, the robot has to counter balance by shifting
the center of gravity to either the neutral position or to the next tending to
out of balance point on the opposite side.
Walking State Methodology
(cont.)
• The velocity and acceleration of the balance control state is determined by
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the weight and dynamics of the robot.
All the specific movements pre-determined (hard coded) for each state
Example (Clyon, Florida International University)
(http://video.eng2all.com/clyon-biped-robot/clyon-biped-robotvideo_89396af9e.html)
http://www.zdnet.com/blog/emergingtech/meet-mabel-worlds-fastestrobot-with-two-legs-w-video/2752
Passive Walking
• An approach to robotics movement control based on utilizing the
gravity and the momentum of swinging limbs for greater efficiency.
– Conserves momentum
– Less number of actuators
– Natural (anthropormorphic)
• In a purely passive dynamic walking, gravity and natural dynamics
alone generate the walking cycle
– Active input is necessary only to modify the cycle, as in turning or changing
speed
• Examples
– 3 legs (http://www.youtube.com/watch?v=fdN0_LO-vCY)
– 2 legs (http://www.youtube.com/watch?v=CK8IFEGmiKY)
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Zero Moment Point (ZMP)
• Introduced in 1968 by Miomir Vukobratovic
• Specifies the point with respect to which dynamic reaction force at
the contact of the foot with the ground does not produce any
moment (i.e. the point where total inertia force equals 0)
• Assumes the contact area is planar and has sufficiently high friction
to keep the feet from sliding (no sliding assumption)
• The trajectory is planned using the angular momentum equation to
ensure that the generated joint trajectories guarantee the dynamical
postural stability of the robot, which usually is quantified by the
distance of the zero moment point in the boundaries of a predefined
stability region.
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Zero Moment Point (ZMP) (cont.)
• Ground reaction force and ZMP are generally measured
with a series of sensors embedded in the feet
– Pressure sensitive transducers, foot switches, strain gage based
sensors, force sensitive resistors, and novel force-torque transducers
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Zero Moment Point (ZMP) (cont.)
• Center of pressure (CoP) is a ground reference point where
the resultant of all ground reaction forces acts
– At this point, it is assumed that all of the forces that act between the
body and the ground through the foot can be simplified to a single
ground reaction force vector and a free torque vector
– If the horizontal forces between the feet and the ground can be
neglected, then the CoP can be defined as the centroid of the vertical
force distribution
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Zero Moment Point (ZMP) (cont.)
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Zero Moment Point (ZMP) (cont.)
• For flat horizontal ground surfaces, ZMP == CoP
• At any point P under the robot, the reaction can be
represented by a force and a moment Mgrf
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Zero Moment Point (ZMP) (cont.)
• Around the ZMP (localized at rzmp ) the moment around the
horizontal axis are zero and there is only a component of
moment around the vertical axis
• The resulting moment of force exerted from the ground on
the body about the ZMP is always around the vertical axis
• At the ZMP is a reference point at the ground in which the
net moment due to inertial and gravitational forces has no
component along the (horizontal) axes (parallel to the
ground)
• The trajectory that the ZMP follows is utilized and planned
such that they are within the supporting polygon defined
by the location and shape of the foot print
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Zero Moment Point (ZMP) (cont.)
• Anyways, in a very brief summary…
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Zero Moment Point (ZMP) (cont.)
• Anyways, in a very brief summary…
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Zero Moment Point (ZMP) (cont.)
• Anyways, in a very brief summary…
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Zero Moment Point (ZMP) (cont.)
• Honda’s Asimo
(http://www.youtube.com/watch?v=VTlV0Y5yAww&feature=PlayL
ist&p=85F8464A742759D1&playnext=1&index=5 )
• AIST’s HRP-2
(http://www.youtube.com/watch?v=iigiFYzwjjE )
• AIST’s HRP-3
(http://www.youtube.com/watch?v=gO9th_Rfk2o )
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Zero Moment Point (ZMP) (cont.)
 Formulas from wikipedia
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Zero Moment Point (ZMP) (cont.)
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Zero Moment Point (ZMP) (cont.)
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Sources (cited within this presentation)
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•
Robot Locomotion by Henrik Christensen
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Walking Robots and Especially Hexapods by Marek Perkowski
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Estimation of ground reaction force and zero moment point on a powered ankle-foot prosthesis
by Martinez Villalpando and Ernesto Carlos (http://dspace.mit.edu/handle/1721.1/37271 )
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Design of a Biped Robot by Andre Senior and Sabri Tosunoglu
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Overview of ZMP-based Biped Walking by Shuuji Kajita
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www.wikipedia.org (on ZMP)
(http://www.nada.kth.se/kurser/kth/2D1426/slides2006/aut-rob2-2up.pdf )
(http://web.cecs.pdx.edu/~mperkows/CLASS_479/May6/024.walking-robots-design.ppt#8 )
(http://www.dynamicwalking.org/dw2008/files/presentations/DW2008_keynotepresentation_Shuu
ji_Kajita.pdf )