Walking Robots Lecture 9 - Week 5

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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)
Rollerwalker (University of Tokyo, Japan)
U-BOT (University of Massachusetts, USA)
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Real Robots (cont.)
The Self Deploying Microglider (EPFL, France)
Aiko (SINTEF Applied Cybernetics, Japan)
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Real Robots (cont.)
Asimo (Honda, Japan)
Battlefield Extraction-assist Robot (Vecna
Technologies, USA)
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Why Legs?

• Potentially less weight
• Better handling of rough terrains
• Only about a half of the worlds land mass is
  accessible by current man-built 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.)

• Arent 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,
  dont 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
• 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 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

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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 robots 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 Dot center
  of gravity
• Quadruped Robot Gait Motion (http//www.youtube.
  com/watch?vlxIy3jYuQCo)

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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?vIMR553sg3-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?vDZscwdXF920)
• - Honda Asimo running (close-up)
• (http//www.youtube.com/watch?vTVSOCb6O-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 robots
  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 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.

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Walking State Methodology (cont.)

• The velocity and acceleration of the balance
  control state is determined by 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-robot-video_89396af9e.html)
• http//www.zdnet.com/blog/emergingtech/meet-mabel-
  worlds-fastest-robot-with-two-legs-w-video/2752

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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?vfdN0_LO-vCY
  )
• 2 legs (http//www.youtube.com/watch?vCK8IFEGmiKY
  )

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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.)

• Hondas Asimo
• (http//www.youtube.com/watch?vVTlV0Y5yAwwfeatu
  rePlayListp85F8464A742759D1playnext1index5
  )
• AISTs HRP-2
• (http//www.youtube.com/watch?viigiFYzwjjE )
• AISTs HRP-3
• (http//www.youtube.com/watch?vgO9th_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)

• Robot Locomotion by Henrik Christensen
  (http//www.nada.kth.se/kurser/kth/2D1426/slides20
  06/aut-rob2-2up.pdf )
• Walking Robots and Especially Hexapods by Marek
  Perkowski (http//web.cecs.pdx.edu/mperkows/CLASS
  _479/May6/024.walking-robots-design.ppt8 )
• 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 )
• Design of a Biped Robot by Andre Senior and Sabri
  Tosunoglu
• Overview of ZMP-based Biped Walking by Shuuji
  Kajita (http//www.dynamicwalking.org/dw2008/files
  /presentations/DW2008_keynotepresentation_Shuuji_K
  ajita.pdf )
• www.wikipedia.org (on ZMP)