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Walking Robots Walking Robots

Lecture 9 - Week 5Lecture 9 - Week 5

Advanced Programming for 3D Advanced Programming for 3D ApplicationsApplicationsCE00383-3CE00383-3

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Types of Locomotion in Types of Locomotion in NatureNature

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Real RobotsReal Robots

U-BOT (University of Massachusetts, USA)

Sneak (Epson, Japan) Rollerwalker (University of Tokyo, Japan)

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Real Robots (cont.)Real Robots (cont.)

The Self Deploying Microglider(EPFL, France)

Aiko (SINTEF Applied Cybernetics, Japan)

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Real Robots (cont.)Real Robots (cont.)

Battlefield Extraction-assist Robot(Vecna Technologies, USA)

Asimo(Honda, Japan)

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Why Legs?Why Legs?

• Potentially less weightPotentially less weight

• Better handling of rough terrainsBetter handling of rough terrains– Only about a half of the world’s land mass is accessible by current Only about a half of the world’s land mass is accessible by current

man-built vehiclesman-built vehicles

• Do less damage to terrains (environmentally conscious)Do less damage to terrains (environmentally conscious)

• More energy-efficientMore energy-efficient

• More maneuverabilityMore maneuverability– Use of isolated footholds that optimize support and tractionUse of isolated footholds that optimize support and traction

(i.e. ladder)(i.e. ladder)

• Active suspensionActive suspension– Decouples the path of body from the path of feetDecouples the path of body from the path of feet

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Why Legs? (cont.)Why Legs? (cont.)

• Aren’t wheels and caterpillars good enough?Aren’t wheels and caterpillars good enough?– Wheels and caterpillars always need “continuous” support Wheels and caterpillars always need “continuous” support

from the ground. Legs can enable a robot to make use of from the ground. Legs can enable a robot to make use of “discreet” footholds.“discreet” footholds.

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Why Bipeds?Why Bipeds?

• Why 2 legs? 4 or 6 legs give more stability, don’t they?Why 2 legs? 4 or 6 legs give more stability, don’t they?– A biped robot body can be made shorter along the walking A biped robot body can be made shorter along the walking

direction and can turn around in small areasdirection and can turn around in small areas– Light weightLight weight– More efficient due to less number of actuators neededMore efficient due to less number of actuators needed

• Everything around us is built to be comfortable for use by Everything around us is built to be comfortable for use by human formhuman form

• Social interaction with robots and our perception (HRI Social interaction with robots and our perception (HRI perspective)perspective)– Form will become as important as functionality in the futureForm will become as important as functionality in the future

• Our instinctive desire to create a replica of ourselves Our instinctive desire to create a replica of ourselves (maybe?)(maybe?)

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Joints in a LegJoints in a Leg

• At least 2 DOF (degrees of freedom) needed to move a legAt least 2 DOF (degrees of freedom) needed to move a leg– A lift motion + a swing motionA lift motion + a swing motion

• A human leg has 30 DOFA human leg has 30 DOF– Hip joint = 3 DOFHip joint = 3 DOF– Knee joint = 1 ~ 2 DOF (almost a hinge)Knee joint = 1 ~ 2 DOF (almost a hinge)– Ankle joint = 1 DOF (hinge)Ankle joint = 1 DOF (hinge)– 24 DOF for the foot!24 DOF for the foot!

• In many cases, a robot leg has 3 DOFIn many cases, a robot leg has 3 DOF– Control becomes increasingly complex with added DOFControl becomes increasingly complex with added DOF

• With 4 DOF, ankle joint can be addedWith 4 DOF, ankle joint can be added

• Reasonably walking biped robots have been built with as few Reasonably walking biped robots have been built with as few as 4 DOFas 4 DOF

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Joints in a Leg (cont.)Joints in a Leg (cont.)

• Picture of a joint modelPicture of a joint model

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StabilityStability

• StabilityStability means the capability to maintain the body means the capability to maintain the body posture given the control patternsposture given the control patterns

• Statically stableStatically stable walking implies that the posture can be walking implies that the posture can be achieved even if the legs are frozen / the motion is stopped achieved even if the legs are frozen / the motion is stopped at any time, without loss of stabilityat any time, without loss of stability

• Dynamic stabilityDynamic stability implies that stability can only be implies that stability can only be achieved through active control of the leg motionachieved through active control of the leg motion

• Statically stable systems can be controlled using kinematic Statically stable systems can be controlled using kinematic modelsmodels

• Dynamic walking requires use of dynamical models Dynamic walking requires use of dynamical models

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GaitsGaits

• Gaits determine the sequence of configurations of the legsGaits determine the sequence of configurations of the legs– A sequence of lift and release events of individual legsA sequence of lift and release events of individual legs

• Gaits can be divided into 2 main classesGaits can be divided into 2 main classes– Periodic gaits Periodic gaits repeat the same sequence of movements repeat the same sequence of movements– Non-periodic or free gaits Non-periodic or free gaits no periodicity in the control and could be no periodicity in the control and could be

controlled by the layout of environmentcontrolled by the layout of environment

• The number of possible events N for a walking machine The number of possible events N for a walking machine with k legs is:with k legs is:

N = (2k – 1)!N = (2k – 1)!

• For a biped robot (k = 2), there are 3! = 6 possible eventsFor 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, Lift left leg, lift right leg, release left leg, release right leg, lift both legs,

release both legsrelease both legs

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Gaits (cont.)Gaits (cont.)

• An example of a static gait with 6 legsAn example of a static gait with 6 legs

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• People, and humanoid robots, are not statically stablePeople, and humanoid robots, are not statically stable

• Standing up and walking appear effortless to us, but we are Standing up and walking appear effortless to us, but we are actually using actually using active control of our balanceactive control of our balance– We use muscles and tendonsWe use muscles and tendons– Robots use motorsRobots use motors

• In order to remain stable, the robot’s Center of Gravity In order to remain stable, the robot’s Center of Gravity must fall under its polygon of supportmust fall under its polygon of support– The polygon is basically the projection between all of its support points The polygon is basically the projection between all of its support points

onto the surfaceonto the surface– In a biped robot, the polygon is really a lineIn 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 The center of gravity cannot be aligned in a stable way with a point on that line to keep the robot uprightline to keep the robot upright

Gaits and Stability

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Gaits and Stability (cont.)Gaits and Stability (cont.)

• Each vertex = support foot Dot = center of Each vertex = support foot Dot = center of gravitygravity

• Quadruped Robot – Gait Motion (Quadruped Robot – Gait Motion (http://www.youtube.com/watch?v=lxIy3jYuQCo))

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Control of a Walking RobotControl of a Walking Robot

• 3 things that control must consider for walking:3 things that control must consider for walking:– Gait: the sequence of leg movementsGait: the sequence of leg movements– Foot placementFoot placement– Body movement for supporting legsBody movement for supporting legs

• Leg control patterns Leg control patterns – Legs have 2 major states:Legs have 2 major states:

• Stance: On the groundStance: On the ground• Fly: In the air moving to a new positionFly: In the air moving to a new position

– Fly state has 3 major components:Fly state has 3 major components:• Lift phase: leaving the groundLift phase: leaving the ground• Transfer: moving to a new positionTransfer: moving to a new position• Landing: smooth placement on the groundLanding: smooth placement on the ground

• More DOF for the legs meansMore DOF for the legs means– Smoother movement, butSmoother movement, but– Increasingly complex controlsIncreasingly complex controls

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Walking vs RunningWalking vs Running

• Motion of a legged system is called walking if in all instances at least one leg is supporting the bodyMotion of a legged system is called walking if in all instances at least one leg is supporting the body- Honda Asimo walking- 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- 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 runningIf there are instances where no legs are on the ground, it is called running- Honda Asimo running- Honda Asimo running (http://www.youtube.com/watch?v=DZscwdXF920)(http://www.youtube.com/watch?v=DZscwdXF920)- Honda Asimo running (close-up)- Honda Asimo running (close-up) (http://www.youtube.com/watch?v=TVSOCb6O-4A)(http://www.youtube.com/watch?v=TVSOCb6O-4A)

• Walking can be statically or dynamically stable Walking can be statically or dynamically stable - With 2 legs, almost always dynamically stable- With 2 legs, almost always dynamically stable

• Running is always dynamically stableRunning is always dynamically stable

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Biped Walking = RollingBiped Walking = Rolling

• Rolling is quite efficientRolling is quite efficient

• Biped walking is similar to Biped walking is similar to rolling a polygonrolling a polygon– Polygon side length = step Polygon side length = step

lengthlength– As step length gets shorter, As step length gets shorter,

more like rolling a circlemore like rolling a circle

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Walking State MethodologyWalking State Methodology

• Walking algorithm for biped robots often derived from Walking algorithm for biped robots often derived from classical control theoryclassical control theory– Uses a reference trajectory for the robot to followUses a reference trajectory for the robot to follow– Reference trajectories can rarely be defined to work in the real worldReference trajectories can rarely be defined to work in the real world

• Irregular terrains and encountering different obstacles, etc.Irregular terrains and encountering different obstacles, etc.

• Uses static balance poses to define points of tending to Uses static balance poses to define points of tending to balance during a gaitbalance during a gait

• The point that a biped robot tends to balance is called a The point that a biped robot tends to balance is called a statestate

• The walking states are chosen as the maximum and The walking states are chosen as the maximum and minimum tending to balance stance equilibrium positions minimum tending to balance stance equilibrium positions where little or no torque needs to be applied to maintain where little or no torque needs to be applied to maintain the statethe state

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Walking State Methodology Walking State Methodology (cont.)(cont.)• Marching gait exampleMarching gait example

• 5 states where the robots tends to either balance or tend to 5 states where the robots tends to either balance or tend to toppletopple

• The center of gravity tends to shift as shown by the cube on The center of gravity tends to shift as shown by the cube on top of the robottop of the robot

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Walking State Methodology Walking State Methodology (cont.)(cont.)

• While advancing to new While advancing to new states during the actual states during the actual walking locomotion, an walking locomotion, an autonomous robot’s autonomous robot’s software should ideally software should ideally extrapolate the gait extrapolate the gait from balanced state to from balanced state to the next.the next.

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Walking State Methodology Walking State Methodology (cont.)(cont.)• In states 2 and 4, we can interpret the robot as tending to an out 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 of balance point. If the leg that is bent continues in the same direction, then the robot will topple.direction, then the robot will topple.

• The control algorithm should not counter the tending to topple The control algorithm should not counter the tending to topple position by bending the other knee on the other leg or shifting the position by bending the other knee on the other leg or shifting the original leg back to its initial position.original leg back to its initial position.

• The control algorithm should continue with the balance control The control algorithm should continue with the balance control state, expecting that to prevent a fall, the robot has to counter state, expecting that to prevent a fall, the robot has to counter balance by shifting the center of gravity to either the neutral balance by shifting the center of gravity to either the neutral position or to the next tending to out of balance point on the position or to the next tending to out of balance point on the opposite side.opposite side.

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Walking State Methodology Walking State Methodology (cont.)(cont.)• The velocity and acceleration of the balance control state is The velocity and acceleration of the balance control state is

determined by the weight and dynamics of the robot.determined by the weight and dynamics of the robot.• All the specific movements pre-determined (hard coded) for each All the specific movements pre-determined (hard coded) for each

statestate• Example (Clyon, Florida International University)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-http://www.zdnet.com/blog/emergingtech/meet-mabel-worlds-fastest-robot-with-two-legs-w-video/2752fastest-robot-with-two-legs-w-video/2752

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Passive WalkingPassive Walking

• An approach to robotics movement control based on An approach to robotics movement control based on utilizing the gravity and the momentum of swinging limbs utilizing the gravity and the momentum of swinging limbs for greater efficiency.for greater efficiency.– Conserves momentumConserves momentum– Less number of actuatorsLess number of actuators– Natural (anthropormorphic)Natural (anthropormorphic)

• In a purely passive dynamic walking, gravity and natural In a purely passive dynamic walking, gravity and natural dynamics alone generate the walking cycledynamics alone generate the walking cycle– Active input is necessary only to modify the cycle, as in turning or Active input is necessary only to modify the cycle, as in turning or

changing speed changing speed

• ExamplesExamples– 3 legs (3 legs (http://www.youtube.com/watch?v=fdN0_LO-vCY))– 2 legs (2 legs (http://www.youtube.com/watch?v=CK8IFEGmiKY))

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• Introduced in 1968 by Miomir VukobratovicIntroduced in 1968 by Miomir Vukobratovic

• Specifies the point with respect to which dynamic reaction Specifies the point with respect to which dynamic reaction force at the contact of the foot with the ground does not force at the contact of the foot with the ground does not produce any moment (i.e. the point where total inertia force produce any moment (i.e. the point where total inertia force equals 0)equals 0)

• Assumes the contact area is planar and has sufficiently high Assumes the contact area is planar and has sufficiently high friction to keep the feet from sliding (no sliding assumption)friction to keep the feet from sliding (no sliding assumption)

• The trajectory is planned using the angular momentum The trajectory is planned using the angular momentum equation to ensure that the generated joint trajectories equation to ensure that the generated joint trajectories guarantee the dynamical postural stability of the robot, guarantee the dynamical postural stability of the robot, which usually is quantified by the distance of the zero which usually is quantified by the distance of the zero moment point in the boundaries of a predefined stability moment point in the boundaries of a predefined stability region.region.

Zero Moment Point (ZMP)

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• Ground reaction force and ZMP are generally Ground reaction force and ZMP are generally measured with a series of sensors embedded in the measured with a series of sensors embedded in the feetfeet– Pressure sensitive transducers, foot switches, strain gage Pressure sensitive transducers, foot switches, strain gage

based sensors, force sensitive resistors, and novel force-based sensors, force sensitive resistors, and novel force-torque transducerstorque transducers

Zero Moment Point (ZMP) (cont.)

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• Center of pressure (CoP) is a ground reference point Center of pressure (CoP) is a ground reference point where the resultant of all ground reaction forces where the resultant of all ground reaction forces actsacts– At this point, it is assumed that all of the forces that act At this point, it is assumed that all of the forces that act

between the body and the ground through the foot can be between the body and the ground through the foot can be simplified to a single ground reaction force vector and a free simplified to a single ground reaction force vector and a free torque vectortorque vector

– If the horizontal forces between the feet and the ground can If the horizontal forces between the feet and the ground can be neglected, then the CoP can be defined as the centroid of be neglected, then the CoP can be defined as the centroid of the vertical force distributionthe vertical force distribution

Zero Moment Point (ZMP) (cont.)

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Zero Moment Point (ZMP) (cont.)

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• For flat horizontal ground surfaces, ZMP == CoPFor flat horizontal ground surfaces, ZMP == CoP

• At any point At any point PP under the robot, the reaction can be under the robot, the reaction can be represented by a force and a moment represented by a force and a moment MMgrfgrf

Zero Moment Point (ZMP) (cont.)

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• Around the ZMP (localized at Around the ZMP (localized at rrzmpzmp ) the moment around ) the moment around the horizontal axis are zero and there is only a component the horizontal axis are zero and there is only a component of moment around the vertical axisof moment around the vertical axis

• The resulting moment of force exerted from the ground on The resulting moment of force exerted from the ground on the body about the ZMP is always around the vertical axisthe body about the ZMP is always around the vertical axis

• At the ZMP is a reference point at the ground in which the At the ZMP is a reference point at the ground in which the net moment due to inertial and gravitational forces has no net moment due to inertial and gravitational forces has no component along the (horizontal) axes (parallel to the component along the (horizontal) axes (parallel to the ground)ground)

• The trajectory that the ZMP follows is utilized and planned The trajectory that the ZMP follows is utilized and planned such that they are within the supporting polygon defined such that they are within the supporting polygon defined by the location and shape of the foot printby the location and shape of the foot print

Zero Moment Point (ZMP) (cont.)

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• Anyways, in a very brief summary…Anyways, in a very brief summary…

Zero Moment Point (ZMP) (cont.)

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• Anyways, in a very brief summary…Anyways, in a very brief summary…

Zero Moment Point (ZMP) (cont.)

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• Anyways, in a very brief summary…Anyways, in a very brief summary…

Zero Moment Point (ZMP) (cont.)

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• Honda’s Asimo Honda’s Asimo

(http://www.youtube.com/watch?(http://www.youtube.com/watch?v=VTlV0Y5yAww&feature=PlayList&p=85F8464A742759v=VTlV0Y5yAww&feature=PlayList&p=85F8464A742759D1&playnext=1&index=5 )D1&playnext=1&index=5 )

• AIST’s HRP-2 AIST’s HRP-2

(http://www.youtube.com/watch?v=iigiFYzwjjE )(http://www.youtube.com/watch?v=iigiFYzwjjE )

• AIST’s HRP-3 AIST’s HRP-3

(http://www.youtube.com/watch?v=gO9th_Rfk2o )(http://www.youtube.com/watch?v=gO9th_Rfk2o )

Zero Moment Point (ZMP) (cont.)

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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)Sources (cited within this presentation)

• Robot LocomotionRobot Locomotion by Henrik Christensen by Henrik Christensen (http://www.nada.kth.se/kurser/kth/2D1426/slides2006/aut-rob2-2up.pdf )(http://www.nada.kth.se/kurser/kth/2D1426/slides2006/aut-rob2-2up.pdf )

• Walking Robots and Especially HexapodsWalking Robots and Especially Hexapods by Marek Perkowski by Marek Perkowski (http://web.cecs.pdx.edu/~mperkows/CLASS_479/May6/024.walking-robots-design.ppt#8 )(http://web.cecs.pdx.edu/~mperkows/CLASS_479/May6/024.walking-robots-design.ppt#8 )

• Estimation of ground reaction force and zero moment point on a powered ankle-foot Estimation of ground reaction force and zero moment point on a powered ankle-foot prosthesisprosthesis by Martinez Villalpando and Ernesto Carlos by Martinez Villalpando and Ernesto Carlos (http://dspace.mit.edu/handle/1721.1/37271 )(http://dspace.mit.edu/handle/1721.1/37271 )

• Design of a Biped RobotDesign of a Biped Robot by Andre Senior and Sabri Tosunoglu by Andre Senior and Sabri Tosunoglu

• Overview of ZMP-based Biped WalkingOverview of ZMP-based Biped Walking by Shuuji Kajita by Shuuji Kajita (http://www.dynamicwalking.org/dw2008/files/presentations/DW2008_keynotepresentatio(http://www.dynamicwalking.org/dw2008/files/presentations/DW2008_keynotepresentation_Shuuji_Kajita.pdf )n_Shuuji_Kajita.pdf )

• www.wikipedia.org (on ZMP)www.wikipedia.org (on ZMP)