legged robot ppt jit 1

Walking Robots

Sung Hyun Park

BHR Seminar

02/05/2009

Types of Locomotion in Nature

Real Robots

U-BOT (University of Massachusetts, USA)

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

Real Robots (cont.)

The Self Deploying Microglider(EPFL, France)

Aiko (SINTEF Applied Cybernetics, Japan)

Real Robots (cont.)

Battlefield Extraction-assist Robot(Vecna Technologies, USA)

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 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

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.

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?)

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

Joints in a Leg (cont.)

Picture of a joint model

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

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

Gaits (cont.)

An example of a static gait with 6 legs

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

Gaits and Stability

Gaits and Stability (cont.)

Each vertex = support foot Dot = center of gravity Quadruped Robot – Gait Motion (

http://www.youtube.com/watch?v=lxIy3jYuQCo)

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

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

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

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

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


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.


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.


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)

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)

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.

Zero Moment Point (ZMP)

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

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


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


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


Anyways, in a very brief summary…


Honda’s Asimo

(http://www.youtube.com/watch?v=VTlV0Y5yAww&feature=PlayList&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 )



Formulas from wikipedia

Sources (cited within this presentation)

Robot Locomotion by Henrik Christensen (http://www.nada.kth.se/kurser/kth/2D1426/slides2006/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.ppt#8 )

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_Kajita.pdf )

www.wikipedia.org (on ZMP)

legged robot ppt jit 1

Documents