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Transcript of Bibliographic report
Humanoid robots designed to look as close as possible to humans
to facilitate robot-human interaction
Humanoid robotics in medicine
Modeling of the humanoid robots
Most popular robots of nowadays
Model of impact
Dynamic model of the impact phase
Zero Moment Point (ZMP)
If the computed ZMP point is located outside of the support polygon that means that ground reaction force acting point is actually on the edge of the support polygon and the mechanism rotates about the support polygon edge will be initiated by the unbalanced moment, such point is called a fake ZMP (FZMP)
Modelling of NAO
Geometric description of the robot NAO
Types of walking gaits
with a topic "Walking gait based on ZMP control"
Iuliia Kralina, ARIA 2 student
Yanick Aoustin, proff ECN/UN
- to help humans in the dangerous area
- assistance of humans
- military applications
- entertainment of humans
came from the
human itself !
The study of the humanoid robotics helps to build a better orthosis and prosthesis for the human beings
Assistance to sick or retired people
HRP-2, HRP-3, HRP-4
some are possible to make for anyone
some has very complex structures
Principles of the humanoid walk were taken from the observation
of the ordinary human walk
Phases of walk:
Single Support (SS)
Double Support (DS)
Dynamic model in the Single Support (SS) phase
Dynamic model in the Double Support (DS) phase
Correct dynamic model is needed to design a control algorithm. Multiple phases of the robot walk should be divided into appropriate dynamic models:
Dynamic model in Single Support phase
Robot is fixed on 1 leg (three structure manipulator -like)
(foot is flat, contact with a ground is unilateral and that there is no slipping in the stance foot )
IDyM model is used to calculate the torques of the end-effector and reaction forces
robot in a SS
Dynamic model in Double Support phase
The impact occurs when a swing leg is touches the ground with non-zero velocity and becoming a stance foot while the previous stance foot leaves the ground and becomes a swing foot.
Impact is assumed to be instantaneous, when the configuration of a robot doesn't change but impulsive forces due to impact may result into the instantaneous change of the velocity of the robot after the impact.
In the case of using the N-E algorithm to calculate the dynamic model in DS we need first to define the configuration space of the robot in order to include the velocities of the origin R0 in the support foot. While representing V0 and w0 - linear and angular velocities of the support foot by the eulerian variables, 6 dof are added to the N dof of the robot.
Impact and DS modeling
position of a robot for impact and DS model
- position and orientation variables of the frame Ro
(equal to 0, when the foot is fixed)
- robot velocity and acceleration
Dynamic model in DS:
The impact model is deduced from the dynamic model in the DS, when we assume that the acceleration of the robot and reaction force are Dirac delta functions. The ground reaction wrench should be considered for each leg in the DS phase.
- Jacobian matrix that translates the effects of the ground reaction
forces on the non-stance foot.
-indicates the vector of the motorized joint variables.
- matrix that translates the effects of the ground reaction on the
- vector of the ground reaction forces
- number of joints constituting the locomotion system
The dynamic equation can be deduced from the equation for the DS phase:
- intensity of Dirac delta-functions for the forces
Because, the velocity of a swing leg should be zero after the impact ( ). The model of impact is transformed to the following system:
It's a special point in which the act of all forces on the mechanism can be replaced with one single force.
ZMP is the indicator of the contact for the humanoid systems
for the dynamic stability, ZMP should be located in the support foot
if the gait is statically stable, ZMP is equivalent to CoP(Center of Pressure)
ZMP is the point on the ground such that the moment exerted by the ground is zero along the axis x0 and y0.
information about ZMP position can be obtained by measuring forces acting at the contact of the ground and the mechanism
(with a help of force sensors)
Zero Moment Point (ZMP)
Stable and unstable systems
4 untrasonic sensors
8 force-sensing resistors
First edition of NAO
Programming possible in:
Matlab, C++, Java, C#, Python
25 dof in total
11 dof in lower part (2 dof in the ankle, 1 dof in the knee and 2 dof in the hip.
A special mechanism composed of 2 coupled joints equips the pelvis.) The rotation axis of these 2 joints is inclined at 45 degrees towards the body. Only one motor is needed
Parameterization of a robot
The modified David-Hardenberd parameterization was used to define the geometric parameters of the NAO robot.
Physical parameters could be taken from the Aldebaran robotics documentation
- ZMP based approach (requires the precise knowledge of robot dynamics, including mass, location of CoM and inertia of each link and mainly relies on the accuracy of the model)
- Ideas based on the Linear Inverted Pendulum (uses limited knowledge of dynamics, the controller relies on a feedback control)
- Other ideas
Characteristics of the model:
Foot size is too small to let the cart (ball)
stay on the edge
Mass of the cart small versus the mass of
If the ball accelerates with a proper rate,
the table can keep upright. At this
moment, the ZMP exists inside of the
table foot (ZMP and Cop points are
The cart (ball) determines the ZMP trajectory
Walking pattern generation
ZMP control as servo problem
Scheme of the preview control
Future work in the master thesis:
Walking gait based on the inverse kinematics
Walking gait via Human-Inspired Hybrid Zero Dynamics
Walking gait based on a sensor-driven Neuronal Controller and Real-time Online Learning
Assuming that the robot is in SS its dynamics can be represented via the Inverted Pendulum model, which connects the supporting foot and the CoM of the robot.
For such configuration it is possible to calculate the dynamics of the IP along x and y.
Some constraints are needed to use IP motion as a walking pattern. For the horizontal plane, dynamics uder constraints:
For a horizontal constraint it's possible to calculate ZMP point as:
So, we obtain the relation equation
between COM and ZMP:
Or, to reorder as:
With cart-table model we can calculate ZMP trajectory from the CoM trajectory.
Walking patter generation is an inverse problem. Here, the trajectory of the CoM must be deduced from the trajectory of ZMP.
Methods to solve the walking pattern problem:
1. Fourier transformation (Takanishi Method)
2. Solving the problem in the descrete time domain (Kagami method)
Defining new variable:
-time derivative of the horizontal acceleration of CoM
And regarding a new valiable as an input to the ZMP equaion we get:
The system generates the CoM trajectory such that the resulted ZMP follows the given reference.
the system on the left generates the CoM trajectory such that the resulted ZMP follows the given trajectory, thus the information on the future ZMP location is needed to compute the actual CoM
Descretizing the system with sampling time T :
The problem can be rewritten as perfomance index:
If the Preview control is correctly designed and tuned we receive the smooth generated trajectory of the CoM and the resulted ZMP follows the reference with a good accuracy.
Firstly, the ZMP reference has to be designed in order to stay in the center of the support foot during the SS and then it moves from the previous support foot to the new one during the DS.
Full understanding and implementation of the Preview control in the Matlab environment
Possible improvements of the Preview control:
- possible usage of the non-linear inverted pendulum
- fast omnidirectional walking
- recovery after the push with capture regions.
Thank you for your attention!
[AMBER 2 bipedal robot]
TOSY Ping Pong Playing Robot
[humanoid Robot “Flame”
Delft Univ. of Technology]
- force exerted from biped to the ground
Foot indictor rotation]
[Maud Pasquier, Master Thesis, ECN}
The value of zc is
[Carlos, Agüero ECN,
Master Thesis, 2013]
"On a winding road, we steer a car by watching ahead, by previewing the future reference."
Concept (Sheridan, 1966)
LQ optimal controller (Tomizuka, Rosenthal 1979; Katayama 1985)
Dynamic model in the Impact phase