Mechanical engineering, robotics.

1. Walking Control Algorithm of Biped
Humanoid Robot on Even , Uneven
and Inclined Floor

2.  INTRODUCTION
This seminar describes walking control algorithm for
the stable walking of a biped humanoid robot on an
even, un even and inclined floor. Many walking control
techniques have been developed based on the
assumption that the walking surface is perfectly flat
with no inclination. Accordingly, most biped humanoid
robots have performed dynamic walking on well
designed flat floors. In reality, however, atypical room
floor that appears to be flat has local and global
inclinations of about 2 degrees. It is important to note
that even slight unevenness of a floor can cause
serious instability in biped walking robots. In this
seminar, propose an online control algorithm that
considers local and global inclinations of the floor by
which a biped humanoid robot can adapt to the floor
conditions. For walking motions, a suitable walking
pattern was designed first. Online controllers were

3.  STATIC WALK
 static walking with a very low walking speed, walking
speed must be low so that inertial forces are negligible
 The step time was over 10 seconds per step and the
balance control strategy was performed through the use
of COG (Center Of Gravity).
 Hereby the projected point of COG onto the ground
always falls within the supporting polygon that is made
by two feet.
 During the static walking, the robot can stop the walking
motion any time without falling down.
 Here robot is statically stable, this mean that, at any
time, if all motion Is stooped the robot will stay
indefinitely in a stable position.
 This king of walking requires large feet, strong ankle
joints and can achieve only slow walking speeds.

4.  Dynamic walk
 It is fast walking with a speed of less than 1 second per step.
 If the dynamic balance can be maintained, dynamic walking
is smoother and more active even when using small body
motions.
 if the inertial forces generated from the acceleration of the
robot body are not suitably controlled, a biped robot easily
falls down.
 cannot stop the walking motion suddenly.
 Hence, the notion of ZMP (Zero Moment Point) was
introduced in order to control inertial forces.
 Zero Moment Point (ZMP)
 The ZMP is the point where the total angular momentum
is zero at the foot.
 The position of the ZMP is computed by finding the
point(X, Y, Z)where the total torque is zero.
 For dynamic balancing the ZMP must lies in the

5.  Where PZMP1 is the ZMP for one foot and PZMP2 is the
ZMP for the other foot.
 ZMP point (black point) in two cases, one with the robot
standing (left), and other after give a step (right). The
pointed line represent the support polygon.
 Total _ PZMP = PZMP1 −PZMP2

6. XY
 Mpx = Mpy = 0
 Fp + FA = 0
 P OP * FP + MA + MPZ + POA * FA = 0
 (P OP * FP ) + (MA)XY + (POA * FA )XY = 0

7.  FICTITIOUS ZMP (FZMP) ????
 RELATION WITH COP AND ZMP
What is COP???????????

8. ZMP & COP Relation….
 If point P is within the SP then the relation P ≡ CoP ≡
ZMP holds. If point P is outside the SP, then points CoP
and FZMP do not coincide and P ≡ FZMP.
 Moreover, if the biped robot is dynamically stable, the
position of the ZMP can be calculated with the CoP, e.g.
using force sensors on the sole of the feet.

9. To calculate the point P, there are
several assumptions that have to be
made:
a) The biped robot consists of n rigid
links.
b) All kinematic information, such as
position of CoM, link orientation,
velocities,
etc. are known and calculated by forward
kinematics.
c) The floor is rigid and motionless.
d) The feet can not slide over the floor
 FIND ZMP COORDINATE (X,Y,Z)

12.  BIPED WALKING AND ONLINE CONTROL
ALGORITHM CONSIDERING FLOOR CONDITION
I. WALKING PATTERN GENERATION For
the design of the walking pattern, the authors
considered the following four design factors.
 1) Walking cycle (2 × step time)
a)Inverted pendulum model

13. 2) Lateral swing amplitude of the pelvis
Ymc = A sinωt
Xmc = A sinωt
3) Double support ratio

14.  4) Forward landing position ratio of the
pelvis

15.  WALKING PATTERN DESIGN

17.  UPRIGHT POSE CONTROL FOR INCLINED SURFACE
a)PITCH CONTROL
b)ROLL CONTROL

18. PI controller using the torso pitch error torso θ on the
prescribed ankle trajectory uankle pitch as follows:
Where, Kp and KI are the proportional and integral gains, U(ankle
pitch) is the compensated ankle pitch angle . The upright pose
controller is activated in all walking stages. Following equations
represents the control law.
Where, Kp and KI are the proportional and integral gains, U′(ankle roll)
is the compensated ankle roll angle . U′(ankle roll) can be calculated
geometrically from lR and lL . In this manner, the robot always keeps
its torso upright against the global inclination of the floor . Therefore,
the robot can walk stably in spite of the global inclination of the floor.

19.  LANDING ANGULAR MOMENTUM CONTROL FOR
UN EVEN SURFACE
Ankle torque control
block diagram

20. END