Gait is the medical term to describe human locomotion or the way that we walk. Mechanism is model to be a 3-degree-of-freedom link system composed of a stance leg and a 2-dof swing leg.

1. Gait and Trajectory Planning for
Legged Robots
-By Aishwary Singh Baghel

2. References
• Kyosuke Ono, Rongqiang Liu, 2012, “Optimal Biped
Walking Locomotion Solved by Trajectory”.
• Kato, T., et al., 1981, ‘‘The Realization of the Quasi
Dynamic Walking by the Biped Walking Machine,’’
Proc. of Int. Symp. on Theory and Practice and
Manipulators, ROMANSY, pp. 341–351.
• Miyazaki, F., and Arimoto, S., 1980, ‘‘A Control
Theoretic Study on Dynamical Biped Locomotion,’’
ASME J. Dyn. Syst., Meas., Control, 102~4!, pp. 233–
239.

3. Gait Analysis
• Gait is the medical term to describe human
locomotion or the way that we walk.
• It is a locomotion achieved through the
movement of limbs.
• Different gait patterns are characterized by
differences in limb movement patterns.
• Every individual has a unique gait pattern.

4. Phases of Gait Cycle

5. Stance Phase
• Heel strike (Initial Contact)
• Foot flat (Loading Response)
• Mid-stance (Mid Stance)
• Heel off (Terminal Stance)
• Toe off (Pre Swing)

7. Swing Phase
• 1) Acceleration (Initial Swing)
• 2) Mid-swing
• 3) Deceleration (Terminal Swing)

9. Representation of complete Gait Cycle

10. Trajectory Planning
• An optimal trajectory planning of walking legged
robots
• Walking mechanism which has thighs, shanks and
small feet.
• Mechanism is model to be a 3-degree-of-freedom
link system composed of a stance leg and a 2-dof
swing leg.
• The swing motion of 2-dof swing until knee collision.
• The swing motion of the straight leg until toe
collision.

11. • The control methods to generate a stable walking gait
that have been proposed are a zero moment point.
• ZMP principle is commonly used because of its
simplicity and clarity of the control strategy.
• The natural walking gait with minimum power
consumption or minimum input can be calculated by
the optimal trajectory planning method.
• The trajectory planning problem can be solved by the
dynamic programing method.

12. Analytical Method
Fig. 1

13. • Disregard the upper body because it has little effect
on walking locomotion.
• Two legs are assumed to be directly connected to
each other through an actuator.
• Both knee and ankle joints can be driven by
individual actuators.
• Knee joint of the stance leg is passively locked by
means of a stopper mechanism to prevent the
mechanism from collapsing.

14. • Ankle of the stance leg is modeled as a rotating joint
fixed to the ground.
• The mechanism is modeled to be a 3-dof link system
as shown in figure 1.

15. 3-dof Analytical Model and Equation
of Motion
Notations are -
• ui is the input torque at joint i,
• li is the i-th link length,
• mi is the i-th link mass,
• ai is the distance of the mass center of the i-th link
from the joint i, and
• Ii is the inertia moment of the i-th link about the mass
center.

16. • Using Lagrange’s equation, the equation of motion
with respect to u1 , u2 , and u3 is derived as follows:

18. Equation of Motion in the Second
Phase
• The mechanical model is a 2-dof link system.
• Substituting

19. Angular Velocity Variation Caused by
Foot Exchange
• It is assumed that the toe collision is plastic and the
foot exchange takes place instantly for the sake of
analytical simplicity.
Fig. 2 Change of constraints by foot change

20. Fig.3 3-dof analytical model of a biped walking mechanism

21. Fig. 4 Analytical model of a link at the instant of collision

22. • Pi and Pi11 are the impulses caused by the collision
at the joints i and i11, respectively.
• The impulse momentum equations for link i are
written in the forms:

23. • After the foot exchange, the model turns into a 3-dof
system.
• The relationship of the link angular velocities during
the foot exchange is derived from (4) as follows:

24. Cyclic Walking Locomotion Condition
• In order to realize the cyclic walking locomotion, the
motion state at posture 5 must be the same as that at
posture 1.
• Therefore, we get

25. • There are two zero elements in [H] as shown
in eq. 5
• Substituting the formula (6) into eq.5 ,

26. • The angular position at posture 4 is calculated as
follows from Fig. 4 and Eq. (6):

27. • From Eqs. (5) and (6),

28. • Apply Runge-Kutta integration method and integrate
Eq. (10) from posture 4–3 during the second apply
the backward phase to calculate the motion variables
at posture 3.
• The time step width is given by:

30. • Using the impulse-momentum equations
similar to Eq. (4) for the knee collision
• The angular velocity vector at posture 2 must
satisfy the following equation.

31. • Assume that no knee collision occurs, instead
of Eq. (14), we have,

32. Dimensions

33. Conclusion
• Biometrics points are useful for making
identifications with camera systems, but they depend
on the existence of a previously generated database so
that gait patterns can be compared.
• Numerically investigated the optimal walking
locomotion.

34. Thank You