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Gait and trajectory planning for legged robots

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Er Aishwary Singh Baghel
Er Aishwary Singh Baghel

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.

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Gait and Trajectory Planning for Legged Robots -By Aishwary Singh Baghel
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. 341351. 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.
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.
Phases of Gait Cycle
Stance Phase Heel strike (Initial Contact) Foot flat (Loading Response) Mid-stance (Mid Stance) Heel off (Terminal Stance) Toe off (Pre Swing)
Gait and trajectory planning for legged robots
Swing Phase 1) Acceleration (Initial Swing) 2) Mid-swing 3) Deceleration (Terminal Swing)
Gait and trajectory planning for legged robots
Representation of complete Gait Cycle
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.
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.
Analytical Method Fig. 1
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.
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.
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.
Using Lagranges equation, the equation of motion with respect to u1 , u2 , and u3 is derived as follows:
Gait and trajectory planning for legged robots
Equation of Motion in the Second Phase The mechanical model is a 2-dof link system. Substituting
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
Fig.3 3-dof analytical model of a biped walking mechanism
Fig. 4 Analytical model of a link at the instant of collision
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:
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:
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
There are two zero elements in [H] as shown in eq. 5 Substituting the formula (6) into eq.5 ,
The angular position at posture 4 is calculated as follows from Fig. 4 and Eq. (6):
From Eqs. (5) and (6),
Apply Runge-Kutta integration method and integrate Eq. (10) from posture 43 during the second apply the backward phase to calculate the motion variables at posture 3. The time step width is given by:
Gait and trajectory planning for legged robots
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.
Assume that no knee collision occurs, instead of Eq. (14), we have,
Dimensions
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.
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Gait and trajectory planning for legged robots

  • 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. 341351. 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.
  • 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)
  • 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.
  • 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 Lagranges 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 43 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,
  • 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.