Differentially Flat Design of Bipeds Ensuring Limit Cycles

For bipedal walking, a set of joint trajectories is acceptable as long as it satisfies certain overall motion requirements, such as: 1) it is repetitive (limit cycles); 2) it allows the foot to clear ground; and 3) it allows the biped to move forward. Since the actual trajectory followed by a biped...

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Bibliographic Details
Published in:IEEE/ASME transactions on mechatronics 2009-12, Vol.14 (6), p.647-657
Main Authors: Sangwan, V., Agrawal, S.K.
Format: Article
Language:English
Subjects:
Actuators
Biped
Constraint optimization
Control systems
Design engineering
Design methodology
differential flatness
Dynamical systems
Foot
Grounds
Humanoid robots
Legged locomotion
Limit-cycles
Methodology
Motion planning
Nonlinear control systems
Nonlinear dynamics
Robots
Trajectories
underactuated
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Summary:For bipedal walking, a set of joint trajectories is acceptable as long as it satisfies certain overall motion requirements, such as: 1) it is repetitive (limit cycles); 2) it allows the foot to clear ground; and 3) it allows the biped to move forward. Since the actual trajectory followed by a biped is not as important, a biped having some unactuated joints can also meet these motion requirements. Furthermore, due to physical constraints, a biped cannot have an actuator between the foot and the ground. Hence, it is underactuated during the phase when the foot is rolling on the ground. Besides underactuation, a bipedal robot has nonlinear dynamics and impacts. In general, it is difficult to prove existence of limit cycles for such systems. In this paper, a design methodology that renders planar bipedal robots differentially flat is presented. Differential flatness allows generation of parameterized limit cycles for this class of planar nonlinear underactuated bipeds. Sequential quadratic-programming-based numerical optimization routines are used to optimize these limit cycles while satisfying the motion constraints. The planning and control methodology is illustrated by a two-link biped.
ISSN:1083-4435
1941-014X
DOI:10.1109/TMECH.2009.2033593