Differentially Flat Design of Bipeds Ensuring Limit Cycles

• 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
• ISSN: 1083-4435; 1941-014X
• DOI: 10.1109/TMECH.2009.2033593

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.