Dynamics of Bipedal Gait: Part I—Objective Functions and the Contact Event of a Planar Five-Link Biped

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Abstract
Previous approaches to the problem of prescribing the motion of bipedal machines do not completely characterize the desired walking patterns in terms of coherent parameters. A well-structured parametric formulation that ties the objective functions to the resulting gait patterns has never been established. This article presents an approach that can be followed to formulate objective functions which can be used to prescribe the gait of a planar, five-element, bipedal automaton during single support phase. The motion of the biped is completely characterized in terms of progression speed, step length, maximum step height, and stance knee bias. Kinematic relations have been derived and the inverse problem has been solved to perform a parametric study that correlates the regions of the four-dimensional parameter space with the respective gait patterns. Major limitations include the assumptions of rigid elements and point contact between the lower limbs and the walking surface. Most importantly, the motion of the biped is assumed to perfectly conform with the objective functions at the instant of contact. The control and stability issues are presented in Part II of this paper.

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