In this paper, we propose the design of a planar biped for which the model is nearly linear, i.e., the inertia matrix is a constant and the gravity terms in the equations of motion are still nonlinear, but simplified. The legs are designed such that the inertia matrix is independent of the joint variables. As a result, the nonlinear terms in the centrifugal and Coriolis terms disappear. In this design, each leg has two links that are connected by a revolute joint at the knee. The two legs are connected to each other at the hip. The center of mass (COM) of each leg is located at the hip using counterweights. We assume that the stance leg is locked at the knee during the support phase. For this system, the dynamic model for the swing phase is considered. The stability of these designs is analysed by considering these as linear systems with nonvanishing perturbations. The paper discusses issues of ultimate stability bounds of the system and tracking of desired trajectories.

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