This paper studies the design, modeling, and control of a novel quadruped, featuring overconstrained robotic limbs employing the Bennett linkage for motion and power transmission. The modular limb design allows the robot to morph into reptile- or mammal-inspired forms. In contrast to the prevailing focus on planar limbs, this research delves into the classical overconstrained linkages, which have strong theoretical foundations in advanced kinematics but limited engineering applications. The study showcases the morphological superiority of overconstrained robotic limbs that can transform into planar or spherical limbs, exemplifying the Bennett linkage. By conducting kinematic and dynamic modeling, we apply model predictive control to simulate a range of locomotion tasks, revealing that overconstrained limbs outperform planar designs in omni-directional tasks like forward trotting, lateral trotting, and turning on the spot when considering foothold distances. These findings highlight the biological distinctions in limb design between reptiles and mammals and represent the first documented instance of overconstrained robotic limbs outperforming planar designs in dynamic locomotion.

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