This paper studies the design, control, and learning of a novel robotic limb that produces overconstrained locomotion by employing the Bennett linkage for motion generation, capable of parametric reconfiguration between a reptile- and mammal-inspired morphology within a single quadruped. In contrast to the prevailing focus on planar linkages, this research delves into adopting overconstrained linkages as the limb mechanism. The overconstrained linkages have solid theoretical foundations in advanced kinematics but are under-explored in robotic applications. This study showcases the morphological superiority of Overconstrained Robotic Limbs (ORLs) that can transform into planar or spherical limbs, exemplified using the simplest case of a Bennett linkage as an ORL. We apply Model Predictive Control (MPC) to simulate a range of overconstrained locomotion tasks, revealing its superiority in energy efficiency against planar limbs when considering foothold distances and speeds. The results are further verified in overconstrained locomotion policies optimized from Reinforcement Learning (RL). From an evolutionary biology perspective, these findings highlight the mechanism distinctions in limb design between reptiles and mammals and represent the first documented instance of ORLs outperforming planar limb designs in dynamic locomotion. Future studies will focus on deploying the model-based and learning-based overconstrained locomotion skills in the robotic hardware to close the Sim2Real gap for developing evolutionary-inspired, energy-efficient control of novel robotic limbs.

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