Overconstrained Locomotion

TL;DR

This work addresses energy-efficient, omnidirectional locomotion for legged robots by introducing Overconstrained Robotic Limbs (ORLs) based on the spatial Bennett linkage and enabling morphologic reconfiguration between reptile- and mammal-inspired forms. It combines a parametric ORL design actuated by quasi-direct drives with a Model Predictive Control (MPC) framework and reinforcement learning (RL) to evaluate performance across multiple terrains. Key findings show that ORLs achieve lower cost of transport (COT) and higher velocity/payload efficiency than planar limbs in simulated tasks, including forward and lateral trotting, turning, gravel traversal, and push recovery, with RL policies further validating energy advantages and transferability. The results suggest a promising direction for reconfigurable, energy-aware limb design, while acknowledging hardware validation and Sim2Real gaps as critical next steps toward real-world deployment and broader biomechanical insights.

Abstract

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.

Figures (20)

• Figure 1: Morphological inspiration from mammal and reptile limbs to the modern design of quadrupedal robotic limbs using closed-loop linkages. (A) Schematic illustrations of quadruped limb designs inspired by i) mammals and ii) reptiles, where $z_i (i=1,2,3)$ is the axis of actuator $A_i$, $w_B$ is the body width, $w_f$ is the foot-ground contact width, and $h_B$ is the robot height. Both limb designs usually have a kinematic singularity, typical for the limbs to stretch straight for mammals and be folded for reptiles. (B) Parametric design reconfiguration of the robotic limbs, including i) the Overconstrained Robotic Limb with a Bennett linkage, ii) the triple-QDD module, iii) the planar 4-bar robotic limb with equal length in opposite links, and design variants of the robotic limb with iv) extended foot, v) diamond-shaped planar 4-bar, and vi) slender-parallelogram planar 4-bar. (C) The engineering prototype in standing posture.
• Figure 2: Generalization of the co-axial, dual-actuator design of the robotic limbs. Here, actuators $A_2$ and $A_3$ drive a planar four-bar linkage or its variations for a more compact center of gravity, which is reflected among a wide range of existing quadrupedal robots with engineering possibilities for new limb designs if spatial four-bar linkages are adopted.
• Figure 3: The schematic diagrams of overconstrained robotic limbs with the green and white cylinders as active and passive joints, respectively. (A) The closed-loop model. (B) The spanning tree model.
• Figure 4: Parametric reconfiguration of the overconstrained robotic limb. (A) Parametric reconfiguration from a Bennett linkage to a parallelogram by constraining all twist angles to zeros, then to a planar limb with different link lengths, where the extension for foot length could be added at any time to enable morphological reconfiguration of the overconstrained quadruped. (B) Exemplified illustration of the engineering prototype parametrically reconfigured into i) reptile- or ii) mammal-inspired morphology.
• Figure 5: The locomotion control framework of the overconstrained quadruped.