In light of global aging and prevalent stroke-related hemiplegia, this study addresses challenges in robot-assisted Sit-to-Stand (STS) movements, a daily activity prone to falls. Supernumerary Robotic Legs (SRL) serve as independent support, enhancing stability and limb movement range. Existing coordination control methods lack personalization for STS assistance, requiring solutions for human intent transmission and rapidly optimize coordination control challenges in the non-coupled human-robot system. The proposed human-SRL coordination control algorithm, grounded in personalized SRL-human coupling models, incorporates surface electromyography (sEMG) signals to design an intent-driven variable stiffness impedance control. The inclusion of incremental learning enables rapid optimization of impedance parameters, facilitating real-time adjustments in SRL assistance for adaptive coupling with users. Practical experiments involving both healthy participants and hemiparetic patients validate the algorithm’s effectiveness during STS. The results validate substantial reductions in STS time (39.54%) and muscle activity (28.01%), highlighting the efficacy of the proposed algorithm-controlled SRL support for hemiparetic individuals.

Supernumerary robotic limbs (SRLs) offer substantial potential in both the rehabilitation of hemiplegic patients and the enhancement of functional capabilities for healthy individuals. Designing a general-purpose SRL device is inherently challenging, particularly when developing a unified theoretical framework that meets the diverse functional requirements of both upper and lower limbs. In this paper, we propose a multi-objective optimization (MOO) design theory that integrates grasping workspace similarity, walking workspace similarity, braced force for sit-to-stand (STS) movements, and overall mass and inertia. A geometric vector quantification method is developed using an ellipsoid to represent the workspace, aiming to reduce computational complexity and address quantification challenges. The ellipsoid envelope transforms workspace points into ellipsoid attributes, providing a parametric description of the workspace. Furthermore, the STS static braced force assesses the effectiveness of force transmission. The overall mass and inertia restricts excessive link length. To facilitate rapid and stable convergence of the model to high-dimensional irregular Pareto fronts, we introduce a multi-subpopulation correction firefly algorithm. This algorithm incorporates a strategy involving attractive and repulsive domains to effectively handle the MOO task. The optimized solution is utilized to redesign the prototype for experimentation to meet specified requirements. Six healthy participants and two hemiplegia patients participated in real experiments. Compared to the pre-optimization results, the average grasp success rate improved by 7.2%, while the muscle activity during walking and STS tasks decreased by an average of 12.7% and 25.1%, respectively. The proposed design theory offers an efficient option for the design of multi-functional SRL mechanisms.