Innovative Design of Multi-functional Supernumerary Robotic Limbs with Ellipsoid Workspace Optimization

TL;DR

This paper tackles designing a general-purpose supernumerary robotic limb (SRL) that simultaneously extends upper-limb grasping capability and supports lower-limb walking. It introduces a multi-objective optimization framework that uses ellipsoid-based workspace quantification, plus sit-to-stand braced force, mass, and inertia as objectives, solved efficiently by a multi-subpopulation correction firefly algorithm (MSCFA). The authors demonstrate the approach with simulations and a waist-mounted prototype, reporting improved grasping success (≈7.2%), reduced lower-limb muscle activity (≈12.7%–25.1%), and enhanced balance metrics in healthy participants, with additional gains in hemiplegia patient experiments (grasping up ≈17.5%, STS EMG down ≈6.2%). Overall, the work provides a scalable design theory and a practical workflow for developing multifunction SRLs that can aid rehabilitation and functional enhancement, while offering insights into computation-efficient workspace representation via ellipsoids.

Abstract

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.

Figures (23)

• Figure 1: Block diagram overview of the system architecture of the general-purpose SRL robot.
• Figure 2: The kinematics description of general-purpose SRL. (a) Case I, SRL kinematics description when using as an upper limb. (b) Case II, SRL kinematics description when using as a lower limb. The solid line links the human and the dashed lines the SRL.
• Figure 3: Pareto Front of MOO problem under 2-dimension condition. The blue dots refer to the solving individuals of MOO problem.
• Figure 4: The description of two workspace ellipsoid.
• Figure 5: Schematic diagram of proposed MSCFA: Each small circle represents an individual firefly in the algorithm. The darker the color of the circle, the higher the fitness of the firefly. Individuals with high fitness will generate an attraction region, represented by a dark-colored background circle with a dashed line. Conversely, individuals with low fitness will generate an repulsion region, represented by a light-colored background circle.