Design Optimization of Musculoskeletal Humanoids with Maximization of Redundancy to Compensate for Muscle Rupture

TL;DR

This work tackles robustness to muscle rupture in musculoskeletal humanoids by optimizing muscle arrangement to maximize the availability of torque in all directions when a single muscle is compromised. It introduces the Radius of hypersphere Inscribed in available Torque Space (RITS) as a quantitative redundancy metric and uses a genetic algorithm to optimize the muscle Jacobian $G$ under tension bounds to enlarge the feasible torque space around the gravity-compensation target $\bm{\tau}_g$. Redundancy evaluation aggregates the inscribed-torque radii across all single-muscle rupture scenarios, enforcing a minimum number of rupturable muscles $M_{min}$ to ensure fault tolerance. The approach is validated through 1-DOF and 2-DOF simulations and demonstrated on the actual Musashi elbow, showing that strategically distributed or reduced moment arms can preserve motion under rupture and that the optimized designs translate to real hardware, thereby enabling more robust, adaptable humanoid robots.

Abstract

Musculoskeletal humanoids have various biomimetic advantages, and the redundant muscle arrangement allowing for variable stiffness control is one of the most important. In this study, we focus on one feature of the redundancy, which enables the humanoid to keep moving even if one of its muscles breaks, an advantage that has not been dealt with in many studies. In order to make the most of this advantage, the design of muscle arrangement is optimized by considering the maximization of minimum available torque that can be exerted when one muscle breaks. This method is applied to the elbow of a musculoskeletal humanoid Musashi with simulations, the design policy is extracted from the optimization results, and its effectiveness is confirmed with the actual robot.

Figures (10)

• Figure 1: The concept of this study. By calculating the radius of the hypersphere (blue circle) inscribed in the available torque space (red polygon) when each muscle is broken, an evaluation value is calculated, and the design (muscle Jacobian) is optimized by a genetic algorithm so that the robot can continue to move even when one muscle is broken.
• Figure 2: The basic musculoskeletal structure.
• Figure 3: Hypersphere (blue circle) inscribed in available torque space (red polygon). The line with a gradient from green to yellow is the line where each edge of the available muscle tension space is transformed into the joint torque space.
• Figure 4: The optimized design when $M=4$ and $\tau_g=\{-5, 0\}$.
• Figure 5: The available torque space and RITS of the optimized design when $\bm{\tau}^T_g=00$, $M=5$, and $M_{min}=5$.