Over the past few decades, robotics has undergone a transformative evolution, yet creating machines capable of dramatic volumetric shape changes while maintaining high structural stability and precision remains elusive. Among various approaches, truss robots and tensegrity robots - which we term looped-graph structures (LGSs) - offer unique advantages through their architecture of nodes and length-changeable edges. These structures leverage their graph topology with loops, where edges can circle back to their starting nodes, to achieve extensive degrees of freedom and distinctive shape-changing capabilities while maintaining structural stability through their distributed network.

LGSs face two fundamental challenges that have limited their practical implementation. First, as their complexity grows exponentially with size, they encounter the Curse of Dimensionality (CoD), making both physical fabrication and control system design increasingly intractable. Second, the discrete nature of their graph topology and categorical parameters like actuator grouping assignments make traditional continuous optimization approaches ineffective, particularly as the design space grows geometrically with robot size.

We present a systematic progression of solutions that addresses both challenges. To tackle the CoD in physical implementation, we introduce an actuator grouping mechanism inspired by biological muscle synergy, where complex movements emerge from coordinated muscle groups rather than individual control. This enables the fabrication of truss robots with over 100 actuators controlled by just a few modules, dramatically reducing system complexity while maintaining shape-changing capabilities. Building on this foundation, we develop an interactive editor with real-time simulation that bridges the gap between conceptual design and physical implementation.

For complex structures capable of multiple tasks, we first implement a customized genetic algorithm that navigates the discrete graph space while respecting connectivity constraints. However, as truss complexity scales up, this discrete optimization becomes inefficient in the geometrically increasing search space. To overcome these limitations and enable topology generation, we develop two complementary approaches using variational auto-encoders (VAE) that transform the discrete design space into continuous latent representations for more efficient optimization. We introduce a novel truss grammar that represents designs through sequential tokens and parameters, enabling translation between discrete structures and continuous latent spaces. Our graph attention network approach achieves 99.925% accuracy in reconstructing actuator groupings, while our long short-term memory network successfully generates complete truss topologies and parameters, creating the first end-to-end framework for optimizing both discrete topology and continuous parameters of truss robots.

Through demonstrations ranging from quadrupedal locomotion to shape-shifting structures, we show that our framework enables the practical implementation of complex morphing LGSs. By bridging the gap between theoretical capability and physical realization, this work establishes foundations for a new generation of adaptive robots that can reshape themselves to meet diverse task requirements.

153 pages

Thesis Committee:
Lining Yao (Chair)
Nikolas Martelaro
Alexandra Ion
Ding Zhao (Mechanical Engineering)

Brad A. Myers, Head, Human-Computer Interaction Institute
Martial Hebert, Dean, School of Computer Science

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