When Rolling Gets Weird: A Curved-Link Tensegrity Robot for Non-Intuitive Behavior

Compliant mechanisms are important in robotics because they can improve adaptability, safety, and energy efficiency while reducing hardware complexity. This paper presents SPiralRoll, a novel torsion-spring-based underactuated compliant mechanism for rolling robots and compliant robotic actuation. The mechanism uses arc-distributed elastic members and two motor inputs to realize three physically observable output motions: rotational motion, radial expansion/contraction, and axial spin induced by nonlinear compliant deformation. Two configurations, namely full-arc and single-arc designs, are developed and experimentally evaluated. Beyond benchtop validation, the mechanism is integrated into a spherical rolling robot, where proof-of-concept experiments demonstrate forward rolling and turning. The results show that the full-arc design provides better structural support and smoother deformation, whereas the single-arc design yields larger deformation and stronger inertial excitation, making it more suitable for pendulum-driven rolling locomotion. Overall, SPiralRoll provides a low-cost, compact, and fully 3D-printable solution for underactuated compliant rolling robots and adaptive robotic joints.

Limbless robots offer exceptional mobility in confined and cluttered environments due to their slender bodies and their ability to exploit body-terrain interactions. Recent designs incorporating compliance demonstrate robust locomotion without complex sensing or control; however, these systems typically rely on fixed body configurations, with each morphology specialized for a single locomotion mode or environment. This raises a key challenge: how can a single limbless robot achieve versatile locomotion while preserving the robustness of compliance-mediated locomotion? To address this challenge, we present a cable-driven limbless robot that reconfigures body morphology and compliance to enable diverse locomotion modes. Distributed cable actuation generates traveling body waves, while programmable passive compliance enables robust contact-rich locomotion without terrain knowledge or high-bandwidth feedback. Rolling joints reorient bending planes along the body, enabling rapid reconfiguration and smooth transitions between locomotion styles, and incorporate geared locking to maintain configuration without continuous power. By combining programmable bending compliance and morphology control, the platform achieves lateral undulation, sidewinding, rolling, and twisting within a single system. Experiments demonstrate reliable gait generation, traversal in obstacle-rich environments, and transitions between modes, establishing a versatile limbless platform for navigating complex environments with applications in search and rescue, environmental monitoring, and inspection.

This paper presents a full nonlinear constrained dynamic model of MonoRollBot, a novel 3-DoF spherical rolling robot driven by a single motor, a lead-screw transmission, and a spring-coupled internal moving mass, together with motion analysis of its behavior. To the best of our knowledge, this is one of the first full nonlinear nonholonomic models reported for a mono-actuated, super-underactuated spherical rolling robot of this kind. Because rolling without slipping is nonholonomic, the dynamics are derived using the Lagrange--d'Alembert formulation, with the lead-screw relation imposed as a holonomic constraint and the rolling condition imposed in Pfaffian form. The formulation retains the complete generalized coordinates of shell translation, shell attitude, screw travel, nut rotation, and radial mass motion. Simulations and representative motion studies show qualitative agreement with prototype behavior and reveal how gravity, compliance, and inertia jointly shape the locomotion and motion capabilities of this strongly underactuated robot. The resulting model also provides a mechanically consistent basis for future state estimation and hybrid controller design for this nonholonomic mono-actuated rolling robot.