Dynamic Coupling and Indirect Control of Jointed Robots Rolling Atop A Moving Platform

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.

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.

This paper presents "PenduMorph", a wireless reconfigurable rolling spherical robot designed as a modular platform for enclosed locomotion and inter-module interaction in challenging environments. The proposed robot extends our previous pendulum-actuated rolling disk concept to a fully enclosed spherical architecture integrating a 2-DoF internal pendulum, onboard control, battery-powered operation, and magnetic docking. The design aims to combine independent rolling mobility with protected hardware and reliable reconfigurability. We first present the robot design and an analytical study of the magnetic coupling mechanism to evaluate retention and interaction between coupled modules. We then experimentally investigate key motion behaviors at both the single-module and dual-module levels, including independent rolling, magnetic coupling, and coordinated coupled motion. The results show that the proposed platform enables stable wireless operation and a set of distinctive reconfigurable rolling behaviors, providing a useful foundation for future modular spherical robots operating in contact-rich and demanding environments.