构建3自由度欠驱动球形机器人的完整非线性动力学模型，揭示其运动机制。
Full Nonlinear Nonholonomic Dynamics and Motion Analysis of a 3-DoF Underactuated Spherical Rolling Robot
- 基于拉格朗日-达朗贝尔原理建立非完整约束模型，保留全部广义坐标。
- 仿真显示重力、柔性和惯性共同影响机器人运动能力，与实物一致。
- 为状态估计与混合控制器设计提供力学一致的理论基础，适合控制研究者。
本文提出一种新型单电机驱动的3自由度球形滚动机器人MonoRollBot的全非线性约束动力学模型，并对其运动行为进行分析。该机器人采用丝杠传动和弹簧耦合内部移动质量，具有强欠驱动特性。由于无滑动滚动属于非完整约束，动力学采用拉格朗日-达朗贝尔公式推导，丝杠关系作为完整约束，滚动条件以Pfaffian形式表示。模型保留了外壳平移、姿态、丝杠行程、螺母旋转及径向质量运动等全部广义坐标。仿真与典型运动研究显示，模型与原型行为定性一致，揭示了重力、弹性与惯性如何协同塑造其运动能力。该模型为未来此类非完整欠驱动滚动机器人的状态估计与混合控制器设计提供了力学一致性基础。
原文摘要 · Abstract (English)
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.
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