The vibration-driven locomotion system subject to the Coulomb dry friction is a typical multi-degree-of-freedom piecewise-smooth dynamical system with rigid-body displacement. Rather than ignoring the sticking behaviors caused by dry friction in previous studies, this paper focuses on the steady-state dynamics and the discontinuity-induced sliding bifurcations of a non-smooth three-module vibration-driven system. It is shown that the presence of sticking partially invalidates the averaging method and prevents an accurate prediction of the locomotion performance. As a result, numerical methods are employed in this research, which not only gives the distribution pattern of the average steady-state velocity with respect to the actuation phase differences but also elucidates its variation trend with respect to the actuation frequency and friction anisotropism, revealing the significance of the resonance effect and phase coordination for locomotion performance enhancement. Subsequently, this paper focuses on the stick–slip dynamics associated with the non-smooth boundaries induced by dry friction. Through comprehensive numerical calculations, we identify four different types of stick–slip motions and their distributed zones, whose boundaries are essentially the sliding bifurcation curves. Analytical expressions of these bifurcation curves are derived by means of the least-square regression, and they together constitute a bifurcation diagram for a given actuation and environment conditions. Each time a sliding bifurcation curve is traversed, the stick–slip trajectories experience qualitative changes. We also systematically reveal the evolution of the bifurcation diagram with the actuation frequency and friction anisotropism.

库仑干摩擦下的振动驱动运动系统是典型的多自由度分段光滑动力系统，具有刚体位移。本文没有忽略以往研究中由干摩擦引起的粘着行为，而是重点研究了非光滑三模振动驱动系统的稳态动力学和不连续性引起的滑动分岔。结果表明，粘连的存在部分地使平均方法无效，并阻止了对运动性能的准确预测。因此，本研究采用数值方法，不仅给出了平均稳态速度相对于驱动相位差的分布模式，而且阐明了其相对于驱动频率和摩擦各向异性的变化趋势，揭示了共振效应和相位协调对运动性能的意义增强。随后，本文重点研究了与干摩擦引起的非光滑边界相关的粘滑动力学。通过综合数值计算，我们确定了四种不同类型的粘滑运动及其分布区域，其边界本质上是滑动分岔曲线。这些分岔曲线的解析表达式是通过最小二乘回归得出的，它们共同构成给定驱动和环境条件的分岔图。每经过一条滑动分岔曲线，粘滑轨迹都会发生质的变化。我们还系统地揭示了分岔图随驱动频率和摩擦各向异性的演变。