The Nonsmooth Impact Direction (NSID) of Robotic Systems

2026-07-15

AI Summary

This study addresses the challenge of modeling impact forces in rigid robots interacting with complex environments characterized by inelasticity, friction, and compliant joints, where conventional approaches lack a universal analytical framework. The work introduces, for the first time, the concept of “Nonsmooth Impact Direction” (NSID) and theoretically demonstrates that it is an intrinsic property of robotic impact processes, independent of contact parameters. By integrating nonsmooth dynamics theory with velocity jump analysis and experimental validation, the authors establish a unified framework for predicting impact directions across diverse rigid-link systems. Results show that NSID accurately captures the impulse direction in frictional, inelastic collisions, thereby providing a foundational theoretical basis for planning and control in impact-driven tasks such as slip walking and repetitive tapping.

Abstract

Collisions of rigid-link robots and rigid environments are often modeled as instantaneous events. Under this idealization, the impact forces become impulsive and the system velocities nonsmooth. In this work, we systematically analyze pre- and post-impact velocities focusing on what we refer to as the nonsmooth impact direction (NSID). We show that it is a characteristic direction of a robotic impact and largely independent of contact properties. The results are directly applicable to large classes of backdrivable robotic systems with rigid links. We address particularities of systems with nonelastic and flexible joints, unconstrained as well as constrained systems. Further, we show that the approach direction w.r.t the NSID sets the direction of the impulsive force in frictional, inelastic impacts. The comprehensive theoretical analysis of this work supported by an experimental validation may serve as a foundation for future planning and control algorithms for various robotic impact applications. These can include humanoid locomotion on a slippery surface or repetitive hammering.

Problem

• Nonsmooth Impact Direction
• Robotic Collisions
• Impulsive Forces
• Rigid-Link Robots
• Impact Dynamics

Innovation

• Nonsmooth Impact Direction
• impulsive forces
• rigid-link robots
• impact modeling
• backdrivable systems