Discrete VHCs for Propeller Motion of a Devil-Stick using purely Impulsive Inputs

2025-08-20

AI Summary

This paper addresses the control of propeller-like underactuated juggling motion of a devil stick actuated by normal impulsive forces in a vertical plane. To handle the discontinuous dynamics induced by purely impulsive inputs, we introduce— for the first time—the concept of Discrete Virtual Holonomic Constraints (DVHC), which encode discrete geometric relationships between the center-of-mass position and the orientation angle, enabling construction of a discrete zero-dynamics model. Based on Poincaré mapping, we design an orbital stabilization controller that achieves precise tracking and robust stability of periodic helical trajectories. DVHC naturally reduces to conventional continuous virtual constraints in the limit, thereby extending virtual constraint theory to discontinuous dynamical systems. Simulation results demonstrate that the proposed method efficiently generates and stabilizes high-precision helical motion orbits, establishing a novel paradigm for dynamic manipulation with underactuated robots.

Technology Category

• Intelligent Robots: Manipulation
• Computer Vision: Low Level & Physics-based Vision
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: The sharing economy
• Systems and Infrastructure for Web, Mobile and WoT: Virtualization and resource management in Web systems and infrastructures

Abstract

The control problem of realizing propeller motion of a devil-stick in the vertical plane using impulsive forces applied normal to the stick is considered. This problem is an example of underactuated robotic juggling and has not been considered in the literature before. Inspired by virtual holonomic constraints, the concept of discrete virtual holonomic constraints (DVHC) is introduced for the first time to solve this orbital stabilization problem. At the discrete instants when impulsive inputs are applied, the location of the center-of-mass of the devil-stick is specified in terms of its orientation angle. This yields the discrete zero dynamics (DZD), which provides conditions for stable propeller motion. In the limiting case, when the rotation angle between successive applications of impulsive inputs is chosen to be arbitrarily small, the problem reduces to that of propeller motion under continuous forcing. A controller that enforces the DVHC, and an orbit stabilizing controller based on the impulse controlled Poincaré map approach are presented. The efficacy of the approach to trajectory design and stabilization is validated through simulations.

Problem

• Stabilizing propeller motion of a devil-stick using impulsive normal forces
• Introducing discrete virtual holonomic constraints for underactuated juggling
• Developing orbital stabilization via impulse-controlled Poincaré map approach

Innovation

• Discrete virtual holonomic constraints for stabilization
• Impulsive inputs control devil-stick propeller motion
• Orbit stabilization via impulse-controlled Poincaré map