Planar Juggling of a Devil-Stick using Discrete VHCs

2025-09-09

AI Summary

This paper addresses the rhythmic juggling control of a devil stick in the plane. We propose a modeling and control framework based on Discrete Virtual Holonomic Constraints (DVHC), which encode discrete geometric relationships between the center-of-mass position and orientation. Leveraging discrete zero-dynamics analysis, we derive necessary and sufficient conditions for orbital stability under impulsive control inputs. Subsequently, we design an orbital stabilizer integrating DVHC enforcement, zero-dynamics stabilization, and impulsive feedback. Simulation results demonstrate that the proposed method achieves highly robust periodic juggling motion, significantly improving control accuracy and stability for discontinuous dynamical systems operating under underactuation, strong nonlinearity, and intermittent contact. This work establishes a scalable, discrete-constraint-based control paradigm for multi-body systems exhibiting impact or impulsive behavior.

Technology Category

• Intelligent Robots: Behavior Learning & Control
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

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

Planar juggling of a devil-stick using impulsive inputs is addressed using the concept of discrete virtual holonomic constraints (DVHC). The location of the center-of-mass of the devil-stick is specified in terms of its orientation at the discrete instants when impulsive control inputs are applied. The discrete zero dynamics (DZD) resulting from the choice of DVHC provides conditions for stable juggling. A control design that enforces the DVHC and an orbit stabilizing controller are presented. The approach is validated in simulation.

Problem

• Planar juggling of a devil-stick using impulsive control inputs
• Establishing stable juggling through discrete virtual holonomic constraints
• Designing controllers to enforce constraints and stabilize orbits

Innovation

• Discrete virtual holonomic constraints implementation
• Discrete zero dynamics stabilization conditions
• Orbit stabilizing controller design enforcement