[Paper Review] Robotic Contact Juggling

J. Zachary Woodruff, Kevin Lynch|arXiv (Cornell University)|Feb 20, 2021

Robot Manipulation and Learning4 citations

TL;DR

This paper presents the first general formulation and solution for robotic contact juggling—controlling a 3D smooth object as it rolls on a motion-controlled robot hand via four integrated components: second-order rolling kinematics, 3D rolling dynamics, trajectory planning using iterative direct collocation, and feedback stabilization via LQR. The method enables stable, dynamic manipulation of arbitrary smooth objects on arbitrary smooth hands, validated through 3D simulations and 2D experiments with high-speed vision feedback.

ABSTRACT

We define "robotic contact juggling" to be the purposeful control of the motion of a three-dimensional smooth object as it rolls freely on a motion-controlled robot manipulator, or "hand." While specific examples of robotic contact juggling have been studied before, in this paper we provide the first general formulation and solution method for the case of an arbitrary smooth object in single-point rolling contact on an arbitrary smooth hand. Our formulation splits the problem into four subproblems: (1) deriving the second-order rolling kinematics; (2) deriving the three-dimensional rolling dynamics; (3) planning rolling motions that satisfy the rolling dynamics; and (4) feedback stabilization of planned rolling trajectories. The theoretical results are demonstrated in simulation and experiment using feedback from a high-speed vision system.

Motivation & Objective

• To develop a general framework for controlling arbitrary 3D smooth objects in single-point rolling contact on arbitrary smooth robot hands.
• To address the lack of a unified formulation for robotic contact juggling beyond specific cases like the butterfly or sphere-on-plate.
• To enable dynamic, nonprehensile manipulation where momentum and contact dynamics are central.
• To provide a complete pipeline from kinematics and dynamics to trajectory planning and feedback stabilization.
• To validate the approach through 3D simulations and 2D experiments with high-speed vision feedback.

Proposed method

• Derives second-order rolling kinematics to model contact point evolution under controlled relative accelerations, correcting prior work and enabling dynamic control.
• Develops 3D rolling dynamics by combining Newton-Euler equations with rolling constraints, computing contact wrenches for force and friction limits.
• Adapts iterative direct collocation (iDC) to solve optimal control problems for dynamic rolling motions, enforcing dynamics via trapezoidal integration.
• Uses a nonlinear programming formulation with constraints on contact wrench, control limits, and configuration bounds to ensure physical feasibility.
• Employs a multi-stage optimization strategy: coarse initial solve with weighting on goal state, followed by refinement with increasing segment count to improve accuracy and convergence.
• Applies linear quadratic regulator (LQR) feedback control to stabilize planned trajectories in real-time using high-speed vision feedback.

Experimental results

Research questions

• RQ1 How can second-order rolling kinematics be derived for arbitrary smooth 3D objects in single-point contact with a robot hand?
• RQ2 What is the general formulation of 3D rolling dynamics that enforces pure rolling and computes contact wrenches?
• RQ3 How can dynamic rolling trajectories be planned under complex constraints, including friction and control limits?
• RQ4 How can feedback control stabilize planned rolling trajectories in the presence of disturbances and modeling errors?
• RQ5 Can the proposed framework enable stable, dynamic juggling of arbitrary smooth objects on arbitrary smooth hands?

Key findings

• The proposed second-order rolling kinematics formulation correctly generalizes prior work and enables accurate modeling of contact acceleration dynamics.
• The rolling dynamics model accurately reproduces analytical solutions for a sphere rolling on a spinning plate, validating its physical fidelity.
• The iterative direct collocation (iDC) method successfully generates feasible, high-quality rolling trajectories by combining coarse initial guesses with adaptive refinement.
• The integration error is reduced by refining the control discretization, and the method converges faster and more reliably than direct fine-grid optimization.
• Feedback stabilization via LQR successfully maintains planned trajectories in 2D experiments using high-speed vision feedback, demonstrating robustness to disturbances.
• The framework enables dynamic, nonprehensile manipulation of arbitrary smooth objects on arbitrary smooth hands, representing a significant generalization over prior work.