Caging in Time: A Framework for Robust Object Manipulation under Uncertainties and Limited Robot Perception

TL;DR

The paper introduces Caging in Time, a framework to achieve robust object manipulation under perception uncertainties by forming cages over time with a single robot. It unifies geometry-based and energy-based cages through a Potential State Set (PSS) propagation mechanism, enabling open-loop tasks in both quasi-static planar pushing and dynamic ball balancing. By combining PSS propagation with heuristic action selection in the quasi-static case and a joint Control Barrier/Control Lyapunov Function (CBF-CLF) based Quadratic Program for the dynamic case, the approach demonstrates robustness to unknown object shapes, perturbations, and sensing gaps, without requiring real-time feedback. Extensive experiments on a Franka Panda robot validate the method across multiple shapes, trajectories, and disturbance scenarios, highlighting its practicality and resilience. The work positions Caging in Time as a complementary strategy to traditional manipulation pipelines, with potential extensions into learning-based propagation and broader manipulation tasks including deformable and extrinsic-dexterity contexts.

Abstract

Real-world object manipulation has been commonly challenged by physical uncertainties and perception limitations. Being an effective strategy, while caging configuration-based manipulation frameworks have successfully provided robust solutions, they are not broadly applicable due to their strict requirements on the availability of multiple robots, widely distributed contacts, or specific geometries of robots or objects. Building upon previous sensorless manipulation ideas and uncertainty handling approaches, this work proposes a novel framework termed Caging in Time to allow caging configurations to be formed even with one robot engaged in a task. This concept leverages the insight that while caging requires constraining the object's motion, only part of the cage actively contacts the object at any moment. As such, by strategically switching the end-effector configuration and collapsing it in time, we form a cage with its necessary portion active whenever needed. We instantiate our approach on challenging quasi-static and dynamic manipulation tasks, showing that Caging in Time can be achieved in general cage formulations including geometry-based and energy-based cages. With extensive experiments, we show robust and accurate manipulation, in an open-loop manner, without requiring detailed knowledge of the object geometry or physical properties, or real-time accurate feedback on the manipulation states. In addition to being an effective and robust open-loop manipulation solution, Caging in Time can be a supplementary strategy to other manipulation systems affected by uncertain or limited robot perception.

Figures (26)

• Figure 1: Example object manipulation tasks via Caging in Time. Top: Object planar pushing to trace "RICE". Without sensing feedback, unknown objects were randomly replaced during the manipulation process. The recordings were taken at different times and concatenated to show all objects. Bottom: Ball catching on a flat end-effector without any sensing feedback.
• Figure 2: The theory of Caging in Time visualized through an example planar pushing task. I: A virtual cage, formed by line-shaped bars (grey), robustly pushes an object through a circular path. II: Along the time dimension, only one bar (red) is effectively making contacts at a time, while other bars seem to be unnecessary. III: If we collapse all configurations of the effective bars (red) through time, a cage is formed, which can be unrolled into time to achieve the task in I with only one bar at a time.
• Figure 3: An illustration of the workspace $\mathcal{W}$ (left) and the C-space $\mathcal{C}_{obj}$ (right) of a circular object surrounded by seven line robots. Left: The red line is the geometry of the $i$-th robot $\mathcal{A}_i$ and the solid grey circle is the geometry of the object $\mathcal{A}_{obj}$. Right: The red region is all the object's configurations at which the object collides with a robot and the green region is the object's free C-space $\mathcal{C}_{free} \subset \mathcal{C}_{obj}$.
• Figure 4: An illustration of the traditional caging condition. Left: The green region and the red region represent $\mathcal{C}_{free}^{obj}$ and $\mathcal{C}_{free}^\infty$, respectively. The object is caged in this case since $\mathcal{C}_{free}^{obj}$ and $\mathcal{C}_{free}^\infty$ are not connected. Right: A non-caging scenario where $\mathcal{C}_{free}^{obj}$ and $\mathcal{C}_{free}^\infty$ become connected. The object may escape following the trajectory shown by the dashed line.
• Figure 5: An illustration of the PSS propagation. Left: The propagation for a single state $\mathbf{q}_t \in \mathcal{Q}_t \subset \mathcal{S}_{obj}$. With a set of possible motions $\mathcal{V}_{\mathbf{q}_t}$, $\mathbf{q}_t$ can be propagated to a set of different states (the orange region). Right: The propagation from the entire PSS $\mathcal{Q}_{t}$ to $\mathcal{Q}_{t+1}$ by propagating all points in $\mathcal{Q}_{t}$. The different colors of regions in $\mathcal{Q}_{t+1}$ illustrate the propagation from multiple different $\mathbf{q}_t \in \mathcal{Q}_t$.

Theorems & Definitions (1)

• Definition 4.1