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Before the Tipping Point: Force-Guided Active Perception for Shape-Agnostic Estimation of 3D Centers of Mass

This paper presents a force-guided active perception method that enables a robot manipulator to accurately estimate the 3D center of mass, mass, and toppling angle of unknown, irregular objects by analyzing force-angle data from a single sub-critical tipping experiment, thereby facilitating reliable non-prehensile manipulation without prior shape information.

Original authors: Steven M. Hyland, Jing Xiao, Cagdas D. Onal

Published 2026-09-14

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Steven M. Hyland, Jing Xiao, Cagdas D. Onal

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Robots are becoming increasingly capable of moving through our world, yet they often struggle with a fundamental question: how heavy is an object, and where exactly is its weight concentrated? In the world of robotics, this weight distribution is known as the center of mass. Knowing this point is essential for a machine to grasp an item securely, push it without causing it to topple, or predict how it will behave when force is applied. While a human can intuitively sense these properties by lifting or nudging an object, a robot typically requires a pre-existing digital model or the ability to pick up the item to calculate them. This creates a significant hurdle when dealing with unknown, irregular, or fragile objects that cannot be grasped or whose shape is not yet mapped. If a robot cannot determine where the weight lies, it risks dropping the object, damaging it, or knocking it over in a way that could be dangerous.

To solve this, researchers at Worcester Polytechnic Institute have developed a new way for robots to "feel" the hidden physics of an object without ever lifting it. Instead of trying to grab an item, the robot performs a carefully controlled, gentle push. By watching how the object begins to tilt and measuring the exact force required to make it move, the robot can deduce the object's total mass and the height of its center of gravity. This process allows the machine to understand the object's stability and physical nature through a single, safe interaction, opening the door to manipulating a much wider variety of items in unstructured environments.

The core of this work is a method called force-guided active perception. Imagine a robot arm equipped with a sensitive sensor at its wrist, pushing against a box sitting on a table. The robot does not simply shove the box; it executes a slow, deliberate motion, pushing the object until it begins to tip, and then immediately pulling back. This cycle is repeated in a quasistatic manner, meaning the movement is so slow that the object's own inertia does not interfere with the measurements. As the robot pushes, it records the angle of the object and the force it is applying. The researchers found that by analyzing the relationship between how hard the robot pushes and how much the object tilts, they could mathematically reverse-engineer the object's mass and the vertical position of its center of mass.

A critical innovation in this approach is the concept of "sub-critical" tipping. In many previous attempts to measure these properties, researchers would push an object until it fell over completely, using the exact moment of collapse to calculate the data. However, this is risky; once an object starts to fall, it is often too late to stop it, and the object could be damaged or the environment disrupted. The new method stops the robot just before the point of no return. The robot pushes the object until it is teetering on the edge of stability but then retracts, keeping the object upright. By observing how the force required to hold the object at a specific angle changes as it gets closer to falling, the system can predict exactly where the tipping point would have been. This safety margin allows the robot to gather the necessary information without ever causing a destructive fall.

The team tested this technique on a variety of objects, including a standard rectangular box, a heart-shaped prism, a handheld flashlight, and a computer monitor. These items varied significantly in shape, weight, and how their mass was distributed. For instance, the flashlight had a curved base that made it prone to wobbling, while the monitor was heavy and top-heavy. In every successful trial, the robot applied a horizontal push at a specific height, recorded the force and angle data, and then used a computer algorithm to fit the data to a physical model. The results were remarkably accurate. Across the different objects, the robot estimated the mass and the height of the center of mass with a relative error of less than 5 percent. In some cases, the error was as low as 0.2 percent for the height of the center of mass.

One of the most significant findings was how the robot handled the friction between its finger and the object. When the robot pushes an object, friction acts against the motion. When the robot pulls back, friction acts in the opposite direction. This creates a slight difference in the force readings between the push and the pull, a phenomenon known as hysteresis. The researchers discovered that by combining the data from both the pushing and the retracting phases, these frictional errors canceled each other out. This allowed the system to produce a clean, reliable estimate of the object's properties without needing to know the exact friction coefficient of the surface or the object's material beforehand.

The study also highlighted the delicate balance between safety and accuracy. The researchers introduced a "safety margin," which determines how close the robot gets to the tipping point before stopping. If the robot stops too early, far from the tipping point, it does not gather enough data to make an accurate prediction. If it goes too close, it risks the object falling. The experiments showed that while a very conservative safety margin kept the object safe, it sometimes led to less accurate estimates, particularly for the height of the center of mass. Conversely, pushing closer to the limit improved accuracy but increased risk. The team found that a moderate safety margin provided the best compromise, allowing the robot to learn enough about the object to make a precise calculation while keeping the object firmly on the table.

There were limits to the method, however. The researchers noted that objects with curved bases, like the flashlight, presented a unique challenge. Because the contact point between the object and the table shifts as the object tilts, the simple model of a fixed pivot point broke down. In these cases, the object would wobble or slide in an unpredictable way, making it difficult for the robot to determine the correct parameters. This suggests that while the method is robust for many rigid objects with flat or angular bases, it may require further adaptation for items with rounded bottoms.

The implications of this work extend beyond just measuring weight. By enabling robots to understand the physical properties of unknown objects through non-grasping interactions, this technique paves the way for more versatile and safe manipulation in real-world settings. A robot could potentially push a heavy crate to see if it is stable enough to be moved, or nudge a fragile vase to understand its balance before attempting to pick it up. The ability to infer mass and stability without prior knowledge or the need to lift the object represents a significant step forward in making robots more adaptable to the unpredictable nature of the human world. The researchers demonstrated that with the right combination of force sensing, visual tracking, and careful control, a machine can learn the hidden physics of an object simply by giving it a gentle, controlled nudge.

Technical Summary: Force-Guided Active Perception for Shape-Agnostic Estimation of 3D Centers of Mass

Problem Statement
Estimating the three-dimensional Center of Mass (CoM) and mass of unknown objects is a critical challenge in robotic manipulation, particularly when grasping is infeasible due to object size, fragility, or irregular geometry. While 2D planar CoM projections can be inferred through planar pushing, determining the vertical CoM coordinate ( $z_c$ ) and total mass ( $m$ ) typically requires either destructive toppling (falling over) or prior knowledge of the object's geometry. Existing methods often rely on stable grasping or multiple interaction cycles, which are not always applicable in non-prehensile scenarios. The core problem addressed is how to reliably estimate 3D inertial parameters of unknown objects using a single, safe, non-destructive interaction without requiring shape priors.

Methodology
The authors propose a force-guided active perception method that utilizes a single sub-critical tipping experiment to estimate $z_c$ and $m$ . The approach operates under the assumptions of a non-deformable rigid body, isotropic Coulomb friction, and quasistatic motion.

Two-Stage Interaction:
- Stage 1 (2D CoM): The method assumes the planar CoM coordinates ( $x_c, y_c$ ) are already known (e.g., derived from prior planar pushing methods).
- Stage 2 (3D Estimation): The robot executes a controlled, elevated push at a specific height to induce tipping. The robot performs a push-retract cycle, applying a quasistatic horizontal force and then retracting.
Physics-Based Modeling:
- The system models the torque balance during tipping: $\tau_{push} + \tau_{grav} = 0$ .
- As the object tips, the gravity torque decreases as the CoM vector approaches collinearity with the gravity vector. At the "toppling angle" ( $\theta^*$ ), the gravity torque drops to zero.
- The method leverages the monotonic coupling between the applied force magnitude ( $F_{push}$ ) and the object angle ( $\theta$ ). As $\theta$ approaches $\theta^*$ , the required force to maintain equilibrium decreases.
Parameter Estimation:
- Friction Mitigation: To eliminate frictional bias, the method analyzes both the push and retract phases of the trajectory. The reversal of motion reverses the direction of friction, creating a hysteresis loop. By fitting the model to both segments, friction-induced biases are canceled out.
- Sub-Critical Safety: To prevent destructive toppling, the interaction is constrained to a sub-critical regime ( $\theta < \theta^*$ ). A safety margin ( $\eta_{safety}$ ) is defined as a fraction of the maximum observed force ( $F_{max}$ ). The interaction is terminated when the force reaches a safe threshold ( $F_{safe} = \eta_{safety} F_{max}$ ), ensuring the object remains stable.
- Fitting: The system uses a cascaded filter for signal conditioning, followed by a heuristic linear regression and a model-based nonlinear least-squares (NLS) optimization to extract $z_c$ and $m$ from the force-angle trajectory.

Key Contributions

Shape-Agnostic Estimation: The method estimates 3D CoM height and mass without requiring prior geometric models or multiple tipping configurations.
Single-Push Sub-Critical Strategy: It introduces a protocol to recover inertial parameters from a single push-retract cycle while strictly avoiding the toppling threshold, enhancing safety and repeatability.
Friction Bias Mitigation: The push-retract cycle design effectively cancels out unmodeled frictional effects through hysteresis analysis, enabling generalized fitting across different object-surface interactions.
Safety-Performance Trade-off Analysis: The paper systematically investigates the trade-off between the safety margin ( $\eta_{safety}$ ) and estimation accuracy, demonstrating that moderate safety margins can yield reliable results without risking object damage.

Experimental Results
The method was validated using an ABB IRB120 manipulator equipped with a force/torque sensor and visual feedback (AprilTags) on four distinct objects: a rectangular box, a heart-shaped prism, a handheld flashlight, and a computer monitor.

Accuracy: Across all tested objects and safety margins, the method achieved relative errors below 5.0% for mass, CoM height, and toppling angle.
Specific Performance: For the reference box object with a safety margin of $\eta_{safety} = 0.1$ , the relative errors were approximately 2.6% for mass, 0.2% for CoM height, and 0.2% for the toppling angle.
Failure Modes: The study identified a failure mode for objects with curved bases (e.g., the flashlight) at low safety margins, where shifting contact geometry violates the fixed-pivot assumption.
Observability: Mass estimates remained stable across varying safety margins, while CoM height and toppling angle estimates showed higher sensitivity to trajectory truncation (conservative safety settings).

Significance and Claims
The authors claim that this work demonstrates reliable 3D inertial parameter estimation under proper safety thresholds in tipping scenarios. The proposed method enables non-prehensile manipulation and robotic grasping of challenging objects that were previously infeasible due to a lack of shape information or the inability to grasp them. By establishing sub-critical tipping as a practical mechanism, the work allows robots to actively probe objects through safe physical interaction to infer inertial structure in real-time, facilitating more robust manipulation in unstructured environments. The paper concludes that while the method is effective, future work could address curved-base geometries and optimize push speeds to improve cycle times and signal-to-noise ratios.

Technical Summary: Force-Guided Active Perception for Shape-Agnostic Estimation of 3D Centers of Mass

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