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Before the Tipping Point: Force-Guided Active Perception for Shape-Agnostic Estimation of 3D Centers of Mass
Steven M. Hyland, Jing Xiao, Cagdas D. Onal
TL;DR
Estimating the 3D CoM of unknown objects is difficult when grasping is infeasible and geometry is not known. The paper uses force-guided, vision-assisted sub-critical tipping to estimate CoM height and mass from a controlled push. Experiments report stable estimates with low errors across tested objects and safety margins.
Problem
Estimating CoM for previously unseen objects without prior geometry or force-distribution models remains challenging, including when grasping is infeasible.
Source: §I · p. 1Method
The method combines planar CoM information with a controlled sub-critical push, using force and visual sensing to estimate CoM height and mass without destructive toppling.
Source: §I · p. 1, §V · pp. 7–8Results
Across tested objects and safety margins, mass and CoM-height estimates remained generally stable with low errors, while moderate margins balanced safety and identifiability.
Source: §V · p. 8Takeaways & Limitations
Sub-critical tipping provides a practical and safe mechanism for 3D inertial-parameter inference in non-prehensile manipulation.
Source: §V · p. 8Inference is less effective for curved or unstable bases without sharp edges; adapting push direction may help.
Source: §V · p. 8
Abstract
from arXiv · showhide
Estimating the 3D center of mass of unknown objects is challenging when grasping is infeasible, geometry is irregular, or mass distribution is uneven. We present a force-based method that estimates CoM height and mass from a single sub-critical tipping experiment by a robot manipulator. The robot applies a quasistatic elevated push and retract motion, using force-angle measurements recorded during tipping to identify parameters from the object trajectory. Our proposed push-retract cycle mitigates frictional bias, enabling generalized fitting. We experimentally validate our method using a robot manipulator with a six-axis force torque sensor on varying types of objects without prior shape information and without specific models. We also propose a method to prevent toppling, keeping the object in a sub-critical tipping regime by leveraging a safety margin. In experimental studies, our method recovers mass, CoM height, and toppling angle with relative errors below 5.0 percent across all unknown objects. This work demonstrates reliable 3D inertial parameter estimation under proper safety thresholds in tipping. Our proposed method informs and enables reliable non-prehensile manipulation and robotic grasping of challenging objects that were previously infeasible.
I. INTRODUCTION
Estimating unknown objects’ CoM remains challenging without prior models, while grasp-based methods depend on stable grasping and planar pushing cannot resolve CoM height. The paper uses controlled pushing and complementary force and visual sensing to estimate inertial properties in non-prehensile settings.
I. INTRODUCTION
- Unknown-object CoM estimation remains challenging without prior models, and CoM estimates matter for stable grasping, motion planning, and predicting object behavior under forces.The introduction frames non-prehensile manipulation as a practical inference route when grasping is infeasible.Source: §I · p. 1
- The proposed interaction uses controlled pushes with visual pose information and force measurements to infer CoM height and mass.The paper describes this as an active perception loop in which purposeful interaction incrementally improves the robot’s understanding.Source: §I · p. 1
A. Grasp-Based Methods
- Grasp-based identification excites grasped or end-effector-fixed objects while measuring wrist forces and motion, but depends on stable grasping and payload constraints.Prior methods use excitation trajectories and least-squares estimation of linearized Newton–Euler equations [5],.Source: A. Grasp-Based Methods · p. 1
B. Planar Pushing and Planar CoM
- Planar pushing supports active inference, but planar interaction alone cannot resolve CoM height because different 3D CoM configurations can share the same planar projection.The paper assumes an estimate of the planar projection is available and focuses on the vertical component.Source: B. Planar Pushing and Planar CoM · p. 2
C. Tipping and Toppling for CoM Inference
Tipping can support 3D CoM inference, but prior tipping-based approaches may require substantial geometry information. This work combines planar CoM estimation with a single sub-critical tipping interaction to estimate height and mass under stated mechanical assumptions.
C. Tipping and Toppling for CoM Inference
- Prior tipping-based 3D inference resolves the CoM through multiple contact lines but requires considerable prior information about object geometry.The cited framework uses Gravity Equi-Effect Planes, extended for curved bases using a passing-CoM line,.Source: C. Tipping and Toppling for CoM… · p. 2
III. APPROACH
- The approach estimates planar CoM coordinates first, then uses a higher push to estimate CoM height and mass through a single sub-critical tipping interaction.It also recovers critical toppling angle without destructive toppling or multiple push/tip configurations.Source: §III · p. 2
A. 2D CoM Estimation
- The method assumes a rigid, non-deformable object, isotropic Coulomb friction with one coefficient, and quasistatic motion with negligible inertial effects.For the planar stage, the study assumes the planar CoM information has already been extracted.Source: §III · p. 2, A. 2D CoM Estimation · p. 2
B. Sliding Condition
The analysis distinguishes sliding from tipping and models tipping through torque balance about the object-frame pivot. The stated geometry and figure clarify the reference frame and tipping configuration.
B. Sliding Condition
- Incipient sliding occurs when the applied finger force reaches the maximum static-friction threshold determined by normal force and the static friction coefficient.The analysis obtains the sliding condition from force balance on the rigid body.Source: B. Sliding Condition · p. 2
C. Tipping Condition
- Tipping equilibrium is modeled by balancing the applied-force and gravity torques about the pivot, with the equation serving as the model for estimating unknown parameters.The analysis defines the object frame, tipping axis, object angle, CoM projection, and force and gravity vectors for this model.Source: C. Tipping Condition · pp. 2–3
- The figure distinguishes resting equilibrium, toppling equilibrium with zero push, and the characteristic toppling angle measured from the object’s pose at threshold.Its vectors are expressed in the object frame located along the pivot edge.Source: C. Tipping Condition · p. 2, Figure 1 · p. 3
D. Mode Selection at Onset
During monotonic pushing, the first balance condition reached determines whether sliding or tipping begins. The onset comparison is constrained by push geometry and by objects for which the required tipping force exceeds contact limits.
D. Mode Selection at Onset
- During monotonic pushing, the first mode to appear is the one whose balance equation is first satisfied, as applied force increases while resistance remains constant.Sliding begins at the static-friction threshold, Fslide = µsN.Source: D. Mode Selection at Onset · p. 3
- Which mode occurs first depends on the relative tipping and sliding forces; tipping force varies with push height and direction, while sliding force depends on the object-surface couple.Equal thresholds produce coupled slide–tip onset.Source: D. Mode Selection at Onset · p. 3
- Objects with low CoM and wide bases may require tipping forces beyond fingertip friction limits and are outside the method’s admissible class.Tipping leverage is maximized when the push is orthogonal to the pivot and vanishes as the force points toward it.Source: D. Mode Selection at Onset · p. 3
E. Estimation of CoM z-coordinate
As the CoM and weight vectors approach collinearity, gravity torque decreases, so quasistatic balance requires less fingertip force. The section describes geometric and curve-fitting approaches for estimating CoM height and mass.
E. Estimation of CoM z-coordinate
- As φ approaches zero, gravity torque decreases, and maintaining quasistatic torque balance requires less fingertip force.φ depends only on the object angle θ.Source: E. Estimation of CoM z-coordinate · p. 3
- Geometric computation uses the angle at which gravity torque reaches zero to determine the toppling angle, then derives CoM height geometrically.Mass is determined by solving the torque balance analytically or numerically.Source: E. Estimation of CoM z-coordinate · pp. 3–4
- A physics-based curve fit regresses coupled force–angle data against the tipping model to estimate CoM height and mass.The procedure also uses geometric and curve-fit methods in experiments.Source: E. Estimation of CoM z-coordinate · p. 4
F. General Procedure
Each trial uses a quasistatic push–retract interaction and fits the resulting force–angle trajectory. Combining both motion phases reduces friction-induced bias in the estimates.
F. General Procedure
- Each trial applies a low-velocity quasistatic push and retract, recording the coupled force–angle trajectory for inertial-parameter estimation.The selected push location uses the planar CoM projection to maximize tipping leverage while avoiding sliding.Source: F. General Procedure · p. 4
- Filtered force data provide a first-order regression warm start, followed by nonlinear least-squares fitting of the force–angle manifold.A cascaded median and Savitzky–Golay filter suppress noise, and median absolute deviation rejects outliers from the linear fit.Source: F. General Procedure · p. 4
- Combining push and retract data reduces frictional bias because motion reversal reverses friction direction, producing hysteresis in the measured trajectory.Friction is not explicitly modeled in the torque equation.Source: F. General Procedure · p. 4
G. Sub-Critical Single-Push Estimation
The method keeps tipping below the toppling angle by constraining measured force within an admissible envelope. Safety margins support geometry-agnostic comparison across objects and conditions.
G. Sub-Critical Single-Push Estimation
- The policy intentionally keeps the object below its toppling angle because reaching that threshold places it in a marginally stable state.The threshold is unknown beforehand, so the method avoids first toppling the object to identify it.Source: G. Sub-Critical Single-Push Estimation · p. 4
- Within the quasistatic regime, force magnitude serves as a proxy for proximity to the unknown toppling angle, and measured force is constrained to an admissible envelope.The envelope is bounded by a safety floor and peak interaction force; the floor is selected for application-specific safety requirements.Source: G. Sub-Critical Single-Push Estimation · p. 4
- The safety-threshold formulation enables geometry-agnostic comparison of estimation performance across objects and safety margins.The threshold is parameterized using the dimensionless safety margin η_safety.Source: G. Sub-Critical Single-Push Estimation · p. 4
IV. EXPERIMENTS, RESULTS, AND DISCUSSION
The experiments use a force/torque-sensing manipulator and visual pose feedback, with a reference acrylic box and a representative sub-critical trial. The supplied captions describe the measurements and model fit, while the table caption identifies the reported error table's scope.
IV. EXPERIMENTS, RESULTS, AND DISCUSSION
- The setup synchronizes applied-wrench measurements with object response using a robot manipulator, wrist force/torque sensor, and camera-based pose feedback.The reference object is a hollow acrylic rectangular prism whose CoM is at its geometric centroid.Source: §IV · pp. 4–5
- A representative sub-critical box trial records force and angle profiles, with hysteresis between phases capturing friction-direction reversal.Applied torque is calculated from measured force and finger position; the caption notes a small force spike around ten seconds.Source: Figure 3 · p. 5
- The box torque–angle model-fit figure shows push/retract phase offset and fitted parameters aligned with the expected force decay as θ approaches θ∗.Table I is identified as reporting experimental estimate errors for the box at η_safety = 0.1; no cell values are supplied here.Source: Figure 4 · p. 5, Table I · p. 5
A. Box Reference Object Sub-Critical Tipping
The reference-box experiment shows that combining push and retract data yields the most accurate sub-critical estimates despite frictional separation between the trajectory segments. Reliable CoM height and mass estimates are recovered without approaching toppling.
A. Box Reference Object Sub-Critical Tipping
- With ηsafety = 0.1, the reference box remained strictly below its toppling threshold during sub-critical evaluation.The margin was selected to approximate full-toppling validation conditions while avoiding toppling.Source: A. Box Reference Object Sub-Critical… · p. 5
- The combined push–retract estimate is most accurate, while each segment alone brackets ground truth because of frictional bias.The measured force–angle fit separates the push and retract segments, consistent with contact-friction hysteresis.Source: A. Box Reference Object Sub-Critical… · p. 5
- Reliable CoM height and mass estimates were recovered without approaching toppling.Source: A. Box Reference Object Sub-Critical… · p. 5
B. Application to Unknown Objects of Different Geometries
The method was evaluated on four objects with distinct geometries and contact properties, using the same push–retract procedure with push height selection as the only modification. Across objects and safety margins, parameter sensitivity varies, and the safety margin trades estimation accuracy against exposure to non-ideal tipping behavior.
B. Application to Unknown Objects of Different Geometries
- The four evaluated objects included a box, heart-shaped prism, flashlight, and computer monitor, with distinct geometries, frictional characteristics, mass distributions, and contact profiles.Source: B. Application to Unknown Objects of… · p. 5
- Figure 6 shows that absolute errors increase with conservative safety settings, while Figure 7 shows greater truncation sensitivity for CoM height and toppling angle than for mass.The aggregate errors cover the four tested objects; the same single push–retract procedure was used, with push height selection as the only modification.Source: Figure 6 · p. 6, Figure 7 · p. 6, B. Application to Unknown Objects of… · p. 6
- Ground-truth mass was measured with a scale, and CoM coordinates were determined by placing each object at a support-surface edge until tipping was detected.The edge measurement was repeated for all three axes.Source: B. Application to Unknown Objects of… · p. 6
- Cycle time correlated positively with object mass rather than θ*, because heavier objects require greater force build-up before reaching the safety-limited envelope.The experiments used identical push velocities across objects.Source: B. Application to Unknown Objects of… · p. 7
- Mass estimates remain comparatively stable across safety margins, while CoM height and toppling-angle estimates are more sensitive to trajectory truncation and measurement noise.Across all but the monitor at ηsafety = 0.65, toppling-angle estimates have lower error than CoM height estimates.Source: Figure 7 · p. 6, B. Application to Unknown Objects of… · p. 7
- Larger ηsafety reduces risk by ending interaction earlier but limits force-decay observations near θ*, whereas smaller margins improve estimation under ideal conditions while increasing exposure to non-ideal behavior.Pivot-edge transitions, intermittent slip, and local compliance can violate quasistatic assumptions.Source: B. Application to Unknown Objects of… · p. 7
- For these experiments, ηsafety values below 0.65 produced usable trajectories, while larger values truncated interaction too early for reliable fitting.No single safety-margin value was universally optimal across the tested objects.Source: B. Application to Unknown Objects of… · p. 7
- The flashlight at ηsafety = 0.1 yielded no valid estimate because its curved base shifted contact geometry, inducing yaw and instability that violated the fixed-pivot assumption.The round edge motivates interaction strategies that stabilize the pivot more directly.Source: B. Application to Unknown Objects of… · p. 7, Figure 8 · p. 7
V. CONCLUSIONS
The conclusions report generally stable, low-error estimates under the tested safety margins and present sub-critical tipping as a practical, safe route to 3D inertial inference. They also identify base geometry, cycle speed and force-measurement noise, and reliance on markers and a known pivot edge as areas for improvement.
V. CONCLUSIONS
- One controlled sub-critical push recovers CoM height and mass without destructive toppling or multiple tipping configurations, which the paper presents as practical and safe for nonprehensile inference.Source: §V · pp. 7–8
- Across tested objects and safety margins, sub-critical tipping yielded generally stable, low-error mass and CoM-height estimates; Fig. 9's pivot-scale check validates computed height, with lower measured weight indicating a better estimate.The objects were placed on an edge pivot at the estimated CoM height, with the scale level with the pivot.Source: Figure 9 · p. 7, §V · p. 8
- Inference is less effective for curved or unstable bases without sharp edges; adapting the push direction is proposed as a possible remedy.Source: §V · p. 8
- Cycle time could improve with higher or varied push speeds only while object motion remains quasistatic, while fit convergence could improve with higher force-measurement signal-to-noise ratio.Source: §V · p. 8
- Further refinement would remove reliance on AprilTags and a fixed-known pivot edge, and evaluation across larger, diverse object sets would be beneficial.Source: §V · p. 8