Bimanual Non-Prehensile Manipulation Primitives

• BiNoMaP is defined as a set of analytical and learning-based bimanual manipulation primitives that use controlled contact forces and sophisticated kinematics.
• It leverages physics-inspired actions—such as coordinated pushing, pressing, and pinching—to extend manipulation to objects beyond the scope of traditional grippers.
• By integrating perception, motion planning, and trajectory optimization, BiNoMaP achieves high success in both structured and cluttered robotic manipulation tasks.

Bimanual Non-Prehensile Manipulation Primitives (BiNoMaP) represent a systematic framework for robotic dual-arm tasks in which objects are manipulated without enclosure or grasp, instead relying on controlled contact forces, motions, and kinematic reasoning. BiNoMaP enables the extension of manipulable object sets beyond those accessible by conventional grippers, particularly for scenarios involving large, irregular, bulky, or tightly packed items. Recent research formalizes BiNoMaP both as a planning/control toolkit based on analytic mechanics and contact topology, and as a learning pipeline converting demonstration to generalizable object-centric skills. Key components include physics-based primitives such as coordinated pushing, pressing, nudging, and bimanual pinching or support, together with pipeline-level strategies for perception, motion generation, and category-level adaptation (Wu et al., 2024, Zhou et al., 25 Sep 2025, Özcan et al., 12 Mar 2026).

1. Formal Definition and Taxonomy

BiNoMaP encompasses a structured set of manipulation primitives for dual-arm robot platforms:

• Problem Setup: The robot A = {A^L, A^R} has two end-effectors, each parameterized by position $p_t \in \mathbb{R}^3$ and orientation $R_t \in SO(3)$. Gripper opening is fixed (no grasping) in non-prehensile phases.
• Task Input: $(T, V, O, A)$, where $T$ is a text description, $V$ is a demonstration video, $O$ is object perception (e.g., point cloud), and $A$ is robot configuration. The learning objective is $f_\theta: (T, V, O, A) \to P$, mapping to a trajectory $P = \{p_t, R_t\}_{t=1}^T$ (Zhou et al., 25 Sep 2025).

The notable taxonomic breakdown includes:

Class	Examples	Bimanual Structure
Single-arm with handedness	Poking, pushing	1 active, 1 idle
Asymmetric stabilize-actuate	Pivoting, occluded grasping	1 moves, 1 supports
Dual-arm cooperative motion	Wrapping, parallel pushing, lifting	Synchronized or coordinated

This organization informs both analytic control frameworks and data-driven primitive libraries (Wu et al., 2024, Zhou et al., 25 Sep 2025, Özcan et al., 12 Mar 2026).

2. Analytic and Algorithmic Foundations

2.1 Physics-Inspired Primitives

BiNoMaP leverages reduced-order models, frictional contact mechanics, and trajectory optimization to define core primitives. Key analytical modes include:

• Nonprehensile Nudging Primitive (Declutter): Plans a QP-based lateral push to clear candidate grasp points using 2D bounding box abstractions, subject to collision, no-pull, and minimal-movement objectives. The resulting displacement plan specifies nudge actions for scene rearrangement, with four discrete nudge amplitudes executed as force-thresholded lateral pushes (Wu et al., 2024).
• Side-Contact Bimanual Grasp Primitive: Samples contact pairs on object contours; scores each via QP-based worst-case resistance to planar disturbance wrenches. Grasp feasibility and quality ($l_g$) are calculated by solving for contact forces/torques under frictional and force-closure constraints. Execution relies on hybrid position/force control (Wu et al., 2024).

2.2 Compact Dynamical Models

• Parallel Pushing: Adopts either an equivalent-bicycle (synchronized tangential forces) or differential-drive (independent normal forces) abstraction. The wrench-twist mapping yields linear or nonholonomic (unicycle-like) kinematics, enabling closed-form path tracking and force allocation.
• Orthogonal Pinch/Pivoting: Two arms push orthogonally, yielding coupled net forces/torques. The feasible twist locus defines distinct unicycle-like regions; trajectory planning proceeds in full 3-DOF (SE(2)) space.
• Dual-Finger Slide: Both arms apply downward normal forces; modulation of normal loads steers the Center of Pressure, affording quasi-holonomic, fully actuated control of planar translation and rotation (Özcan et al., 12 Mar 2026).

All analytic primitives are framed with explicit algebraic force allocation; optimization is typically not required except for reachability and inverse-kinematics path planning.

3. Learning-Based Synthesis and Generalization

BiNoMaP enables robust category-level primitive acquisition from demonstration without reinforcement learning:

1. Trajectory Extraction: RGB-D human demonstrations are processed via hand mesh reconstruction (e.g., MANO+WiLoR) to extract per-frame bimanual contact points and orientations. Averaged fingertip positions and a heuristic for orientation generate $R_t \in SO(3)$0, a temporal sequence of hand poses (Zhou et al., 25 Sep 2025).
2. Geometry-Aware Post-Optimization:
   • Motion Smoothing: Each arm’s trajectory is projected onto a best-fit plane and smoothed via 2D cubic B-splines. Rotations are interpolated with quaternion SLERP.
   • Contact Adjustment: Iteratively refines initial trajectory on the robot by scaling the inter-arm distance and adjusting clearance. Execution failures trigger incremental clearance reduction.
3. Category-Level Parameterization: Structural adaptation is performed by measuring characteristic object size (e.g., width) and scaling inter-arm distances accordingly. The primitive becomes $R_t \in SO(3)$1, parameterized by geometric attributes (Zhou et al., 25 Sep 2025).

This pipeline yields transferable bimanual primitives across object instances and categories, directly from (potentially noisy) visual human demonstrations.

4. Pipeline Integration and Execution Strategies

A typical BiNoMaP deployment integrates perception, primitive planning, sequencing, and control:

• Perception: Scene segmentation yields target, adjacent, and environmental point clouds, which are projected for 2D contour and bounding box fitting.
• Grasp Planning & Decluttering: Candidate grasp pairs are generated and scored. If occluded, a nudge plan is computed via QP. All candidate actions are ranked according to declutter cost $R_t \in SO(3)$2 (preference for no-declutter), grasp quality $R_t \in SO(3)$3, and heuristic centering penalties.
• Primitive Execution:
  • Nudge: Executed in four increments of increasing amplitude by approaching along the principal axis, establishing contact, applying lateral displacement, and retracting.
  • Grasp: Both arms approach from opposite directions, make contact at pre-planned side-contacts, and extract the object while maintaining constant clamping force via hybrid position/force control.
• Long-Horizon Planning: For dynamic primitives (e.g., parallel push, sliding), 3-DOF object trajectories are computed, then mapped to joint-space trajectories that respect manipulator kinematics and maintain dual contact throughout the maneuver. Impedance and frictional force control close the loop during execution (Wu et al., 2024, Özcan et al., 12 Mar 2026).

5. Experimental Performance and Comparative Benchmarks

5.1. Picking and Rearrangement in Structured and Unstructured Settings

Empirical studies demonstrate substantial advantages of the BiNoMaP approach:

Scenario	Reported Success Rate	Context	Main Failure Modes
Free-space picking	90.2% (102 trials)	34 items, no clutter	Kinematic/IK limits, heavy/narrow items
Cluttered picking	66.7% (45 trials)	Randomly cluttered shelves	Insufficient clearance, item rotation
Ablation w/o nudge	33.3% (cluttered)	Identical scenes as above	Unable to clear grasp points
Category-level gen.	76.2% (343/450)	Category transfer, 4 bimanual tasks	Force/pose error with rigid objects
Instance-level gen.	86.7% (avg. 6 tasks)	Baseline: DyWA ≈48.3%, DP3 ≈25.5% (Zhou et al., 25 Sep 2025)	Wrapping instability, asymmetric objects

Qualitative results highlight compositionality and robustness: primitives are composed in sequential pipelines (e.g., pre-grasp pivot, then grasp and stack) and support recovery from non-nominal events such as object failures or slips (Wu et al., 2024, Zhou et al., 25 Sep 2025).

5.2. Simulated Planar Manipulation

Simulation benchmarks for analytic BiNoMaP show:

• Control loop rates of 200–500 Hz, force allocation per-step in $R_t \in SO(3)$4 time.
• Translation tracking errors under 1 cm, orientation errors below 2–3°.
• Planning times for 10 s trajectories on the order of 1–2 s.
• Tasks include meter-scale parallel pushes, tight 90° pivots, and press-fitting objects into constrained environments (Özcan et al., 12 Mar 2026).

6. Guidelines for Adaptation and Limitations

To adapt BiNoMaP primitives to new objects, environmental constraints, or hardware, the following parameters and heuristics are essential:

• Friction Coefficient ($R_t \in SO(3)$5): Tune per material for grasp QP permissivity.
• QP Weights: Increase for fragile items to minimize push-induced disturbance.
• Nudge Sequence: Adjust number and amplitude for wider/taller scenes.
• Contact Normal and Pose Sampling: Increase density for curved or noisy objects.
• End-Effector Models: Modify geometric/collision parameters for different grippers.
• Perception Strategy: Add multi-view perception for extreme shelf heights or occlusions.
• Kinematic Feasibility: Early IK-based pruning of sample contacts prevents invalid plans.
• Heuristic Centering Penalty ($R_t \in SO(3)$6): Adjust to mitigate toppling for off-center mass distributions (Wu et al., 2024).

Limitations include difficulties with extremely rigid or asymmetric items, reliance on accurate perception for dense or occluded scenes, and occasional failure modes in contact adjustment or slip when inter-arm distance calibration errors exceed tight tolerances (Wu et al., 2024, Zhou et al., 25 Sep 2025).

7. Relationship to Broader Research Themes

BiNoMaP diverges from prior paradigms in several respects:

• Analytic Modeling vs. RL: Eschews computationally expensive dynamics learning or simulation-to-real transfer, instead using frictional mechanics and geometric scaling for policy synthesis.
• Category-Level Generalization: Provides explicit mechanisms for geometric primitive parameterization, yielding ~76% generalization rates with only ~10% success drop vs. instance-level trials (Zhou et al., 25 Sep 2025).
• Closed-Form Optimization: Most pipeline steps employ direct, algebraic solutions (force allocation, contact planning), rather than iterative or sampling-based methods, supporting real-time execution (Özcan et al., 12 Mar 2026).
• Integration with Standard Mobile Manipulation Stacks: The framework is compatible with segmentation, force-control, and standard IK solutions. No specialized hardware is required beyond dual arms and force feedback (Wu et al., 2024).

A plausible implication is that discrete, library-based bimanual non-prehensile models are sufficient for a wide operational envelope, provided scene estimation and basic contact reasoning are robust. This suggests directions for integrating such models with future learning-augmented perception and contact-rich tactile feedback.