Object-wise Motion Manipulation

• Object-wise motion manipulation is an object-centric paradigm that defines and controls motions using explicit object states, poses, and constraints.
• It leverages relative coordinate frames, ontological reasoning, and physics-based planning to significantly improve efficiency and success rates.
• Applications span robotic manipulation, nonprehensile tasks, video generation, and human-object interactions, while challenges remain in handling complex and deformable objects.

Object-wise motion manipulation is the algorithmic and representational paradigm in which the motions, actions, or control policies for a system are formulated, optimized, or conditioned explicitly in terms of object representations—object poses, object states, contact dynamics, or object motion constraints—rather than solely in terms of robot-centric or global task coordinates. This paradigm permeates robotic manipulation planning, task and motion planning (TAMP), visual imitation learning, video generation, and simulation-based physical reasoning, and is central to research streams seeking efficient, generalizable solutions across robotic, computer vision, and animation domains.

1. Fundamental Problem Formulations

Object-wise motion manipulation formalizes both the state and the control or plan in terms of object-centric variables, often leveraging the following structures:

• Augmented State Space: Let a scenario contain $N$ objects and at least one robot. The full state at time $t$ is

$$x(t) = (q_0(t), ..., q_N(t)), \quad q_i(t) = (p_i, o_i, v_i, \omega_i, \eta_i)$$

where $p_i \in \mathbb{R}^3$ (position), $o_i \in SO(3)$ (orientation), $v_i$ (linear velocity), $\omega_i$ (angular velocity), and $\eta_i$ manipulation-constraint flags. The state evolves under physics-based propagation:

$x_{t+1} = f(x_t, u_t, \kappa_t)$

with $u_t$ the admissible actuator input and $t$0 the knowledge instantiating manipulation constraints (Muhayyuddin et al., 2017).

• Object-Centric Frames: In TAMP, relative-frame parametrization is used. The decision variable is

$t$1

denoting the position and axis-angle orientation of the control frame relative to the target object, allowing for explicit encoding of geometric and task constraints directly in object coordinates (Migimatsu et al., 2019).

• Object-Centric Manipulation Behaviors: Constant-time planners represent manipulation as a two-step process: robot motion to a behavior initiation state followed by a predefined object-centric manipulation policy (e.g., grasp, insertion) (Gandotra et al., 30 Nov 2025).
• Object-Wise Trajectory Optimization: For nonprehensile manipulation, plans specify desired object trajectories (SE(2) or SE(3) paths) that the robot drives via appropriate control—pushing, pivoting, rolling—rather than specifying exclusive robot arm trajectories (Ren et al., 2024, Boroji et al., 2024).
• Semantic, Symbolic, or Ontological Encoding: The manipulation actions and object affordances are encoded in ontologies (e.g., OWL), linking object types, manipulation primitives, regions, and relevant constraints, enabling semantic-driven planning and reduced sampling complexity (Muhayyuddin et al., 2017).

2. Algorithmic Principles and Methodologies

Physics-Based and Knowledge-Driven Planning

• Explicit object state and object-motion variables enable planners to directly encode Newton–Euler dynamics, contact conditions, and manipulation constraints, while embedding semantic reasoning through dynamic ontological knowledge (e.g., object is "constraint-oriented," "pushable from front/rear only") (Muhayyuddin et al., 2017).
• Planners integrate these semantics to selectively enable/disable collision modes, re-bias sampling spaces, and efficiently locate valid manipulation regions (demonstrated by doubling the success rate from ∼20% to ∼90% with ontological reasoning in cluttered environments) (Muhayyuddin et al., 2017).

Object-Centric TAMP

• Plans are generated in the relative object frames, such that action constraints (e.g., "grasp in pose X of object A") can be robust to unintended changes in absolute coordinates.
• The symbolic action skeleton (STRIPS-generated) constraints and the path/switch constraints in trajectory optimization are expressed in terms of object-relative configurations, yielding plans that directly adapt to moving or perturbed objects without global replanning (Migimatsu et al., 2019).

Push and Rolling-Based Manipulation

• For nonprehensile tasks, object-step planners select an object, propose an object-wise motion subgoal, and realize it via robot motion, dynamically interleaving open-loop plan construction and closed-loop push execution (Ren et al., 2024).
• Edge-rolling exploits screw-theoretic decomposition—any object pose displacement is described as a sequence of constant-screw (twist) motions, allowing highly efficient, contact-respecting trajectory generation for objects with curved edges (Boroji et al., 2024).

Structured Policy Learning

• Reinforcement and imitation learning frameworks encode object-wise action representations, grounding each motion primitive (push, grasp, move, open) at a point on the observed object and jointly selecting parameters (primitive type, grounding location, motion parameters) (Jiang et al., 2024, Gandotra et al., 30 Nov 2025).
• Subspace-wise hybrid RL partitions control into task-aligned subspaces (e.g., kinematic, geometric, redundant) in the object's frame, enabling adaptive force modulation and dexterous pose optimization in articulated manipulation (Kim et al., 2024).

3. Object-Wise Motion in Perception, Video, and Data-Driven Animation

Recent advances extend object-wise paradigms beyond robotics into perception, image/video editing, and human modeling:

• Motion-Supervision in Imitation Learning: The MBA framework decomposes action generation into a stage that samples future object pose sequences via diffusion, conditioning the generation of robot action sequences on predicted object motion (Su et al., 2024), consistently improving policy robustness and task success rates by 6–15 pp in simulation and 10–20 pp on real-world tasks.
• Object-Wise Video Generation and Editing: Systems like TRACE, Drag4D, Perception-as-Control, ObjectMover, and MotionShot explicitly encode object trajectories, segmentation, or keypoint correspondences, allowing precise spatiotemporal object manipulation in novel scenes and video domains (Yu et al., 11 Mar 2025, Kang et al., 26 Sep 2025, Phung et al., 26 Mar 2026, Chen et al., 9 Jan 2025, Liu et al., 22 Jul 2025).
• Learning Human-Object Relations: OMOMO and the Object Augmentation Algorithm extract, encode, or synthesize object trajectories and contact points, using them as conditions in full-body human motion generation or augmenting physical datasets with inferred joint torques and wrenches (Li et al., 2023, Herneth et al., 2024).

4. Knowledge Representation and Semantic Reasoning

Object-wise manipulation increasingly relies on high-level knowledge and semantic reasoning:

• Ontological Models: Manipulation-specific ontologies define types, regions, actions, and affordance relations in a structured language (OWL), supporting in-planner reasoning about manipulation affordances, object–region–action relationships, and semantic region validity (Muhayyuddin et al., 2017).
• Dynamic Knowledge Instantiation: Semantic query predicates update at each planning iteration, dynamically altering allowed collision regions and sampling distributions, thereby tailoring planners to the evolving state of objects and workspaces (Muhayyuddin et al., 2017).

5. Experimental Results and Validation

Empirical studies consistently validate object-centric formulations:

System/Paper	Task(s)	Object-wise Formulation	Quantitative Gain
Ontological physics-based planner (Muhayyuddin et al., 2017)	constrained push	ontology+physics	Planning time ↓50%, success ↑ (20% → 90%)
Object-centric TAMP (Migimatsu et al., 2019)	pick & place	relative frame NLP	Zero-replan under object perturbations
Edge-rolling (Boroji et al., 2024)	edge rolling	SE(3) screw path	Slippage <0.03 mm, joint limits enforced
MBA imitation (Su et al., 2024)	manipulation	staged diffusion	+14.2 pp on DP baseline
HACMan++ (Jiang et al., 2024)	RL manipulation	spatially grounded a	+30–50% vs baselines across tasks
Subspace Hybrid RL (Kim et al., 2024)	articulated obj	task-aligned subspace	Valve RMP: +31.5% over manual
ObjectMover/TRACE/Drag4D (Yu et al., 11 Mar 2025Phung et al., 26 Mar 2026Kang et al., 26 Sep 2025)	video edit/generation	object trajectory/box/mesh	FID, SSIM, user preference ↑

These results underscore that formulating the plan, control, or manipulation policy in object-centric terms yields both computational and execution robustness advantages.

6. Limitations, Open Challenges, and Future Directions

While object-wise motion manipulation has been empirically validated across robotics, animation, and video, certain limitations persist:

• Generalization to Complex, Articulated, or Deformable Objects: Most frameworks currently assume rigid objects or fixed-pivot manipulation; generalization to free-form, articulated, or deformable bodies remains an open challenge (Boroji et al., 2024, Kim et al., 2024).
• Domain Knowledge Transfer and Ontology Construction: Defining and extending ontologies for novel object types or actions can be labor-intensive; learning these structures automatically remains an aspirational goal (Muhayyuddin et al., 2017).
• Perception-Action Coupling Noise: Filtering noise in object pose estimation, especially with thin or soft objects, impacts manipulation stability and repeatability (Su et al., 2024).
• Multi-Object and Multi-Agent Manipulation: Extending object-centric planners and policies to simultaneously coordinate multiple manipulable objects (with occlusion, collision, or task interdependencies) is nascent (Ren et al., 2024).
• Integration of High-Dimensional Constraints: Some optimization schemes approximate joint constraints coarsely (e.g., as roll- or pivot-length bounds) instead of integrating the full configuration space constraints (Boroji et al., 2024).
• End-to-End Differentiability and Global Consistency: Achieving end-to-end learning, especially across perception, planning, and control in object-centric representations, is nontrivial, with issues of mode collapse or trajectory drift still observed in video/simulation (Yu et al., 11 Mar 2025, Li et al., 2023).

Anticipated future work includes: enhanced force- and slip-aware control strategies; seamless scaling of ontological models; robust perception-to-action pipelines for real-time physical scenes; unified policy learning across manipulation, navigation, and video editing tasks; and more versatile formulations able to encompass geometry, semantics, and dynamic interactions of arbitrary object sets.

7. Summary and Impact

Object-wise motion manipulation unifies state-of-the-art algorithmic planning, trajectory optimization, control policy learning, perception-guided generation, and data augmentation by explicitly representing and controlling the states, trajectories, and constraints of objects as first-class entities. This object-centric formalism enhances robustness to dynamic scenes, reduces search space complexity, enables zero-shot adaptation and transfer, and aligns naturally with human-like manipulation strategies. As evidenced by recent work across physical simulation, robotics, and vision-based animation pipelines, explicitly encoding and exploiting object-wise structure is a driving force behind advances in scalable, general-purpose manipulation systems (Muhayyuddin et al., 2017, Migimatsu et al., 2019, Boroji et al., 2024, Su et al., 2024, Gandotra et al., 30 Nov 2025, Jiang et al., 2024, Kim et al., 2024, Yu et al., 11 Mar 2025, Phung et al., 26 Mar 2026, Kang et al., 26 Sep 2025, Li et al., 2023, Herneth et al., 2024).