Belief-Overlap Partial Inversion: Object-Centric Flow Replanning for Humanoid Loco-Manipulation

Chen Yu; Sudarshan S Harithas; Juan Borbon; Dingqi Zhang; Jiuguang Wang

cs.ROOct 9, 2026

Belief-Overlap Partial Inversion: Object-Centric Flow Replanning for Humanoid Loco-Manipulation

Authors: Chen Yu, Sudarshan S Harithas, Juan Borbon, Dingqi Zhang, Jiuguang Wang

Organizations: Northwestern University, USA · Multiply Labs, USA

Abstract

People often learn how an unfamiliar object moves through a small exploratory push, using its response to guide their next motion. Inspired by this behavior, we study humanoids pushing carts whose mass and caster stiffness are initially unknown. Our object-centric framework closes online estimation, flow-based planning, and whole-body control into a loop, creating a tension: replacing the plan whenever the belief shifts disrupts the maneuver under way, while keeping it strands the robot on a path its evidence has ruled out. Belief-Overlap Partial Inversion (BOPI) scales revision to agreement, inverting the flow under the old belief only as far as the beliefs disagree before reconstructing under the new one. Across 18 simulated goals it lowers pooled final position and yaw error by roughly 33% and 47% against fixed-depth replanning, and on hardware it translates and turns a non-holonomic cart.

Figures & tables

Fig. 2: An object-centric estimation–planning–control framework. Online estimation informs object planning and whole-body control (trajectory waypoint tracking) . As estimates change, the planner can revise the remaining path using (A) BOPI, which uses belief overlap to decide how far to run the flow backward under the old belief, then runs it forward under the updated belief; (B) RDM [ 1 ] , which blends the current plan with a fixed proportion of random noise, then runs the flow forward under the updated belief to reconstruct the path; or (C) FlowEdit [ 2 ] , which uses shared noise to evaluate the flow under both beliefs, then edits the path using the difference between the flow directions under the updated and old beliefs. Orange/purple denote old/new plans and beliefs.

Fig. 3: Planning in a nonlinear toy problem. At 10 s (squares), BOPI is near the goal at low speed; RDM and FlowEdit overshoot with higher residual speeds. Background color shows mechanical energy $H$ .

Method	Success (%)	Position error	Final speed error	Cumulative mutation	Strategy switches
BOPI (Ours)	$\mathbf{54.9\pm 14.6}$	0.189	0.116	0.704	2.144
RDM	$40.0\pm 6.1$	0.283	0.211	2.212	8.617
FlowEdit	$12.6\pm 3.7$	1.043	0.367	4.026	9.260
Fresh FM	$4.0\pm 0.9$	1.567	0.422	23.631	21.045
Retain	$2.4\pm 0.3$	2.090	0.491	N/A	N/A

TABLE I: Toy problem results.

Fig. 4: Flow-generated plans adapt to wheel constraints. With the same initial flow noise, the flow generates different paths as rear-caster stiffness changes: move one meter left (A), or turn $180^{\circ}$ and return to the starting position (B). Color indicates stiffness; bold curves mark its extremes.

Fig. 5: From property estimates to updated plans. As estimates of cart dynamic properties evolve (A), BOPI revises the initial near-straight path into a curved maneuver (B). Matching colors and numbers link estimates to plan updates; black shows the executed motion.

Fig. 6: Accurate cart tracking with a changing body–cart distance. We design a path covering common maneuvers:

0.8\,\mathrm{m}

forward travel,

0.6\,\mathrm{m}

reverse travel without changing heading, and a

45^{\circ}

rolling turn. Panel A compares tracking across masses and wheel constraints. In an example execution with a

20\,\mathrm{kg}

cart (B), body–cart distance changes during turning while tracking error remains low, illustrating that the robot can follow the object’s path without maintaining a fixed body–cart offset.

Task category	BOPI (Ours)	RDM	FlowEdit	Fresh FM	Retain
Translation	0.349 / 0.163	0.625 / 0.561	0.637 / 0.590	0.870 / 1.039	0.927 / 0.330
Rotation	0.109 / 0.150	0.134 / 0.195	0.251 / 0.693	0.754 / 1.209	0.286 / 0.306
Translation + rotation	0.209 / 0.205	0.296 / 0.336	0.240 / 0.228	0.835 / 1.165	0.495 / 0.329
Translation + rotation (wrong mass)	0.105 / 0.039	0.163 / 0.139	0.277 / 0.129	1.353 / 1.114	0.352 / 0.115
Pooled	0.179 / 0.152	0.267 / 0.286	0.295 / 0.349	0.936 / 1.149	0.465 / 0.277

TABLE II: Simulation results: end-to-end planning. Entries are mean final position error (m) / yaw error (rad).

Fig. 7: BOPI maintains goal-directed motion during replanning in simulation. Planning examples span translation (A–E), rotation (F–J), combined translation–rotation (K–O), and combined motion with an incorrect initial mass estimate (P–T). BOPI makes smaller changes between successive plans, producing consistent replanned trajectories as the robot progresses toward the goal. This consistency helps explain the lower final position and yaw errors reported in Table II . Grid spacing is

0.5\,\mathrm{m}

in both directions.

Table 9

Fig. 8: BOPI produces consistent trajectories for a non-holonomic cart in real-robot experiments. The goals are one-meter lateral motion (A–E) and a $90^{\circ}$ clockwise turn returning to the starting position (F–J). Corresponding BOPI photos appear in Fig. (E–J). Light curves show five estimated cart trajectories; solid curves and shading show their time-aligned mean and pointwise $95\%$ confidence regions. Squares mark the mean at each trajectory’s end. All paths share display-only smoothing ( $\sigma=0.20\,\mathrm{s}$ ). Tables IV and IV compare complete trials.

Panel of Figure 11 — Fig. 9: Unstable executions of the Fresh FM baseline. Excessive leaning (A) and sideways leg extension (B) during lateral pushing illustrate how replanning can disrupt whole-body motion.

Robotic Object Pushing

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Open paper AskPDF arXiv

Learning a single perceptive policy for diverse humanoid loco-manipulation requires unifying high-level task decisions without losing the state-dependent physical responses that make each interaction succeed. This makes the representation between high-level planning and whole-body control critical: kinematic or contact targets provide compact abstractions but do not directly encode interaction-specific control responses, while directly predicting low-level actions requires the planner to model high-frequency closed-loop feedback. We propose FIBER, a framework that uses the executable latent space of a frozen behavioral foundation model (BFM) as a shared planning representation for heterogeneous interaction skills. Our latent policy projection (LPP) maps independently acquired task-specific policies into this representation by identifying latent commands whose induced actions match their local control responses, enabling lower-rate planning while retaining the BFM's high-frequency state feedback. After projection, we aggregate closed-loop latent rollouts from all skills and train a single perceptive flow planner entirely offline. We further introduce AH-BFM, an adaptive-horizon BFM trained with multi-gamma forward-backward (FB) learning to support both precise control and temporally extended whole-body behavior. We evaluate FIBER on box pickup, door opening, and object grasping in simulation and on a real Unitree G1 humanoid. Across 128 diverse variations per task in simulation, FIBER achieves 42.0% mean success, more than tripling projected latent replay (11.6%) and substantially outperforming kinematic planning (3.5%). Real-world experiments further demonstrate sim-to-real transfer, skill chaining, and conditional steering through the same unified planner.

Abstract

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