Ego-Vision World Model for Humanoid Contact Planning
1. Paper overview
In one sentence: A short-horizon latent planner turns offline random humanoid interactions into purposeful contact, trading greedy value selection for a biased but potentially less variable sequence score. e-identitye-probleme-datae-mpce-real
| At a glance | What to know |
|---|---|
| Research problem | Source description Contact can stabilize a humanoid, intercept an object, or cause an unwanted collision. Planning must distinguish these outcomes despite sparse rewards, unobserved contact forces and noisy vision. The paper targets wall support, ball blocking and low-arch traversal using a common predictive representation. e-probleme-protocol |
| Core mechanism | Source description A demonstration-free simulated interaction dataset trains latent dynamics, observation reconstruction, termination prediction and a surrogate action-value together. e-datae-latente-training |
| A key reported result | Traverse the Arch: N=4: 0.0157 ± 0.0015 Reward, higher is better; mean ± standard deviation. Single-task simulation, Table I. The paper reports ten independent trials across three random seeds, without specifying their allocation. N=1: −0.0396 ± 0.0121; N=6: 0.0115 ± 0.0099; ARWM: −0.0018 ± 0.0183; Rew-MPC: −0.0211 ± 0.0092; TD-MPC: 0.0145 ± 0.0005. Planning beyond one step helps substantially. These are reward statistics, not success percentages or a significance test. e-protocole-tablee-ablation |
| Reading caution | Reader analysis All quantitative comparisons are simulated. Physical demonstrations have no reported trial counts or success rates. SAC-like off-policy baselines are explicitly excluded, so the sample-efficiency conclusion is limited to PPO. e-protocole-efficiencye-real |
Core contributions
- Source description
A demonstration-free simulated interaction dataset trains latent dynamics, observation reconstruction, termination prediction and a surrogate action-value together. e-datae-latente-training
- Source description
The main planning contribution is a short-horizon average of action-values, treating the learned value as an imperfect heuristic. Mixed-task training and physical demonstrations support a reusable contact planner within the tested task family. e-mpce-multitaske-real
Figure 2. The model learns command consequences under an already-trained tracking controller. Original paper, p. 2 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Begin with panel (a): the robot explores end-effector position and body height, and stores observation, action, reward and termination. Panel (b) separates blue dynamics memory h_t from purple observation latent z_t. Follow the horizontal action-conditioned arrows to the next memory state, then the downward branches to the prior latent, failure probability and surrogate value. The value branch receives the action as well as the latents; the termination branch receives the latents, consistent with Equations (4)–(5). The upper reconstruction path supplies training supervision. Equations (2)–(3) additionally condition encoding and decoding on h_t, connections abbreviated in that upper cartoon. e-controllere-datae-latente-training
What it supports. The predictive representation serves several objectives at once: reconstruct observations, anticipate latent changes, detect termination and evaluate candidate commands. Offline data can therefore train a planner-relevant model without a demonstration trajectory for each successful contact. The controller that makes the commands executable is trained separately before this collection stage.
Where the evidence stops. The figure is a training schematic, not a full implementation specification. Its upper bottleneck omits explicit h_t inputs present in the equations; it also supplies no layer widths or complete optimization settings.
2. Motivation
2.1 The problem and the proposed response
Contact can stabilize a humanoid, intercept an object, or cause an unwanted collision. Planning must distinguish these outcomes despite sparse rewards, unobserved contact forces and noisy vision. The paper targets wall support, ball blocking and low-arch traversal using a common predictive representation. e-probleme-protocol
2.2 What this reading follows
A humanoid facing a wall, a flying ball or a low arch needs different kinds of contact reasoning: brace, intercept or avoid. This paper learns the consequences of posture commands from simulated random interactions, then searches those consequences at deployment. Its central choice is to score short imagined sequences with a learned action-value instead of relying on sparse predicted rewards. The figures below separate representation learning, online search and executed behavior. Read the evidence at three levels: simulation reward comparisons, qualitative prediction diagnostics and physical demonstrations. Their conclusions differ, particularly because a human supplies base velocity in the hardware tests. This edition reviews the supplied March 2026 arXiv v2. e-identitye-probleme-datae-mpce-real
3. Research context
We place the paper in the collection through its world–action interface. The catalog labels and the reading’s assessment are shown separately.
| Catalog dimension | Recorded classification |
|---|---|
| Major category | WAMs |
| Architecture | Dual-system |
| Prediction paradigm | Other mechanisms |
| Quadrant | Outside quadrants |
3.1 Evidence-based assessment
Supports the recorded classification
Architecture supports Dual-system: a learned predictive world model is used by an explicit CEM planner and a separately trained controller. Action-conditioned forward rollouts are Other mechanisms, outside joint action/future generation or inverse-dynamics quadrants. The broad visual-planning tag fits; explicit 3D multiview reconstruction and an IDM are not demonstrated by ego-depth latent prediction. e-controllere-latente-mpc
This is the collection’s architectural analysis, not a new related-work survey. Benchmark comparisons and their protocols appear in Section 6.
4. Problem formulation
4.1 Inputs and outputs
| Inputs | Outputs |
|---|---|
|
|
4.2 Equations and their role
5. Method in detail
5.1 Learn consequences at the command level
Start with what an action means. The low-level PPO controller already converts desired velocity, end-effector position and body height into motor behavior. The high-level learner then explores only the posture-related part of that interface. Its random finite differences yield trajectories with observations, rewards and termination labels, rather than demonstrations of expert contacts. The world model learns the resulting closed-loop dynamics through recurrent memory and an observation bottleneck. Reconstruction makes the latent retain sensory information; prior matching makes that information predictable without another camera frame; termination and value losses make it useful for planning. Reader interpretation: this command interface simplifies the prediction problem, but also ties the learned consequences to the underlying controller. Changing that controller is a meaningful distribution shift, not merely swapping an actuator backend. e-controllere-datae-latente-training
Figure 3. Imagine several steps, score their values, execute one command and observe again. Original paper, p. 3 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Follow the real camera observation into z_t at the left. Later purple blocks carry hats because they come from the model's prior, without future camera frames. Each sampled command advances the recurrent dynamics; the lower value heads contribute to a sequence score searched by CEM. The plus signs denote accumulation, while Equation (17) specifies an average over the horizon. The crossed-circle icons denote termination predictions, not an explicit multiplication instruction. The caption and page 5 supply the actual rule: when termination probability exceeds 0.9, subsequent values become zero. The reported default searches 1,024 trajectories over four steps and executes only the first selected action. e-latente-mpce-theorye-real
What it supports. Prediction is open-loop inside each candidate sequence, but control is closed-loop across planning cycles. A fresh observation corrects the latent estimate before another search. Averaging several surrogate values is the paper's proposed way to reduce sensitivity to a noisy single value estimate, with an acknowledged change in optimization objective.
Where the evidence stops. Equation (17) writes predicted latents throughout, whereas the figure and accompanying text initialize the current step from the observation posterior. The termination gate is specified in prose. Neither the schematic nor CEM supplies an optimality guarantee.
5.2 Use a value estimate without treating it as an oracle
A greedy planner would pick the action with the largest current surrogate value. The paper instead samples short sequences, propagates their latent consequences and averages the values along them. Its motivation is that partial observability and imperfect offline coverage make individual estimates unreliable. In the variance analysis, averaging can help when residual errors are not too strongly correlated, but the new score also changes the control objective and retains bias. CEM searches this score; it does not repair errors in the learned model. Only the first command is executed, so the next camera observation can correct the prediction before another decision. Reader interpretation: Table I establishes the practical benefit of multistep planning in these tasks, while the claimed variance-reduction mechanism still needs direct error-covariance measurement. e-theorye-mpce-tablee-ablation
5.3 Separate contextual reuse from unrestricted autonomy
The value head can infer task context from the observation latent, allowing one world model to train on the mixed ball, wall and arch dataset. Figure 6 compares this shared model with specialized models: wall and arch improve, while ball drops. Its t-SNE plots show separable task structure, but do not prove that the representation has disentangled physics from appearance. Figure 7 adds a second kind of evidence: the preferred hand position changes as an object approaches, and decoded predictions preserve aspects of its trajectory. Figure 4 then shows actual physical behavior, including an unseen box. Reader interpretation: these pieces support reuse across the tested contact contexts. They leave open broader object diversity, unseen task definitions and autonomous velocity selection, which was handled by an operator in deployment. e-traininge-multitaske-diagnostice-real
5.4 Training and inference
During training
The offline world-model loss sums observation negative log-likelihood and termination binary cross-entropy, two KL terms with alternating stop-gradient placement, and squared value error against Monte Carlo return targets. Both KL terms use the posterior-to-prior direction; they differ in which distribution receives gradients. The authors report more stable Monte Carlo targets than TD-error training. e-training
Single-task models and one model trained on mixed-task data are evaluated. The paper describes staged controller and world-model training, but does not specify a detailed freezing schedule, latent widths or a complete optimizer configuration. e-controllere-traininge-multitask
During inference
Encode the current real observation, then use prior latents for open-loop candidate rollouts. CEM searches 1,024 action trajectories with default horizon four. If predicted termination exceeds 0.9, subsequent values are zeroed. Execute only the first chosen action and replan from feedback; physical planning runs at 25 Hz. e-mpce-real
5.5 Implementation flow
- Define the control interface
A PPO-trained proprioceptive controller tracks desired velocity, end-effector position and body height. The planner controls only end-effector position and height; desired velocity lies outside its action space. The world model therefore predicts closed-loop behavior under this controller, rather than directly issuing motor torques. e-controllere-data
- Collect smooth random interactions
After training the controller, collect ball, wall and arch trajectories. Normalize the planner task space and increment the preceding action by a uniform random finite difference with scale 0.32. Store observations, actions, rewards and termination signals. Demonstration-free refers to this collection procedure, not to an untrained low-level controller. e-controllere-data
- Maintain a predictive belief
An RNN updates deterministic memory h_t. An observation-conditioned Gaussian latent z_t supports reconstruction; a prior predicts that latent from memory alone for imagined futures. A CNN extracts image features. The termination head depends on the latents, while the value head additionally conditions on the candidate action. e-latente-training
6. Experiments & results
An offline-trained recurrent world model predicts the consequences of humanoid posture commands from ego-centric depth and proprioception. Sampling MPC averages learned action-values over short latent rollouts, then sends one command to a separate motor controller. Simulation ablations favor this approach for ball blocking and arch traversal; physical demonstrations establish feasibility with operator-controlled base velocity, rather than autonomous navigation or measured deployment reliability.
6.1 Read the original evidence
Figure 5. The offline planner reaches useful rewards with fewer transitions in the tested PPO comparison. Original paper, p. 5 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Red denotes the proposed method trained from random offline interactions; blue denotes PPO collecting new on-policy data. Compare rewards at a common transition count before asking where the blue curve eventually catches up. The horizontal spacing changes around the dashed one-million-step marker, so visual slopes across that point are not directly comparable. Vertical scales also differ by task. The caption caps the offline dataset at one million steps; Section IV.A claims task completion using half a million. Wall and ball show that giving PPO more data can close or reverse the reward gap. Arch traversal retains the clearer advantage in the plotted range. e-controllere-efficiencye-protocol
What it supports. The benefit is earlier useful contact behavior under the tested data budget, especially when the robot's viewpoint changes during arch traversal. The plot also prevents an overstatement: a fixed offline model need not achieve the highest reward once PPO receives substantially more interaction data.
Where the evidence stops. Transition count is not wall-clock training cost, and this plot does not account for the full low-level-controller training budget. Off-policy alternatives are not compared. The paper does not provide exact raw curve values or a numerical success criterion for its completion claim.
Figure 4. The hardware examples show purposeful hand contact alongside head-contact avoidance. Original paper, p. 4 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Panel (a) combines two contexts in sequence: lower the body to traverse the arch, then intercept a box. Panel (b) contrasts desired hand contact against the wall with undesired head collision during a disturbance. Panel (c) compares blocking a training-like ball and an unseen box; panel (d) isolates low-clearance traversal. The repeated translucent poses show motion over time, not multiple simultaneous robots. Read these photographs with Section IV.E: the Unitree G1 runs the planner at 25 Hz using 1,024 candidate trajectories and four-step predictions. A human operator supplies desired base velocity while the planner selects posture and end-effector commands. e-reale-protocole-data
What it supports. The demonstrations extend the evidence beyond simulated reward and show both contact exploitation and avoidance on a physical humanoid. The unseen box is a concrete example of transfer beyond the training object type. Sequential task behavior is also shown, although the publication does not provide a numerical hardware comparison.
Where the evidence stops. Photographic examples cannot establish a success probability or robustness range. Trial counts, failure rates and a fully autonomous navigation evaluation are absent. Operator-controlled velocity is part of the demonstrated system and must remain explicit.
6.2 Results and evaluation conditions
| Task & protocol | Reported result | Comparison & interpretation |
|---|---|---|
| Traverse the Arch Single-task simulation, Table I. The paper reports ten independent trials across three random seeds, without specifying their allocation. | N=4: 0.0157 ± 0.0015 Reward, higher is better; mean ± standard deviation | N=1: −0.0396 ± 0.0121; N=6: 0.0115 ± 0.0099; ARWM: −0.0018 ± 0.0183; Rew-MPC: −0.0211 ± 0.0092; TD-MPC: 0.0145 ± 0.0005. Planning beyond one step helps substantially. These are reward statistics, not success percentages or a significance test. e-protocole-tablee-ablation |
| Block the Ball Same single-task simulation protocol as Table I. | N=4: 0.0061 ± 0.0003 Reward, higher is better; mean ± standard deviation | N=1: −0.0066 ± 0.0050; TD-MPC: −0.0016 ± 0.0047. This task strongly distinguishes the surrogate objective from both greedy value maximization and the tested TD-MPC variant. e-protocole-table |
| Support the Wall Same single-task simulation protocol as Table I. | N=4: 0.0614 ± 0.0027 Reward, higher is better; mean ± standard deviation | N=6: 0.0617 ± 0.0031; TD-MPC: 0.0699 ± 0.0035. Four steps is a cross-task choice, not the best mean on every task; TD-MPC leads this column. e-protocole-table |
| Offline data efficiency across contact tasks Figure 5 compares fixed random offline datasets with PPO's continuing on-policy interactions in simulation. | Authors report task completion using 0.5 million steps; plotted offline datasets extend to at most 1 million. Average step reward versus data transitions | PPO receives additional transitions and eventually catches up or exceeds the method on some tasks; arch traversal remains the clearer advantage in the plotted range. This supports transition efficiency in the tested comparison, not a measured compute-speedup or superiority to off-policy RL. e-efficiency |
| Mixed-task planning and physical deployment Figure 6 simulation comparison; Figure 4 physical Unitree G1 demonstrations with a RealSense D435i camera. | Mixed-task performance improves on wall and arch and drops on ball; hardware demonstrations include arch traversal followed by unseen-box blocking. Normalized simulation performance and qualitative executed behavior | Mixed-task model is compared with specialized models; hardware has no numerical baseline comparison. A single model covers the tested contexts. Human-controlled base velocity and absent hardware success counts limit claims of autonomy and reliability. e-protocole-multitaske-real |
6.3 Ablations and diagnostic examples
Read component removals and qualitative examples within their stated evaluation conditions.
Table I. Four steps performs well across tasks, while the wall column favors other settings. Original paper, p. 6 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Read within each task column because reward scales differ. The upper block changes planning horizon: N=1 is greedy value selection, while larger N averages values along predicted futures. The middle block replaces the world-model training approach with ARWM. The final block changes the objective to predicted rewards or rewards plus a terminal value. For arch traversal, N=4 reports 0.0157 ± 0.0015, compared with −0.0396 ± 0.0121 at N=1. The experimental text identifies mean and standard deviation from ten independent trials across three random seeds; it does not specify how those trials are distributed among seeds. e-protocole-tablee-ablation
What it supports. The ball and arch columns favor multistep planning, and both show poorer means at six steps than four. Wall support is an exception: N=6 slightly exceeds N=4, and TD-MPC reaches 0.0699 ± 0.0035 versus 0.0614 ± 0.0027. The evidence supports a useful cross-task default, not uniform dominance.
Where the evidence stops. These are simulation rewards, not success rates. Standard deviations do not establish statistical significance. The authors' explanations involving overfitting and model bias are not isolated causal measurements, and the tested TD-MPC variant should not stand for every implementation.
Figure 7. A changing contact preference and a long rollout illustrate what the latent model has retained. Original paper, p. 7 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. The upper row maps candidate right-hand positions in the X–Z plane. Yellow indicates higher plotted value, with a shared color bar from zero to one; the figure does not establish physical coordinate units. Around steps 60–70, the preferred region shifts as the ball approaches. The lower row begins with a real depth image, then its reconstruction, then imagined frames decoded from future latents. These frames illustrate a longer rollout than the deployed planning horizon. The caption calls the upper panels Q-value maps, while Section IV.D identifies the quantity as the Equation (11) objective; treat them as a planning-value visualization rather than calibrated returns. e-diagnostice-theorye-mpce-table
What it supports. The visual supports the authors' interpretation that the model changes its preferred hand target with context and retains aspects of the ball's motion in its latent predictions. It also makes reconstruction error visible before any long rollout: the decoded horizon-zero image already differs from the original observation.
Where the evidence stops. The exact map normalization and construction are not specified. Sixteen-step images are a qualitative diagnostic, not evidence of sixteen-step control or measured physical accuracy. The actual controller replans using a four-step horizon.
7. Analysis & limitations
7.1 What the evidence leaves open
All quantitative comparisons are simulated. Physical demonstrations have no reported trial counts or success rates. SAC-like off-policy baselines are explicitly excluded, so the sample-efficiency conclusion is limited to PPO. e-protocole-efficiencye-real
The variance argument is conditional: averaging changes the optimization objective and does not remove bias. Its correlation bound is printed for all i,j despite rho < 1; for nonzero diagonal variance this needs an off-diagonal qualification. Random action increments do not themselves establish weak value-error correlation. e-datae-theory
The 16-step decoded ball rollout and t-SNE task clusters are qualitative diagnostics. They do not measure calibrated dynamics accuracy, prove latent disentanglement, or establish that longer planning improves control. The authors' overfitting and bias explanations for ablations remain interpretations. e-diagnostice-multitaske-ablation
7.2 Questions for discussion
- Does value-error covariance actually fall enough for averaging to explain the horizon ablation?
- How does performance change when a learned planner also chooses base velocity, or when evaluated against an off-policy baseline?
8. Reproducibility audit
8.1 Requirements and known gaps
Reproduction requires the trained tracking controller, simulated object interactions, reward and termination definitions, Monte Carlo targets and CEM implementation. The PDF omits exact reward formulas, train/test partitions, return discount/truncation details, CEM elite counts and iterations, network widths, and training/runtime compute hardware. References name Isaac Sim 5.0.0 and Legged lab 1.0.0, but do not establish a complete runnable environment. e-controllere-datae-traininge-mpce-protocole-software
Proposed checks: hold the learned model fixed while comparing greedy and multistep objectives under controlled observation noise; separately measure actual ball prediction errors alongside reward as planning horizon changes. Report per-seed outcomes and equalize search computation. These tests could distinguish value averaging from search-budget and model-bias effects. e-theorye-tablee-diagnostic
8.2 Proposed reproduction checks
The following checks are proposals motivated by the paper. They have not been run as part of this reading.
Check 1: Does averaging reduce value error under matched search effort?
Reader-proposed simulation check: freeze one trained model and compare horizons one, two, four and six on the same held-out task initializations. Repeat with controlled depth-noise levels. Match the total number of world-model transitions evaluated by CEM, and additionally report the original fixed-trajectory-budget setting. Use independent repeated simulator continuations to estimate returns for candidate state–action pairs, then measure value residual covariance and the error of each averaged score. The variance explanation is weakened if reward gains appear only with extra search computation or if strongly correlated residuals prevent the predicted error reduction. Report per-seed reward and failure rates; none of these checks was run here. e-theorye-mpce-tablee-protocol
Check 2: Does a plausible ball rollout predict useful control?
Reader-proposed simulation check: hold the controller and trained model fixed, and replay identical action sequences from matched ball states while decoding predictions through horizon sixteen. Compare ball location and contact timing against simulator ground truth, separating horizon-zero reconstruction error from later prediction drift. Then compare four-step and longer-horizon MPC under matched search computation on those same initial conditions, recording reward and executed hand contacts. Include held-out ball trajectories and box shapes as explicit separate conditions. If longer rollouts look plausible but contact-time error grows and longer planning worsens control, the result would support the paper's stated distinction between qualitative physical intuition and useful planning horizon. e-diagnostice-ablatione-tablee-reale-data
8.3 Reading coverage
Visual audit: All eight supplied PDF pages were rendered and visually inspected after reading all four text chunks. The title, eight authors, affiliations and v2 date were checked on page 1. Figures 1–7 and Table I were read; six final original crops were individually inspected, including the recropped Figure 7 labels. Pages 2–5 cover method equations and training, pages 5–7 cover simulation protocols and ablations, pages 4 and 7–8 cover physical deployment, and page 8 covers cited software versions. Figure 6 was inspected in its full-page render but is not a separate crop. Diagram arrows and latent conditioning were checked against Eqs. (1)–(5); the current-posterior notation and prose termination gate were checked against Eq. (17) and the Figure 3 caption. Figure 7's caption versus objective-label ambiguity is preserved in its reading guide. No appendix is present in this PDF. Separate supplements, videos and code remain outside the supplied reading.
PDF pages inspected for this edition: 1, 2, 3, 4, 5, 6, 7, 8. Appendix coverage: not present.
Original figures and tables remain the work of the source’s authors. Extractions preserve their scientific content; any HTML wrapper layout is disclosed with each figure. The surrounding reading notes are our own.
Text reading scope & known omissions
- Abstract
- I. Introduction
- II. Related Work, A–C
- III. Methods, A–D
- IV. Experiments, A–E
- V. Conclusion
- Acknowledgment
- References [1]–[38]
Outside the original text pass
- Text extraction does not reconstruct figure images; inspect the retained PDF for figures and equation/table layout.
- Separate supplemental material availability has not been fully verified.
- The supplied artifact is arXiv:2510.11682v2 [cs.RO], dated 8 March 2026. Its exact title and eight authors match the catalog; the catalog submission date is 13 October 2025. The earlier edition was not supplied, so changes between versions are unverified.
- Text extraction does not reconstruct figure images; this gap was addressed by inspecting all eight PDF pages and all seven figures, plus Table I.
- Separate supplemental material availability has not been fully verified; no separate supplement was supplied.
- The linked website, code, dataset and videos were not inspected. No installation or experiment was performed.
The visual audit above records the subsequent illustrated pass.
8.4 Traceable evidence
e-identityPDF p. 1, title, author block, affiliation footnotes and arXiv margin stamp
Exact catalog title and all eight authors appear; the artifact identifies arXiv:2510.11682v2, 8 March 2026. Affiliations are UC Berkeley, University of Michigan Ann Arbor and The Chinese University of Hong Kong.
Go to primary source ↓e-problemPDF pp. 1–2, Abstract, I and II.B–C
Contact planning combines visual partial observability, sparse contacts and sample-efficiency challenges; the proposed system uses offline latent prediction with sampling MPC.
Go to primary source ↓e-controllerPDF p. 2, III.A
The PPO-trained low-level controller tracks velocity, end-effector position and height from angular velocity, projected gravity, commands, joint positions and velocities.
Go to primary source ↓e-dataPDF pp. 2–3, III.B and Figure 2(a)
Simulated ball, wall and arch interactions use 64 × 48 ego-depth and proprioception. Planner actions exclude velocity and follow normalized finite differences a_t = a_(t−1) + eta delta, delta uniform on (−1,1), eta = 0.32.
Go to primary source ↓e-latentPDF p. 2, Figure 2(b); p. 3, III.C, Eqs. (1)–(5)
The recurrent latent supports posterior encoding, Gaussian reconstruction and observation-free prior prediction. Equation (4) conditions termination on h_t,z_t; Equation (5) adds a_t for value prediction. The top encoder–decoder drawing suppresses h_t conditioning given in Eqs. (2)–(3).
Go to primary source ↓e-trainingPDF p. 4, III.C, Eqs. (6)–(9)
CNN image features and MLP components are described. Training combines observation NLL, termination BCE, two posterior-to-prior KL terms with alternating stop-gradients, and Monte Carlo value MSE; detailed return and optimizer settings are absent.
Go to primary source ↓e-mpcPDF p. 3, Figure 3 and caption; p. 5, Eq. (17) and following III.D paragraphs
CEM searches latent action rollouts using mean surrogate value. The current observation supplies the posterior; future states use the prior. Termination probability above 0.9 zeroes subsequent values. Only the first action is executed; default horizon is four.
Go to primary source ↓e-theoryPDF pp. 4–5, III.D, Eqs. (10)–(16) and bounded-correlation assumption
The paper acknowledges different optimal-control objectives and bias. Its variance argument uses bounded residual variance and correlation rho below one, printed for all i,j, with an approximately inverse-horizon limit as rho tends to zero.
Go to primary source ↓e-protocolPDF pp. 5–6, IV opening paragraphs and Task/Baselines definitions
G1 and D435i are named. All quantitative comparisons and ablations are simulated. Statistics are described as mean and standard deviation from ten independent trials across three seeds, without trial allocation; reward definitions and dataset partitions are not enumerated.
Go to primary source ↓e-tablePDF p. 6, Table I, Horizon N, World Model and Objective Function blocks
N=4 wall/ball/arch rewards are 0.0614±0.0027, 0.0061±0.0003 and 0.0157±0.0015. Table I provides N=1–6, ARWM, Rew-MPC and TD-MPC comparisons; TD-MPC leads wall with 0.0699±0.0035.
Go to primary source ↓e-efficiencyPDF p. 5, Figure 5 axes, curves and caption; p. 6, IV.A
Figure 5 plots average step reward versus transition counts for offline data and PPO, with a change of horizontal scale near 1M. The text claims completion with 0.5M steps and excludes SAC-like comparisons; offline curves use at most 1M steps.
Go to primary source ↓e-ablationPDF pp. 6–7, IV.B, read with Table I and IV Baselines
The authors interpret N=1 as myopic, longer planning as biased, autoregressive training as potentially overfitting value, and reward/TD objectives as unreliable. TD-MPC is the specified reward-plus-terminal-value baseline variant.
Go to primary source ↓e-multitaskPDF p. 6, Figure 6(a–c); p. 7, IV.C
A combined-task dataset trains one model. Normalized performance rises on wall and arch and falls on ball relative to specialized models. t-SNE plots show task clusters and temporal evolution; exact normalized values are not tabulated.
Go to primary source ↓e-diagnosticPDF p. 7, Figure 7(a–b), caption and IV.D
Hand-position value maps run from step 30 to 80; the caption places ball appearance at step 60. Decoded open-loop frames extend to horizon 16, while deployed planning uses four. No numerical rollout-error measure is provided.
Go to primary source ↓e-realPDF p. 4, Figure 4(a–d); pp. 7–8, IV.E
Physical G1 planning runs at 25 Hz, evaluating 1,024 trajectories with horizon four. A human commands base velocity. Demonstrations include wall support, arch traversal and blocking an unseen box; hardware trial counts and success rates are absent.
Go to primary source ↓e-softwarePDF p. 8, References [8] and [35], linked from III.A on p. 2
The references name NVIDIA Isaac Sim version 5.0.0 and Legged lab version 1.0.0; these citations alone do not specify the complete implementation environment.
Go to primary source ↓8.5 Primary sources
Ego-Vision World Model for Humanoid Contact Planning ↗
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