Long-Horizon Planning

World Action Models (WAMs) have recently emerged as a promising paradigm for robotic manipulation by jointly predicting future visual observations and future actions. However, current WAMs typically execute a fixed number of predicted actions after each model inference, leaving the robot blind to whether the imagined future remains consistent with the actual physical rollout. In this work, we formulate adaptive WAM execution as a future-reality verification problem: the robot should execute longer when the WAM-predicted future remains reliable, and replan earlier when reality deviates from imagination. To this end, we propose Future Forward Dynamics Causal Attention (FFDC), a lightweight verifier that jointly reasons over predicted future actions, predicted visual dynamics, real observations, and language instructions to estimate whether the remaining action rollout can still be trusted. FFDC enables adaptive action chunk sizes as an emergent consequence of prediction-observation consistency, preserving the efficiency of long-horizon execution while restoring responsiveness in contact-rich or difficult phases. We further introduce Mixture-of-Horizon Training to improve long-horizon trajectory coverage for adaptive execution. Experiments on the RoboTwin benchmark and in the real world demonstrate that our method achieves a strong robustness-efficiency trade-off: on RoboTwin, it reduces WAM forward passes by 69.10% and execution time by 34.02%, while improving success rate by 2.54% over the short-chunk baseline; in real-world experiments, it improves success rate by 35%.

A central challenge of visual control with model-based reinforcement learning (RL) is reliable long-horizon planning: long rollouts with learned latent dynamics exhibit branching futures and multi-modal action-value distributions. In addition, compounding model errors amplified by visual occlusions make deep imagination brittle. We present ELVIS, a latent model predictive controller (MPC) designed to make long-horizon planning practical. ELVIS plans in a Dreamer-style recurrent state space model (RSSM) and replaces standard unimodal model predictive path integral (MPPI) with a Gaussian-mixture MPPI that maintains multiple coherent hypotheses over long horizons, avoiding mode averaging under branching rollouts. In parallel, ELVIS stabilizes deep imagination with a shared uncertainty-aware lambda-return: an ensemble of latent critics defines an upper-confidence-bound (UCB) score that gates a time-varying lambda, adaptively trading off bootstrapping versus look-ahead to limit compounding error during planning. The same return is used both to train an actor-critic prior from imagined rollouts and to score candidate trajectories inside GMM-MPPI, aligning RL objectives with the planner's long-horizon optimization. On fourteen DeepMind Control Suite visual tasks, ELVIS establishes state-of-the-art performance compared with TD-MPC2 and DreamerV3. Finally, ELVIS transfers zero-shot to a real-world sand-spraying task with severe occlusions, improving surface-quality metrics and demonstrating robustness beyond simulation.

Compositional diffusion planning generates long-horizon trajectories by stitching together overlapping short-horizon segments through score composition. However, when local plan distributions are multimodal, existing compositional methods suffer from mode-averaging, where averaging incompatible local modes leads to plans that are neither locally feasible nor globally coherent. We propose Refining Compositional Diffusion (RCD), a training-free guidance method that steers compositional sampling toward high-density, globally coherent plans. RCD leverages the self-reconstruction error of a pretrained diffusion model as a proxy for the log-density of composed plans, combined with an overlap consistency term that enforces consistency at segment boundaries. We show that the combined guidance concentrates sampling on high-density plans that mitigate mode-averaging. Experiments on challenging long-horizon tasks from OGBench, including locomotion, object manipulation, and pixel-based observations, demonstrate that RCD consistently outperforms existing methods.

Frontier software engineering agents have saturated short-horizon benchmarks while regressing on the work that constitutes senior engineering: long-horizon, multi-engineer, ambiguous-specification deliverables. This paper takes a position on what training data is needed to close the gap. The substrate for the next generation of SWE agents is neither larger GitHub scrapes nor more solo-agent trajectories nor -- sufficient by itself -- open human-AI dialogue logs. It is triadic data: synchronized capture of the human-human conversations where engineering context is formed, the human-AI sessions where that context is partially consumed, and the multi-week cross-functional work that surrounds both. We argue that the canonical instantiation of triadic data is two complementary products: long-horizon expert trajectories captured under stimulated-recall protocols, and simulated cross-functional companies -- instrumented teams of senior engineers, product managers, designers, and data scientists working through ambiguous deliverables on shared infrastructure. We further specify a four-tier evidence framework through which any such corpus -- triadic or otherwise -- must justify its quality to a fine-tuning researcher: mechanical verification, statistical corpus characterization, probe experiments, and pre-registered blind evaluation. We argue that this data is capturable in 12-18 months with methods already mature in adjacent fields, that it is the empirical key to four open questions in agent training, and that the field's near-term research agenda should include it explicitly.

Language model (LM)-based agents have demonstrated promising capabilities in automating complex tasks from natural language instructions, yet they continue to struggle with long-horizon planning and reasoning. To address this, we propose an enhanced multi-agent framework that decomposes automation into three roles: a planner for high-level decision-making, an actor for task execution, and a memory manager for contextual reasoning. While this modular decomposition aligns with established design patterns, our core contribution lies in a systematic compute-allocation analysis, revealing that planning is the dominant factor influencing task performance. Execution and memory management require significantly less compute and model capacity to achieve competitive results. Building on these insights, we introduce a planner-centric reinforcement learning approach, which exclusively optimizes the planner using trajectory-level rewards from a VLM-as-judge, while freezing the other components. Extensive experiments on benchmarks spanning web navigation, OS control, and tool use demonstrate that concentrating model capacity and learning on high-level planning yields robust and compute-efficient improvements in long-horizon agent automation. Our code is publicly released.

World models enable long-horizon planning by internally generating and evaluating imagined trajectories, making them a promising foundation for generalist agents. However, this imagination-driven decision process also introduces new security risks. Existing backdoor attacks typically aim to manipulate local features, one-step predictions, or instantaneous policy outputs. While such objectives may suffice for weaker reactive models, they are often ineffective against world models, where the learned dynamics prior and planning process can absorb or wash out the effects of shallow perturbations. More importantly, we find that world models exhibit a distinct backdoor vulnerability rooted in the long-tailed ranking structure of imagined trajectories, where disrupting the ordering of a few decision-critical trajectories can systematically hijack planning. To exploit this vulnerability, we propose TRAP, a backdoor attack framework for world models that targets imagined trajectory ranking. TRAP combines a tail-aware ranking loss to focus optimization on decision-critical trajectories with dual gating mechanisms that stabilize optimization and regulate when and where the attack penalty is applied. Under trigger conditions, TRAP alters the relative ranking of imagined trajectories to redirect planning outcomes, while largely maintaining the normal ranking structure on clean inputs. Experiments on DreamerV3 and TD-MPC2 across diverse tasks show that TRAP consistently induces sustained behavioral deviations and significant performance degradation, highlighting the need for dedicated security evaluation of world-model-based agents.

Vision-Language-Action (VLA) models have emerged as a powerful paradigm for embodied intelligence, enabling robots to perform tasks based on natural language instructions and current visual input. However, existing VLA models struggle with long-horizon tasks due to compounding errors. Prior methods decompose tasks into subtasks of fixed granularity, which cannot adapt to the varying complexity of execution states, limiting their robustness in long-horizon tasks. To overcome this, we introduce Anticipation Model, which adaptively and recursively generates future subgoals. This model continuously adapts as the task unfolds, adjusting future subgoals in response to evolving dynamics, facilitating more reliable planning paths. Building on this concept, we propose Anticipation-VLA, a hierarchical VLA model that leverages the anticipation model to generate actionable subgoals that guide VLA policy execution. We implement Anticipation-VLA with finetuning a Unified Multimodal Model (UMM) for high-level subgoal generation and a goal-conditioned VLA policy for low-level action execution. Experiments in both simulated and real-world robotic tasks demonstrate the effectiveness of Anticipation-VLA, highlighting the importance of adaptive and recursive subgoal generation for robust policy execution.

Foundation model-driven agents often struggle with long-horizon planning due to the transient nature of purely prompting-based reasoning. While existing skill induction methods mitigate this by distilling experience into state-blind parameterized scripts, they fail to capture the conditional logic required for robust execution in dynamic environments. In this paper, we propose Neuro-Symbolic Skill Induction (NSI), a framework that lifts interaction traces into modular, \textit{logic-grounded} programs. By synthesizing explicit control flows and dynamic variable binding, NSI empowers agents to discover \textit{when} and \textit{why} to act. This paradigm enables the efficient generalization, allowing agents to induce skills from few-shot examples and flexibly adapt to unseen goals. Experiments on a series of agentic tasks demonstrate that NSI consistently outperforms state-of-the-art baselines, empowering agents to self-evolve into architects of logic-grounded skills.

Long-horizon robotic manipulation requires plans that are both logically coherent and geometrically grounded. Existing Vision-Language-Action policies usually hide planning in latent states or expose only one modality: text-only chain-of-thought encodes causal order but misses spatial constraints, while visual prediction provides geometric cues but often remains local and semantically underconstrained. We introduce Interleaved Vision--Language Reasoning (IVLR), a policy framework built around \trace{}, an explicit intermediate representation that alternates textual subgoals with visual keyframes over the full task horizon. At test time, a single native multimodal transformer self-generates this global semantic-geometric trace from the initial observation and instruction, caches it, and conditions a closed-loop action decoder on the trace, original instruction, and current observation. Because standard robot datasets lack such traces, we construct pseudo-supervision by temporally segmenting demonstrations and captioning each stage with a vision-language model. Across simulated benchmarks for long-horizon manipulation and visual distribution shift, \method{} reaches 95.5% average success on LIBERO, including 92.4% on LIBERO-Long, and 59.4% overall success on SimplerEnv-WidowX. Ablations show that both modalities are necessary: without traces, LIBERO-Long success drops to 37.7%; text-only and vision-only traces reach 62.0% and 68.4%, while the full interleaved trace reaches 92.4%. Stress tests with execution perturbations and masked trace content show moderate degradation, suggesting that the trace can tolerate local corruption and moderate execution drift, but remains limited under stale or incorrect global plans.

Production agentic systems make many model calls per user request, and most of those calls are short, structured, and routine. This raises a practical routing question that existing evaluations do not directly answer: which parts of an agent workflow truly require large frontier intelligence, and which can be handled by smaller models? We introduce AgentFloor, a deterministic 30-task benchmark organized as a six-tier capability ladder, spanning instruction following, tool use, multi-step coordination, and long-horizon planning under persistent constraints. We evaluate 16 open-weight models, from 0.27B to 32B parameters, alongside GPT-5 across 16,542 scored runs. Our results reveal a clear boundary of model necessity. Small and mid-sized open-weight models are already sufficient for much of the short-horizon, structured tool use work that dominates real agent pipelines, and in aggregate, the strongest open-weight model matches GPT-5 on our benchmark while being substantially cheaper and faster to run. The gap appears most clearly on long-horizon planning tasks that require sustained coordination and reliable constraint tracking over many steps, where frontier models still hold an advantage, though neither side reaches strong reliability. We also find that this boundary is not explained by scale alone: some failures respond to targeted interventions, but the effects are model-specific rather than universal. These findings suggest a practical design principle for agentic systems: use smaller open-weight models for the broad base of routine actions, and reserve large frontier models for the narrower class of tasks that truly demand deeper planning and control. We release the benchmark, harness, sweep configurations, and full run corpus.

The robotic manipulation of Deformable Linear Objects (DLOs) is a fundamental challenge due to the high-dimensional, non-linear dynamics of flexible structures and the complexity of maintaining topological integrity during contact-rich tasks. While recent data-driven methods have utilized Recurrent and Graph Neural Networks for dynamics modeling, they often struggle with self-intersections and non-physical deformations, such as tangling and link stretching. In this paper, we propose a latent dynamics framework that combines a Recurrent State Space Model with a Quaternionic Kinematic Chain representation to enable robust, long-term forecasting of DLO states. By encoding the DLO as a sequence of relative rotations (quaternions) rather than independent Cartesian positions, we inherently constrain the model to a physically valid manifold that preserves link-length constancy. Furthermore, we introduce a dual-decoder architecture that decouples state reconstruction from future-state prediction, forcing the latent space to capture the underlying physics of deformation. We evaluate our approach on a large-scale simulated dataset of complex pick-and-place trajectories involving self-intersections. Our results demonstrate that the proposed model achieves a 40.52% reduction in open-loop prediction error over 50-step horizons compared to the state-of-the-art baseline, while reducing inference time by 31.17%. Our model further maintains superior topological consistency in scenarios with multiple crossings, proving its efficacy as a compositional primitive for long-horizon manipulation planning.

Assisting humans in open-world outdoor environments requires robots to translate high-level natural-language intentions into safe, long-horizon, and socially compliant navigation behavior. Existing map-based methods rely on costly pre-built HD maps, while learning-based policies are mostly limited to indoor and short-horizon settings. To bridge this gap, we propose Walk with Me, a map-free framework for long-horizon social navigation from high-level human instructions. Walk with Me leverages GPS context and lightweight candidate points-of-interest from a public map API for semantic destination grounding and waypoint proposal. A High-Level Vision-Language Model grounds abstract instructions into concrete destinations and plans coarse waypoint sequences. During execution, an observation-aware routing mechanism determines whether the Low-Level Vision-Language-Action policy can handle the current situation or whether explicit safety reasoning from the High-Level VLM is needed. Routine segments are executed by the Low-Level VLA, while complex situations such as crowded crossings trigger high-level reasoning and stop-and-wait behavior when unsafe. By combining semantic intent grounding, map-free long-horizon planning, safety-aware reasoning, and low-level action generation, Walk with Me enables practical outdoor social navigation for human-centric assistance.

Vision-Language-Action (VLA) models promise generalist robot manipulation, but are typically trained and deployed as short-horizon policies that assume the latest observation is sufficient for action reasoning. This assumption breaks in non-Markovian long-horizon tasks, where task-relevant evidence can be occluded or appear only earlier in the trajectory, and where clutter and distractors make fine-grained visual grounding brittle. We present CodeGraphVLP, a hierarchical framework that enables reliable long-horizon manipulation by combining a persistent semantic-graph state with an executable code-based planner and progress-guided visual-language prompting. The semantic-graph maintains task-relevant entities and relations under partial observability. The synthesized planner executes over this semantic-graph to perform efficient progress checks and outputs a subtask instruction together with subtask-relevant objects. We use these outputs to construct clutter-suppressed observations that focus the VLA executor on critical evidence. On real-world non-Markovian tasks, CodeGraphVLP improves task completion over strong VLA baselines and history-enabled variants while substantially lowering planning latency compared to VLM-in-the-loop planning. We also conduct extensive ablation studies to confirm the contributions of each component.

Long-horizon manipulation remains challenging for vision-language-action (VLA) policies: real tasks are multi-step, progress-dependent, and brittle to compounding execution errors. We present LoHo-Manip, a modular framework that scales short-horizon VLA execution to long-horizon instruction following via a dedicated task-management VLM. The manager is decoupled from the executor and is invoked in a receding-horizon manner: given the current observation, it predicts a progress-aware remaining plan that combines (i) a subtask sequence with an explicit done + remaining split as lightweight language memory, and (ii) a visual trace -- a compact 2D keypoint trajectory prompt specifying where to go and what to approach next. The executor VLA is adapted to condition on the rendered trace, thereby turning long-horizon decision-making into repeated local control by following the trace. Crucially, predicting the remaining plan at each step yields an implicit closed loop: failed steps persist in subsequent outputs, and traces update accordingly, enabling automatic continuation and replanning without hand-crafted recovery logic or brittle visual-history buffers. Extensive experiments spanning embodied planning, long-horizon reasoning, trajectory prediction, and end-to-end manipulation in simulation and on a real Franka robot demonstrate strong gains in long-horizon success, robustness, and out-of-distribution generalization. Project page: https://www.liuisabella.com/LoHoManip

Industrial robotic manipulation demands reliable long-horizon execution across embodiments, tasks, and changing object distributions. While Vision-Language-Action models have demonstrated strong generalization, they remain fundamentally reactive. By optimizing the next action given the current observation without evaluating potential futures, they are brittle to the compounding failure modes of long-horizon tasks. Cortex 2.0 shifts from reactive control to plan-and-act by generating candidate future trajectories in visual latent space, scoring them for expected success and efficiency, then committing only to the highest-scoring candidate. We evaluate Cortex 2.0 on a single-arm and dual-arm manipulation platform across four tasks of increasing complexity: pick and place, item and trash sorting, screw sorting, and shoebox unpacking. Cortex 2.0 consistently outperforms state-of-the-art Vision-Language-Action baselines, achieving the best results across all tasks. The system remains reliable in unstructured environments characterized by heavy clutter, frequent occlusions, and contact-rich manipulation, where reactive policies fail. These results demonstrate that world-model-based planning can operate reliably in complex industrial environments.

Vision-Language-Action (VLA) models fail systematically on long-horizon manipulation tasks despite strong short-horizon performance. We show that this failure is not resolved by extending context length alone in the current reactive execution setting; instead, it stems from three recurring execution-loop deficiencies: the memory gap, the verification gap, and the recovery gap. We present HELM, a model-agnostic framework that addresses these deficiencies with three components: an Episodic Memory Module (EMM) that retrieves key task history via CLIP-indexed keyframes, a learned State Verifier (SV) that predicts action failure before execution from observation, action, subgoal, and memory-conditioned context, and a Harness Controller (HC) that performs rollback and replanning. The SV is the core learning contribution: it consistently outperforms rule-based feasibility checks and ensemble uncertainty baselines, and its effectiveness depends critically on access to episodic memory. On LIBERO-LONG, HELM improves task success rate by 23.1 percentage points over OpenVLA (58.4% to 81.5%), while extending the context window to H=32 yields only a 5.4-point gain and same-budget LoRA adaptation remains 12.2 points below HELM. HELM also improves long-horizon performance on CALVIN and substantially boosts recovery success under controlled perturbations. Ablations and mechanism analyses isolate the contribution of each component, and we release LIBERO-Recovery as a perturbation-injection protocol for evaluating failure recovery in long-horizon manipulation.

Vision-Language Navigation(VLN) requires an agent to navigate through 3D environments by following natural language instructions. While recent Video Large Language Models(Video-LLMs) have largely advanced VLN, they remain highly susceptible to State Drift in long scenarios. In these cases, the agent's internal state drifts away from the true task execution state, leading to aimless wandering and failure to execute essential maneuvers in the instruction. We attribute this failure to two distinct cognitive deficits: Progress Drift, where the agent fails to distinguish completed sub-goals from remaining ones, and Memory Drift, where the agent's history representations degrade, making it lose track of visited landmarks. In this paper, we propose a Dual-Anchoring Framework that explicitly anchors the instruction progress and history representations. First, to address progress drift, we introduce Instruction Progress Anchoring, which supervises the agent to generate structured text tokens that delineate completed versus remaining sub-goals. Second, to mitigate memory drift, we propose Memory Landmark Anchoring, which utilizes a Landmark-Centric World Model to retrospectively predict object-centric embeddings extracted by the Segment Anything Model, compelling the agent to explicitly verify past observations and preserve distinct representations of visited landmarks. Facilitating this framework, we curate two extensive datasets: 3.6 million samples with explicit progress descriptions, and 937k grounded landmark data for retrospective verification. Extensive experiments in both simulation and real-world environments demonstrate the superiority of our method, achieving a 15.2% improvement in Success Rate and a remarkable 24.7% gain on long-horizon trajectories. To facilitate further research, we will release our code, data generation pipelines, and the collected datasets.

Robotic manipulation policies often degrade over extended horizons, yet existing benchmarks provide limited insight into why such failures occur. Most prior benchmarks are either simulation-based or report aggregate success, making it difficult to disentangle the distinct sources of temporal difficulty in real-world execution. We introduce LongBench, a real-world benchmark for evaluating long-horizon manipulation. LongBench consists of over 1,000 real-world episodes, covering two complementary regimes: Context-Independent (fully observable) and Context-Dependent (ambiguity-driven). By organizing tasks into capability- and ambiguity-specific subsets, LongBench enables mechanism-aware evaluation of execution robustness, temporal consistency, and context-dependent reasoning. Evaluating six state-of-the-art policies reveals that long-horizon performance is not governed by a single factor. We observe that performance in fully observable settings is more strongly associated with execution robustness, while contextual difficulty varies across tasks and is not consistently improved by memory-based methods. We hope that LongBench serves as a useful benchmark for studying long-horizon manipulation and for developing policies with stronger robustness across both execution and contextual challenges.

Vision-Language-Action (VLA) models have emerged as a promising paradigm for building embodied agents that ground perception and language into action. However, most existing approaches rely on direct action prediction, lacking the ability to reason over long-horizon trajectories and evaluate their consequences, which limits performance in complex decision-making tasks. In this work, we introduce World-Value-Action (WAV) model, a unified framework that enables implicit planning in VLA systems. Rather than performing explicit trajectory optimization, WAV model learn a structured latent representation of future trajectories conditioned on visual observations and language instructions. A learned world model predicts future states, while a trajectory value function evaluates their long-horizon utility. Action generation is then formulated as inference in this latent space, where the model progressively concentrates probability mass on high-value and dynamically feasible trajectories. We provide a theoretical perspective showing that planning directly in action space suffers from an exponential decay in the probability of feasible trajectories as the horizon increases. In contrast, latent-space inference reshapes the search distribution toward feasible regions, enabling efficient long-horizon decision making. Extensive simulations and real-world experiments demonstrate that the WAV model consistently outperforms state-of-the-art methods, achieving significant improvements in task success rate, generalization ability, and robustness, especially in long-horizon and compositional scenarios. Code is available at https://github.com/Win-commit/WAV.

Deep Reinforcement Learning (DRL) is widely recognized as sample-inefficient, a limitation attributable in part to the high dimensionality and substantial functional redundancy inherent to the policy parameter space. A recent framework, which we refer to as Action-based Policy Compression (APC), mitigates this issue by compressing the parameter space $Θ$ into a low-dimensional latent manifold $\mathcal Z$ using a learned generative mapping $g:\mathcal Z \to Θ$. However, its performance is severely constrained by relying on immediate action-matching as a reconstruction loss, a myopic proxy for behavioral similarity that suffers from compounding errors across sequential decisions. To overcome this bottleneck, we introduce Occupancy-based Policy Compression (OPC), which enhances APC by shifting behavior representation from immediate action-matching to long-horizon state-space coverage. Specifically, we propose two principal improvements: (1) we curate the dataset generation with an information-theoretic uniqueness metric that delivers a diverse population of policies; and (2) we propose a fully differentiable compression objective that directly minimizes the divergence between the true and reconstructed mixture occupancy distributions. These modifications force the generative model to organize the latent space around true functional similarity, promoting a latent representation that generalizes over a broad spectrum of behaviors while retaining most of the original parameter space's expressivity. Finally, we empirically validate the advantages of our contributions across multiple continuous control benchmarks.

We introduce Distribution Contractive Reinforcement Learning (DICE-RL), a framework that uses reinforcement learning (RL) as a "distribution contraction" operator to refine pretrained generative robot policies. DICE-RL turns a pretrained behavior prior into a high-performing "pro" policy by amplifying high-success behaviors from online feedback. We pretrain a diffusion- or flow-based policy for broad behavioral coverage, then finetune it with a stable, sample-efficient residual off-policy RL framework that combines selective behavior regularization with value-guided action selection. Extensive experiments and analyses show that DICE-RL reliably improves performance with strong stability and sample efficiency. It enables mastery of complex long-horizon manipulation skills directly from high-dimensional pixel inputs, both in simulation and on a real robot. Project website: https://zhanyisun.github.io/dice.rl.2026/.

Long-horizon indoor mobile manipulation (MoMa) requires robots to execute extended navigation-manipulation sequences whose feasibility depends on state changes induced by preceding skills. Vision-language models (VLMs) can decompose instructions into plausible skill sequences, but they do not reliably track such cumulative embodiment constraints or revise a plan when execution deviates from expectation. We present MoMaStage, a map-light framework for state-consistent planning and closed-loop execution in long-horizon indoor MoMa. MoMaStage couples a frozen VLM with robot execution through three mechanisms: (i) a hierarchical library of grounded, executable skills and a topology-only projection of a Skill-State Graph (SSG) that constrains the VLM's planning space; (ii) an SSG verifier that propagates scene-region and gripper-occupancy state to reject infeasible plans before execution; and (iii) an event-driven monitor that triggers graph-grounded repair only when an observed outcome invalidates the remaining plan. The SSG captures the compact embodiment state needed for skill sequencing without requiring a dense scene map, while geometric and contact-level conditions remain within the underlying controllers. Experiments in physics-rich simulation and on a real mobile manipulator show that MoMaStage improves planning validity and long-horizon execution survival over the evaluated baselines, while reducing latency and model token consumption.

Data-driven surrogate models can significantly accelerate the simulation of continuous dynamical systems, yet the step-wise accumulation of errors during autoregressive time-stepping often leads to spectral blow-up and unphysical divergence. Existing global regularization techniques can enforce contractive dynamics but uniformly damp high-frequency features, causing over-smoothing; meanwhile, long-horizon trajectory optimization methods are severely constrained by memory bottlenecks. This paper proposes Jacobian-Adaptive Weighting for Stability (JAWS), which reformulates operator learning as a Maximum A Posteriori (MAP) estimation problem with spatially heteroscedastic uncertainty, enabling the regularization strength to adapt automatically based on local physical complexity: enforcing contraction in smooth regions to suppress noise while relaxing constraints near singular features such as shocks to preserve gradient information. Experiments demonstrate that JAWS serves as an effective spectral pre-conditioner for trajectory optimization, allowing short-horizon, memory-efficient training to match the accuracy of long-horizon baselines. Validations on the 1D viscous Burgers' equation and 2D flow past a cylinder ($\text{Re}=400$ out-of-distribution generalization) confirm the method's advantages in long-term stability, preservation of physical conservation properties, and computational efficiency. This significant reduction in memory usage makes the method particularly well-suited for stable and efficient long-term simulation of large-scale flow fields in practical engineering applications.

This paper develops LongNav-R1, an end-to-end multi-turn reinforcement learning (RL) framework designed to optimize Visual-Language-Action (VLA) models for long-horizon navigation. Unlike existing single-turn paradigm, LongNav-R1 reformulates the navigation decision process as a continuous multi-turn conversation between the VLA policy and the embodied environment. This multi-turn RL framework offers two distinct advantages: i) it enables the agent to reason about the causal effects of historical interactions and sequential future outcomes; and ii) it allows the model to learn directly from online interactions, fostering diverse trajectory generation and avoiding the behavioral rigidity often imposed by human demonstrations. Furthermore, we introduce Horizon-Adaptive Policy Optimization. This mechanism explicitly accounts for varying horizon lengths during advantage estimation, facilitating accurate temporal credit assignment over extended sequences. Consequently, the agent develops diverse navigation behaviors and resists collapse during long-horizon tasks. Experiments on object navigation benchmarks validate the framework's efficacy: With 4,000 rollout trajectories, LongNav-R1 boosts the Qwen3-VL-2B success rate from 64.3% to 73.0%. These results demonstrate superior sample efficiency and significantly outperform state-of-the-art methods. The model's generalizability and robustness are further validated by its zero-shot performance in long-horizon real-world navigation settings. All source code is open-sourced at https://github.com/UMich-CURLY/LongNav-R1.

Many aerial tasks involving quadrotors demand both instant reactivity and long-horizon planning for obstacle avoidance, energy efficiency, or trajectory tracking. High-fidelity models enable accurate control but are too slow for long horizons. Low-fidelity planners scale but cannot directly control the system, necessitating cascaded architectures. Prevailing hierarchical approaches plan with a simplified model and use a high-fidelity controller for tracking, yet this decomposition is inherently suboptimal. The controller is limited by the coarse plan, and conventional MPC alternatives shorten the horizon to stay real-time feasible. We present UNIQUE, an MPC architecture that replaces this hierarchical stacking with temporal cascading. The planning problem is formulated as the second-tail horizon of a single multi-phase MPC, rather than being solved separately. We align costs across horizons, derive feasibility constraints for the point-mass planning model, and introduce transition constraints that convert high-fidelity states into meaningful low-fidelity states. Parallel point-mass and mixed-integer solvers address nonconvexities while incorporating progressive 3D obstacle smoothing over the planning horizon. In simulations and real flights, under equal computational budgets, UNIQUE improves closed-loop tracking by up to 75% compared with standard MPC and hierarchical baselines. Ablations and Pareto analyses confirm performance gains across variations in horizon, constraint approximations, and smoothing schedules.

Scalable embodied intelligence is constrained by the scarcity of diverse, long-horizon robotic manipulation data. Existing video world models in this domain are limited to synthesizing short clips of simple actions and often rely on manually defined trajectories. To this end, we introduce MIND-V, a cognitive hierarchical world model designed to synthesize physically plausible and logically coherent videos of long-horizon robotic manipulation. Inspired by cognitive science, MIND-V bridges high-level reasoning with pixel-level synthesis through three core components: a Semantic Reasoning Hub (SRH) that leverages a pre-trained vision-language model for task planning; a Behavioral Semantic Bridge (BSB) that translates abstract instructions into domain-invariant representations; and a Motor Video Generator (MVG) for conditional video rendering. MIND-V employs Staged Visual Future Rollouts, a test-time optimization strategy to enhance long-horizon robustness. To enforce adherence to physical laws, we introduce a GRPO reinforcement learning post-training phase guided by a novel Physical Foresight Coherence (PFC) reward. PFC leverages the V-JEPA2 world model as a physics referee to penalize implausible dynamics in the latent feature space. Experiments confirm MIND-V's SOTA performance in long-horizon simulation and its significant value for policy learning, introducing a scalable and fully autonomous framework for embodied data synthesis.

Physics-based human motion control can make a simulated character walk, sit, and manipulate objects with high physical realism. Almost always, though, this happens in short, isolated clips that are re-initialized between interactions. We instead aim for continuous, reset-free long-horizon motion: a physically simulated humanoid that repeatedly walks to a displaced object, lifts it with a balanced whole-body posture, carries it past obstacles, and places it at a goal, over and over within a single uninterrupted take. The hard part is not any individual motion but the transitions between them. Without a reset, each cycle must end in a state that both leaves the object just placed undisturbed and lets the next cycle begin, yet every placement leaves the character off-balance in a non-canonical pose where naive end-to-end reinforcement learning fails. Our key idea is to treat this handoff as a two-sided problem of recoverability: the character must disengage from the object it just placed so the prior success is preserved, and settle into a state from which a balanced continuation exists. Instead of engineering a transition by hand, we learn to shape where each cycle ends so that it lands in this recoverable region. We introduce LHM-Humanoid. One goal-conditioned controller completes a fetch--carry--place cycle and, through a learned release-and-retreat behavior, steers its terminal state into this region; a second controller then takes over from the resulting state distribution. Both are regularized by an adversarial motion prior and distilled into a single goal-conditioned policy that runs the whole sequence as one reset-free rollout. Across 350 cluttered layouts spanning four room types, LHM-Humanoid produces far more successful and stable long-horizon motion than end-to-end RL, hierarchical RL, and prior physics-based human-scene-interaction methods, on both seen and unseen scenes.

Planning long-horizon manipulation motions using a set of predefined skills is a central challenge in robotics; solving it efficiently could enable general-purpose robots to tackle novel tasks by flexibly composing generic skills. Solutions to this problem lie in an infinitely vast space of parameterized skill sequences -- a space where common incremental methods struggle to find sequences that have non-obvious intermediate steps. Some approaches reason over lower-dimensional, symbolic spaces, which are more tractable to explore but may be brittle and are laborious to construct. In this work, we introduce MOSAIC, a skill-centric, multi-directional planning approach that targets these challenges by reasoning about which skills to employ and where they are most likely to succeed, by utilizing physics simulation to estimate skill execution outcomes. Specifically, MOSAIC employs two complementary skill families: Generators, which identify ``islands of competence'' where skills are demonstrably effective, and Connectors, which link these skill-trajectories by solving boundary value problems. By focusing planning efforts on regions of high competence, MOSAIC efficiently discovers physically-grounded solutions. We demonstrate its efficacy on complex long-horizon problems in both simulation and the real world, using a diverse set of skills including generative diffusion models, motion planning algorithms, and manipulation-specific models. Visit skill-mosaic.github.io for demonstrations and examples.