CMR: Contractive Mapping Embeddings for Robust Humanoid Locomotion on Unstructured Terrains

Robust disturbance rejection remains a longstanding challenge in humanoid locomotion, particularly on unstructured terrains where sensing is unreliable and model mismatch is pronounced. While perception information, such as height map, enhances terrain awareness, sensor noise and sim-to-real gaps can destabilize policies in practice. In this work, we provide theoretical analysis that bounds the return gap under observation noise, when the induced latent dynamics are contractive. Furthermore, we present Contractive Mapping for Robustness (CMR) framework that maps high-dimensional, disturbance-prone observations into a latent space, where local perturbations are attenuated over time. Specifically, this approach couples contrastive representation learning with Lipschitz regularization to preserve task-relevant geometry while explicitly controlling sensitivity. Notably, the formulation can be incorporated into modern deep reinforcement learning pipelines as an auxiliary loss term with minimal additional technical effort required. Further, our extensive humanoid experiments show that CMR potently outperforms other locomotion algorithms under increased noise.

CRL-VLA: Continual Vision-Language-Action Learning

Lifelong learning is critical for embodied agents in open-world environments, where reinforcement learning fine-tuning has emerged as an important paradigm to enable Vision-Language-Action (VLA) models to master dexterous manipulation through environmental interaction. Thus, Continual Reinforcement Learning (CRL) is a promising pathway for deploying VLA models in lifelong robotic scenarios, yet balancing stability (retaining old skills) and plasticity (learning new ones) remains a formidable challenge for existing methods. We introduce CRL-VLA, a framework for continual post-training of VLA models with rigorous theoretical bounds. We derive a unified performance bound linking the stability-plasticity trade-off to goal-conditioned advantage magnitude, scaled by policy divergence. CRL-VLA resolves this dilemma via asymmetric regulation: constraining advantage magnitudes on prior tasks while enabling controlled growth on new tasks. This is realized through a simple but effective dual-critic architecture with novel Goal-Conditioned Value Formulation (GCVF), where a frozen critic anchors semantic consistency and a trainable estimator drives adaptation. Experiments on the LIBERO benchmark demonstrate that CRL-VLA effectively harmonizes these conflicting objectives, outperforming baselines in both anti-forgetting and forward adaptation.

Embodied Robot Manipulation in the Era of Foundation Models: Planning and Learning Perspectives

Recent advances in vision, language, and multimodal learning have substantially accelerated progress in robotic foundation models, with robot manipulation remaining a central and challenging problem. This survey examines robot manipulation from an algorithmic perspective and organizes recent learning-based approaches within a unified abstraction of high-level planning and low-level control. At the high level, we extend the classical notion of task planning to include reasoning over language, code, motion, affordances, and 3D representations, emphasizing their role in structured and long-horizon decision making. At the low level, we propose a training-paradigm-oriented taxonomy for learning-based control, organizing existing methods along input modeling, latent representation learning, and policy learning. Finally, we identify open challenges and prospective research directions related to scalability, data efficiency, multimodal physical interaction, and safety. Together, these analyses aim to clarify the design space of modern foundation models for robotic manipulation.

HiF-VLA: Hindsight, Insight and Foresight through Motion Representation for Vision-Language-Action Models

Vision-Language-Action (VLA) models have recently enabled robotic manipulation by grounding visual and linguistic cues into actions. However, most VLAs assume the Markov property, relying only on the current observation and thus suffering from temporal myopia that degrades long-horizon coherence. In this work, we view motion as a more compact and informative representation of temporal context and world dynamics, capturing inter-state changes while filtering static pixel-level noise. Building on this idea, we propose HiF-VLA (Hindsight, Insight, and Foresight for VLAs), a unified framework that leverages motion for bidirectional temporal reasoning. HiF-VLA encodes past dynamics through hindsight priors, anticipates future motion via foresight reasoning, and integrates both through a hindsight-modulated joint expert to enable a ''think-while-acting'' paradigm for long-horizon manipulation. As a result, HiF-VLA surpasses strong baselines on LIBERO-Long and CALVIN ABC-D benchmarks, while incurring negligible additional inference latency. Furthermore, HiF-VLA achieves substantial improvements in real-world long-horizon manipulation tasks, demonstrating its broad effectiveness in practical robotic settings.

Executable Analytic Concepts as the Missing Link Between VLM Insight and Precise Manipulation

Enabling robots to perform precise and generalized manipulation in unstructured environments remains a fundamental challenge in embodied AI. While Vision-Language Models (VLMs) have demonstrated remarkable capabilities in semantic reasoning and task planning, a significant gap persists between their high-level understanding and the precise physical execution required for real-world manipulation. To bridge this "semantic-to-physical" gap, we introduce GRACE, a novel framework that grounds VLM-based reasoning through executable analytic concepts (EAC)-mathematically defined blueprints that encode object affordances, geometric constraints, and semantics of manipulation. Our approach integrates a structured policy scaffolding pipeline that turn natural language instructions and visual information into an instantiated EAC, from which we derive grasp poses, force directions and plan physically feasible motion trajectory for robot execution. GRACE thus provides a unified and interpretable interface between high-level instruction understanding and low-level robot control, effectively enabling precise and generalizable manipulation through semantic-physical grounding. Extensive experiments demonstrate that GRACE achieves strong zero-shot generalization across a variety of articulated objects in both simulated and real-world environments, without requiring task-specific training.

Integrating Trajectory Optimization and Reinforcement Learning for Quadrupedal Jumping with Terrain-Adaptive Landing

Jumping constitutes an essential component of quadruped robots' locomotion capabilities, which includes dynamic take-off and adaptive landing. Existing quadrupedal jumping studies mainly focused on the stance and flight phase by assuming a flat landing ground, which is impractical in many real world cases. This work proposes a safe landing framework that achieves adaptive landing on rough terrains by combining Trajectory Optimization (TO) and Reinforcement Learning (RL) together. The RL agent learns to track the reference motion generated by TO in the environments with rough terrains. To enable the learning of compliant landing skills on challenging terrains, a reward relaxation strategy is synthesized to encourage exploration during landing recovery period. Extensive experiments validate the accurate tracking and safe landing skills benefiting from our proposed method in various scenarios.

Robust Online Residual Refinement via Koopman-Guided Dynamics Modeling

Imitation learning (IL) enables efficient skill acquisition from demonstrations but often struggles with long-horizon tasks and high-precision control due to compounding errors. Residual policy learning offers a promising, model-agnostic solution by refining a base policy through closed-loop corrections. However, existing approaches primarily focus on local corrections to the base policy, lacking a global understanding of state evolution, which limits robustness and generalization to unseen scenarios. To address this, we propose incorporating global dynamics modeling to guide residual policy updates. Specifically, we leverage Koopman operator theory to impose linear time-invariant structure in a learned latent space, enabling reliable state transitions and improved extrapolation for long-horizon prediction and unseen environments. We introduce KORR (Koopman-guided Online Residual Refinement), a simple yet effective framework that conditions residual corrections on Koopman-predicted latent states, enabling globally informed and stable action refinement. We evaluate KORR on long-horizon, fine-grained robotic furniture assembly tasks under various perturbations. Results demonstrate consistent gains in performance, robustness, and generalization over strong baselines. Our findings further highlight the potential of Koopman-based modeling to bridge modern learning methods with classical control theory.

VLA-Adapter: An Effective Paradigm for Tiny-Scale Vision-Language-Action Model

Vision-Language-Action (VLA) models typically bridge the gap between perceptual and action spaces by pre-training a large-scale Vision-Language Model (VLM) on robotic data. While this approach greatly enhances performance, it also incurs significant training costs. In this paper, we investigate how to effectively bridge vision-language (VL) representations to action (A). We introduce VLA-Adapter, a novel paradigm designed to reduce the reliance of VLA models on large-scale VLMs and extensive pre-training. To this end, we first systematically analyze the effectiveness of various VL conditions and present key findings on which conditions are essential for bridging perception and action spaces. Based on these insights, we propose a lightweight Policy module with Bridge Attention, which autonomously injects the optimal condition into the action space. In this way, our method achieves high performance using only a 0.5B-parameter backbone, without any robotic data pre-training. Extensive experiments on both simulated and real-world robotic benchmarks demonstrate that VLA-Adapter not only achieves state-of-the-art level performance, but also offers the fast inference speed reported to date. Furthermore, thanks to the proposed advanced bridging paradigm, VLA-Adapter enables the training of a powerful VLA model in just 8 hours on a single consumer-grade GPU, greatly lowering the barrier to deploying the VLA model. Project page: https://vla-adapter.github.io/.

Balancing Signal and Variance: Adaptive Offline RL Post-Training for VLA Flow Models

Vision-Language-Action (VLA) models based on flow matching have shown excellent performance in general-purpose robotic manipulation tasks. However, the action accuracy of these models on complex downstream tasks is unsatisfactory. One important reason is that these models rely solely on the post-training paradigm of imitation learning, which makes it difficult to have a deeper understanding of the distribution properties of data quality, which is exactly what Reinforcement Learning (RL) excels at. In this paper, we theoretically propose an offline RL post-training objective for VLA flow models and induce an efficient and feasible offline RL fine-tuning algorithm -- Adaptive Reinforced Flow Matching (ARFM). By introducing an adaptively adjusted scaling factor in the VLA flow model loss, we construct a principled bias-variance trade-off objective function to optimally control the impact of RL signal on flow loss. ARFM adaptively balances RL advantage preservation and flow loss gradient variance control, resulting in a more stable and efficient fine-tuning process. Extensive simulation and real-world experimental results show that ARFM exhibits excellent generalization, robustness, few-shot learning, and continuous learning performance.

Long-VLA: Unleashing Long-Horizon Capability of Vision Language Action Model for Robot Manipulation

Vision-Language-Action (VLA) models have become a cornerstone in robotic policy learning, leveraging large-scale multimodal data for robust and scalable control. However, existing VLA frameworks primarily address short-horizon tasks, and their effectiveness on long-horizon, multi-step robotic manipulation remains limited due to challenges in skill chaining and subtask dependencies. In this work, we introduce Long-VLA, the first end-to-end VLA model specifically designed for long-horizon robotic tasks. Our approach features a novel phase-aware input masking strategy that adaptively segments each subtask into moving and interaction phases, enabling the model to focus on phase-relevant sensory cues and enhancing subtask compatibility. This unified strategy preserves the scalability and data efficiency of VLA training, and our architecture-agnostic module can be seamlessly integrated into existing VLA models. We further propose the L-CALVIN benchmark to systematically evaluate long-horizon manipulation. Extensive experiments on both simulated and real-world tasks demonstrate that Long-VLA significantly outperforms prior state-of-the-art methods, establishing a new baseline for long-horizon robotic control.