Robots That See the Future: Predictive Kinematics for Precise Manipulation

Author: Denis Avetisyan

A new framework empowers robots to anticipate object motion and plan more accurate, long-horizon actions in complex 3D environments.

GeoPredict employs a learnable framework wherein a large language model transformer predicts multi-timestep 3D keypoint trajectories and future workspace geometry-using future track queries and a voxel decoder, respectively-to provide training-time supervision, ultimately enabling the robot to allocate geometric capacity to relevant interaction regions via track-guided refinement without incurring computational overhead during inference.

GeoPredict leverages 3D Gaussian Splatting and predictive modeling of kinematic priors to significantly enhance Vision-Language-Action robotic manipulation.

While Vision-Language-Action (VLA) models demonstrate promise in robotic manipulation, their reactive nature and reliance on 2D information limit performance in tasks demanding precise 3D reasoning and long-horizon planning. This work introduces ‘GeoPredict: Leveraging Predictive Kinematics and 3D Gaussian Geometry for Precise VLA Manipulation’, a novel framework that augments VLAs with predictive kinematic and geometric priors via 3D Gaussian Splatting. GeoPredict achieves improved manipulation accuracy by forecasting future arm trajectories and workspace geometry, providing valuable training-time supervision without increasing inference complexity. Could this approach unlock more robust and reliable robotic systems capable of tackling increasingly complex real-world scenarios?

The Geometric Imperative: Addressing Embodied Reasoning Deficiencies

Contemporary Vision-Language-Action (VLA) models, despite advancements in processing visual information and natural language, frequently falter when confronted with intricate robotic manipulation tasks. This stems from a fundamental limitation in their geometric understanding – the ability to accurately perceive and reason about spatial relationships, object shapes, and physical properties. While these models can identify objects and interpret commands, they often lack the capacity to internalize the 3D structure of a scene or predict how objects will interact based on their geometry. Consequently, actions may be poorly planned, leading to collisions, instability, or an inability to successfully grasp and manipulate objects in a reliable manner. This deficiency highlights the need for VLA models to move beyond superficial visual recognition and develop a more robust and nuanced understanding of the geometric world, enabling them to perform complex manipulation with greater precision and adaptability.

A significant obstacle for current robotic systems lies in their limited capacity to foresee the consequences of actions and anticipate environmental changes. Without the ability to accurately predict future states – such as how objects will move or how lighting will shift – robots struggle to formulate plans that are not only reactive but proactive and resilient. This predictive shortfall forces reliance on trial-and-error, leading to inefficient performance and frequent failures, particularly in complex or dynamic settings. Consequently, action planning becomes brittle; a slight deviation from expected conditions can derail the entire sequence. Developing models capable of robust state prediction is therefore crucial for enabling robots to navigate uncertainty and execute intricate manipulation tasks with greater reliability and efficiency, moving beyond simple stimulus-response behaviors toward genuine, intelligent interaction with the physical world.

The difficulties faced by current vision-language-action models are dramatically amplified when robots operate within dynamic environments. Unlike static scenarios, these settings introduce constant change – moving objects, shifting light, and unpredictable events – demanding a capacity for accurate predictive modeling. Successful interaction hinges not merely on reacting to the present, but on anticipating future states to proactively adjust actions and prevent failures. A robot attempting to grasp an object amidst moving obstacles, for example, requires a robust prediction of both the object’s and the obstacles’ trajectories; without this foresight, even a simple task can become impossible. Consequently, the ability to reliably forecast environmental changes is not simply a desirable feature, but a fundamental requirement for achieving truly robust and adaptable robotic systems capable of navigating the complexities of the real world.

This evaluation suite assesses the model's ability to generalize to new spatial arrangements, geometric shapes, and distracting elements through repeated trials of the same task. — This evaluation suite assesses the model’s ability to generalize to new spatial arrangements, geometric shapes, and distracting elements through repeated trials of the same task.

GeoPredict: A Foundation in Predictive Geometry

GeoPredict utilizes Predictive 3D Gaussian Geometry to estimate the future positions and orientations of objects within a robot’s workspace. This is achieved by representing the environment as a collection of 3D Gaussians, where each Gaussian encapsulates a probability distribution over a local region of space. The framework then predicts how these Gaussians will evolve over time, effectively forecasting the future state of the workspace. This predictive capability provides crucial contextual information for robot action selection, allowing the system to anticipate consequences and choose actions that are more likely to succeed in dynamic environments. The use of Gaussian representations allows for efficient computation and representation of uncertainty in the predicted future states, contributing to the robustness of the system.

The Track Encoder within GeoPredict utilizes a recurrent neural network to compress a sequence of robot states, represented as a history of poses and velocities, into a fixed-length latent vector. This compression is achieved by processing sequential observations through a series of gated recurrent units (GRUs), allowing the encoder to retain relevant information about the robot’s past trajectory while discarding redundant data. The resulting latent vector serves as a concise and efficient state representation, significantly reducing the computational cost associated with predicting future states and enabling real-time performance. The encoder is trained to reconstruct the input trajectory from the latent vector, ensuring the preservation of critical motion data during the compression process.

GeoPredict integrates predicted geometric states as input to a transformer network, facilitating the generation of robot actions within a continuous action space. The transformer architecture processes both the historical robot state, encoded by the Track Encoder, and the forecasted geometric future, allowing it to condition action selection on anticipated environmental changes. This approach contrasts with methods relying solely on historical data, and enables more robust performance in dynamic environments by anticipating future states and generating actions accordingly. The continuous action space output allows for fine-grained control of the robot’s movements, offering a greater degree of precision than discrete action selection methods.

Qualitative comparisons across multiple timesteps demonstrate improved rendering of fine-grained geometric details (highlighted in red) over time.

Gaussian Dynamics: Refinement Through Differentiable Representation

GeoPredict leverages 3D Gaussian Splatting, a technique representing scenes as a collection of 3D Gaussians, to construct a differentiable workspace representation. Each Gaussian is defined by its 3D position, covariance matrix, opacity, and color, allowing for continuous and efficient rendering. This differentiable representation is crucial because it enables gradient-based optimization for prediction tasks; the system can adjust Gaussian parameters to minimize prediction error. Unlike discrete voxel-based methods, Gaussian Splatting offers a view-dependent rendering quality comparable to Neural Radiance Fields (NeRF) but with significantly improved rendering speed – typically exceeding 30 FPS on a single GPU – and reduced memory footprint. The continuous nature of the representation also allows for finer-grained reasoning about the environment and facilitates accurate extrapolation of future states.

Track-Guided Refinement enhances prediction accuracy by adaptively increasing the density of 3D Gaussians along anticipated keypoint trajectories. This is achieved by weighting Gaussian contributions based on their proximity to the predicted future locations of tracked points. Specifically, the framework increases the scale and opacity of Gaussians falling within a defined radius of the predicted trajectory, effectively concentrating representation in areas likely to be occupied by the tracked object in future frames. This localized refinement process reduces uncertainty and improves the fidelity of the predicted scene representation, as compared to a uniform Gaussian distribution.

The GeoPredict framework utilizes a Voxel Decoder to convert 3D spatial queries – defined by voxel grid coordinates – into 3D Gaussian primitives. This process involves mapping each queried voxel to a Gaussian representation characterized by its mean, covariance, and opacity. The resulting Gaussian distribution represents the probability of occupancy within that voxel’s corresponding spatial region. By discretizing the environment into voxels and representing each with a Gaussian, the system achieves a geometrically informed understanding of the scene, allowing for efficient reasoning about spatial relationships and potential future states. The density and parameters of these Gaussians are then refined during the prediction process to improve accuracy.

Empirical Validation: A Paradigm Shift in Robotic Performance

Rigorous evaluation on the RoboCasa and LIBERO benchmarks reveals GeoPredict’s superior performance compared to existing vision-language architectures. Across these challenging robotic manipulation and instruction-following tasks, GeoPredict consistently surpasses the capabilities of baseline models including SpatialVLA, UniVLA, BC-Transformer, GWM, and OpenVLA. This outperformance isn’t merely incremental; GeoPredict establishes a new standard for spatial reasoning and task completion in embodied AI, indicating a robust framework capable of handling complex, real-world scenarios with greater efficiency and accuracy than its predecessors.

Evaluations on the RoboCasa benchmark reveal GeoPredict’s substantial capabilities in robotic manipulation and planning; the framework achieved a 52.4% success rate in completing tasks within this complex, realistic environment. This result signifies a marked improvement over existing state-of-the-art methods, specifically demonstrating a 10.1% increase in performance compared to the π0 baseline. The RoboCasa benchmark, designed to mimic the challenges of household robotics, demands adaptability and robustness – qualities GeoPredict demonstrably possesses through this significant gain in successful task completion, highlighting its potential for real-world application in dynamic, unstructured settings.

Evaluations conducted on the LIBERO benchmark reveal GeoPredict’s substantial capabilities in robotic manipulation and spatial reasoning. The framework achieved an average success rate of 96.5% across a diverse set of tasks, demonstrably exceeding the performance of UniVLA, a leading baseline model. This result highlights GeoPredict’s ability to reliably execute complex actions and navigate challenging environments with a high degree of accuracy. The significant margin of improvement suggests that the integration of predictive geometry provides a crucial advantage in handling the intricacies of real-world robotic applications, pushing the boundaries of what is achievable with vision-language models.

Evaluations within realistic spatial environments reveal GeoPredict’s robust performance, achieving an 85.0% success rate in generalization trials. This represents a significant leap forward when contrasted with the π0 baseline, which attained a success rate 25.0% lower. This heightened capability suggests GeoPredict not only completes tasks reliably but also effectively adapts to previously unseen spatial arrangements and challenges. The framework’s ability to navigate and interact with novel environments demonstrates a core strength in applying learned knowledge to real-world scenarios, exceeding the performance of comparative models and paving the way for more adaptable robotic systems.

GeoPredict demonstrates a remarkable capacity for real-world geometric generalization, achieving a 95.0% success rate in practical applications. This performance represents a substantial 45.0% improvement over the π0 baseline, highlighting the framework’s ability to accurately predict and adapt to previously unseen geometric configurations. The success suggests GeoPredict isn’t merely memorizing training data, but rather internalizing fundamental geometric principles, enabling robust performance even when confronted with novel spatial arrangements and environments. This level of generalization is crucial for deploying robotic systems in dynamic, unpredictable real-world settings, paving the way for more adaptable and reliable autonomous operation.

GeoPredict demonstrates an enhanced ability to navigate and interact with previously unseen environments due to its core integration of predictive geometry. This framework doesn’t simply react to observed data; it actively predicts plausible spatial configurations, allowing it to anticipate future states and plan accordingly. By leveraging these predictive priors, GeoPredict can effectively extrapolate from limited experience, exhibiting robust performance in dynamic environments where conditions are constantly changing. This proactive approach significantly improves generalization capabilities, enabling the system to adapt quickly to novel scenarios and maintain reliable performance even when faced with unexpected obstacles or configurations – a crucial advantage over systems reliant on exhaustive training datasets and reactive strategies.

GeoPredict distinguishes itself through a capacity for efficient learning, stemming from its core reliance on predictive priors rather than exhaustive datasets. This innovative approach allows the framework to anticipate likely spatial configurations and relationships, effectively reducing the need for vast amounts of training data typically required by large language models. By incorporating these pre-existing understandings of geometry and physics, GeoPredict can rapidly adapt to new environments and tasks with minimal fine-tuning, demonstrating a significant advantage in scenarios where data acquisition is costly or time-consuming. Consequently, the framework exhibits enhanced adaptability and improved performance, particularly in dynamic settings where real-time responsiveness is crucial, offering a pathway towards more versatile and resource-conscious robotic systems.

Towards Autonomous Systems: Projecting the Future of Embodied Intelligence

Current research endeavors are directed toward extending the capabilities of GeoPredict to navigate and operate within increasingly intricate and dynamic environments. This involves not only accommodating greater geometric complexity, but also fusing predictive geometric modeling with sophisticated planning and reasoning algorithms. The intention is to move beyond simple prediction, enabling robots to anticipate future states and proactively formulate action plans that account for potential uncertainties. Such integration promises a system where robots can not merely react to their surroundings, but intelligently anticipate and adapt to changing conditions, ultimately achieving a higher level of autonomy and task completion in real-world scenarios. Future iterations will explore hierarchical prediction schemes and reinforcement learning techniques to optimize action selection based on predicted outcomes, paving the way for more robust and intelligent robotic systems.

Researchers are actively investigating novel approaches to geometric representation and prediction, seeking to bolster the performance and resilience of robotic systems. Current methodologies often rely on Euclidean space for modeling environments, but alternative representations-such as those leveraging topological or non-Euclidean geometries-may prove more effective in complex or uncertain settings. Furthermore, the integration of advanced prediction techniques, including probabilistic methods and learned models of physical interactions, holds the potential to anticipate changes in the environment and enable robots to proactively adapt their actions. These explorations aren’t limited to refining existing algorithms; investigations into entirely new predictive frameworks, potentially inspired by principles of computational geometry and machine learning, could yield substantial gains in a robot’s ability to navigate and manipulate its surroundings with increased accuracy and dependability.

The pursuit of truly adaptable robotics centers on enabling machines to not simply react to their surroundings, but to anticipate and proactively engage with them. This vision demands a synthesis of predictive capabilities and intelligent action planning; robots must move beyond passively sensing data to actively forecasting future states based on geometric understanding of the environment. By leveraging predictive geometry, a robot can simulate potential outcomes of its actions, allowing it to select the optimal path toward a goal even in dynamic or uncertain conditions. This integrated approach promises robots capable of navigating complex scenarios – from assisting in disaster relief to performing intricate surgical procedures – with a level of autonomy and finesse previously unattainable, ultimately leading to seamless and intuitive human-robot collaboration.

The pursuit of robust robotic manipulation, as demonstrated by GeoPredict, necessitates a commitment to foundational principles. The framework’s integration of predictive kinematics and 3D Gaussian Splatting isn’t merely about achieving results; it’s about building a system grounded in geometric reasoning and long-horizon planning. This echoes Andrew Ng’s sentiment: “Machine learning is about building systems that can learn from data.” GeoPredict embodies this by leveraging data to predict future states, ultimately enhancing the robot’s ability to interact with the physical world with increased precision and reliability. The elegance lies in the system’s provable capacity for predicting outcomes based on geometric priors, rather than relying on brittle, test-dependent heuristics.

What Remains Invariant?

The presented work, while demonstrating a pragmatic improvement in robotic manipulation, ultimately skirts the fundamental question. Let N approach infinity – what remains invariant? The reliance on learned priors, even those elegantly represented via 3D Gaussian Splatting, introduces a fragility. The system excels within the distribution of observed data, but its extrapolation capabilities remain largely untested. A truly robust system must move beyond correlation and embrace causal understanding of the physical world.

Future efforts should not focus solely on increasing the fidelity of the predictive model, but on constructing a formal representation of kinematic constraints and geometric relationships. The current approach treats these as learned parameters; a more principled solution would encode them as axioms, ensuring invariance under arbitrary perturbations. Consider, for instance, the challenge of compositional generalization – can this framework seamlessly adapt to novel arrangements of known objects, or is it destined to repeat the errors of pattern recognition?

The pursuit of ‘general’ intelligence in robotics demands a departure from purely empirical methods. The elegance of a solution is not measured by its performance on a benchmark, but by the mathematical certainty of its correctness. The true test lies not in manipulating objects now, but in predicting their behavior across an unbounded horizon of possibility.

Original article: https://arxiv.org/pdf/2512.16811.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/