Constraining Gaussian Process Implicit Surfaces for Robot Manipulation via Dataset Refinement

Robotic manipulation has evolved from rigid, pre-programmed tasks to adaptive, perception-driven approaches. Early methods relied heavily on precise maps or multi-view stereo vision, which are limited in occluded or dynamic environments. Recent advances include neural implicit surfaces, such as DeepSDF and Neural Radiance Fields, but these often require extensive data and multi-view setups. Gaussian Process Implicit Surfaces (GPIS) emerged as a probabilistic alternative, offering continuous surface representations with uncertainty quantification. Despite progress, existing methods struggle with partial observability, high-dimensional deformable objects, and real-time adaptation. Addressing these gaps, recent research focuses on online environment modeling, contact-based sensing, and constraint enforcement, aiming to improve safety and robustness in autonomous manipulation.

The core challenge is to enable robots to accurately model and avoid obstacles in environments where perception is limited and obstacles may be unobserved or dynamic. Traditional static maps or purely visual methods cannot adapt quickly enough, especially with deformable objects like cables or cloth. The problem becomes more complex in high-dimensional spaces, where modeling the environment continuously and enforcing task-specific constraints is computationally demanding. Achieving reliable, real-time obstacle estimation and path planning under these conditions remains an open problem, crucial for advancing autonomous manipulation in unstructured settings.

This work introduces COGIS, a framework that combines Gaussian Process Implicit Surfaces with a constraint-driven dataset refinement process. Key innovations include:

• �� Online contact inference using visual and state data, informed by nominal dynamics predictions.
• �� GPIS fitting that incorporates uncertainty, enabling probabilistic obstacle modeling.
• �� Constraint enforcement via CMA-ES optimization, ensuring the obstacle surface satisfies geometric and task-specific constraints.
• �� Use of GPIS uncertainty to guide exploration, reducing local minima and improving obstacle detection.
• �� Integration with Model Predictive Control (MPC), allowing safe, constraint-aware path planning.

These components collectively enable robust, online environment modeling suitable for complex manipulation tasks.

• �� Generate contact data: Use nominal dynamics and state tracking to predict contact points, combining visual cues to identify potential obstacle regions.
• �� Fit GPIS: Train a Gaussian process on contact points and environmental data, modeling the obstacle as a probabilistic surface with uncertainty estimates.
• �� Dataset refinement: Use CMA-ES to optimize the subset of contact data, enforcing constraints such as no penetration and path feasibility.
• �� Uncertainty-guided exploration: Leverage GPIS variance to explore unobserved regions, avoiding local minima.
• �� Path planning: Employ MPC that incorporates the GPIS model and its uncertainty to generate safe trajectories toward goals.
• �� Data update: After each control step, update contact data and refine the obstacle model, iteratively improving accuracy.
• �� Validation: Test on peg-in-hole and deformable object tasks, comparing success rates, errors, and robustness against baselines.

Experiments involved real robot setups performing peg-in-hole insertion and cable manipulation tasks, with limited visual perception. The models used a Matern kernel for GPIS, with parameters tuned for smoothness and uncertainty estimation. Baselines included static point cloud fitting and pure dynamics models. Success metrics included task completion rate, positional error, and computational time. Multiple trials assessed robustness, with ablation studies removing dataset refinement or uncertainty-guided exploration to evaluate their impact. Results showed that COGIS achieved 100% success in cable tasks, with errors below 0.5mm, outperforming baselines significantly. The experiments validated the method’s ability to identify unobserved obstacles and plan safe paths in real-time.

In cable manipulation, COGIS achieved perfect success (10/10), surpassing baseline success (1/10). The model accurately identified obstacles not seen visually, reducing penetration errors. In peg-in-hole tasks, positional errors averaged 0.5mm, with path planning times reduced by 20%. Dataset refinement effectively eliminated collision penetrations, and uncertainty-guided exploration improved obstacle detection in cluttered environments. The approach demonstrated single-episode task completion, indicating high efficiency and robustness. These results confirm the effectiveness of the probabilistic, constraint-driven environment modeling in complex manipulation scenarios.

COGIS can be applied to industrial automation involving high-dimensional deformable objects, autonomous navigation in cluttered environments, and assistive robotics where environment perception is limited. Its ability to online model obstacles from sparse data makes it suitable for real-world deployment in unstructured or dynamic settings. The framework can also serve as a foundation for multi-modal perception integration, enabling more resilient autonomous systems. Future applications include adaptive manufacturing, service robots in homes, and exploration robots in unknown terrains.

The current framework assumes static environments; dynamic obstacle handling requires further development. Computational complexity of Gaussian process inference and CMA-ES limits real-time scalability in high-dimensional scenarios. Sensitivity to perception noise can cause inaccuracies, especially in highly cluttered or noisy environments. Extending to dynamic, multi-agent, or highly deformable environments remains a challenge. Future work should focus on improving computational efficiency, robustness to perception errors, and dynamic environment adaptation.