Natural Functional Gradients for Smooth Trajectory Optimization

2026-05-27

AI Summary

This work addresses the challenge of robotic trajectory planning in cluttered, narrow environments, where feasible regions are severely constrained and fragmented. The authors propose a function-space-based, geometry-aware trajectory optimization framework that introduces natural functional gradients to this domain for the first time. By employing a Gaussian-smoothed surrogate objective, the method enables discretization-free smoothness control over trajectories. It eliminates the need for analytical gradients, decouples time parameterization, and effectively handles non-differentiable operations—such as collision checking—through Monte Carlo estimation combined with black-box evaluations. Experimental results demonstrate that the approach substantially outperforms existing baselines in complex geometric scenarios, achieving significant improvements in both trajectory feasibility and smoothness.

Abstract

Generating collision-free and smooth motions remains a central challenge in robotic manipulation, particularly in cluttered environments and narrow passages where feasible regions are highly constrained and fragmented. We propose a trajectory optimization framework that performs geometry-aware updates directly in function space using natural functional gradients. The method optimizes a Gaussian-smoothed surrogate objective that regularizes the optimization landscape through smooth trajectory perturbations while preserving trajectory-level structure. Because the updates are defined intrinsically in function space, trajectory regularity can be controlled independently of a particular time discretization. We derive a practical Monte-Carlo estimator of the natural functional gradient that requires only black-box trajectory evaluations, making the method applicable when analytic gradients are unavailable or unreliable due to collision checking and contact-rich simulation. Experiments on constrained robotic manipulation tasks demonstrate that the proposed method improves trajectory feasibility and produces smoother motions than representative planning and trajectory optimization baselines in environments with narrow geometric clearances. Additional results, videos, and implementation details are available at the project page: https://kisangpark.github.io/natural-functional-gradient/

Problem

• trajectory optimization
• collision-free motion
• smooth trajectories
• cluttered environments
• narrow passages

Innovation

• natural functional gradients
• trajectory optimization
• function space
• Gaussian-smoothed surrogate
• collision-free motion planning