Natural Functional Gradients for Smooth Trajectory Optimization

Generating collision-free and smoothly executable motions is a persistent challenge in robotic manipulation, espe- cially in cluttered workspaces and narrow passages where the feasible set is highly nonconvex and fragmented.

We propose a trajectory optimization method that performs geometry-aware updates directly in function space via natural functional gra- dients. Our approach optimizes a Gaussian-smoothed surrogate objective that regularizes the landscape through trajectory per- turbations while preserving trajectory-level structure. Because updates are defined intrinsically in function space, trajectory regularity is controlled independently of the time grid, avoiding discretization-tuned smoothness penalties. We derive a practical Monte-Carlo estimator of the natural functional gradient that requires only black-box cost evaluations, making the method applicable when analytic gradients are unavailable or unreliable due to collision checking and contact-rich simulation. Across manipulation benchmarks with dense clutter and narrow clear- ances, the proposed optimizer achieves higher success rates and produces trajectories with lower acceleration and jerk than representative state-of-the-art baselines.