Stochastic Neural Signed Swept Volume for Real-time Chance-Constrained Trajectory Optimization

Autonomous flight in cluttered environments requires a robot to build a geometric map of its surroundings and plan safe, dynamically feasible trajectories, all onboard and in real time. Conventional approaches treat mapping and planning as separate stages and often rely on binary occupancy for collision checking. We argue that these two stages should be co-designed around a single representation: a signed distance function (SDF). By encoding distance to the nearest obstacle, an SDF provides richer information for planning and trajectory optimization than occupancy alone. We develop an Octree REsidual Network (OREN) that pairs an explicit octree prior with an implicit neural residual to reconstruct SDFs online from point cloud observations with the efficiency of volumetric methods and the accuracy and differentiability of neural methods. In tandem, we develop Bubble$^\star$, a search-based planner that exploits the distance information to grow maximal collision-free balls, which we call bubbles, with formal guarantees of termination, completeness, and failure detection. Planning over a graph of bubbles significantly reduces collision checks compared to a grid-based A$^\star$ search and returns a bubble sequence that forms a safe corridor for trajectory optimization. We demonstrate the integrated OREN-Bubble$^\star$ approach onboard a quadrotor, navigating unseen indoor environments in real time under tight compute constraints. OREN improves SDF estimation by $22$% compared to baselines, while Bubble$^\star$ finds trajectories spanning $\approx 90$ m through a cluttered environment in $1$-$3$ sec., whereas baselines take up to $10$ sec. in the same environment.

Uncertainties arising from localization error, trajectory prediction errors of the moving obstacles and environmental disturbances pose significant challenges to robot's safe navigation. Existing uncertainty-aware planners often approximate polygon-shaped robots and obstacles using simple geometric primitives such as circles or ellipses. Though computationally convenient, these approximations substantially shrink the feasible space, leading to overly conservative trajectories and even planning failure in narrow environments. In addition, many such methods rely on specific assumptions about noise distributions, which may not hold in practice and thus limit their performance guarantees. To address these limitations, we extend the Optimization-Based Collision Avoidance (OBCA) framework to an uncertainty-aware formulation, termed U-OBCA. The proposed method explicitly accounts for the collision risk between polygon-shaped robots and obstacles by formulating OBCA-based chance constraints, and hence avoiding geometric simplifications and reducing unnecessary conservatism. These probabilistic constraints are further tightened into deterministic nonlinear constraints under mild distributional assumptions, which can be solved efficiently by standard numerical optimization solvers. The proposed approach is validated through theoretical analysis, numerical simulations and real-world experiments. The results demonstrate that U-OBCA significantly mitigates the conservatism in trajectory planning and achieves higher navigation efficiency compared to existing baseline methods, particularly in narrow and cluttered environments.

High-dimensional manipulator operation in unstructured environments requires a differentiable, scene-agnostic distance query mechanism to guide safe motion generation. Existing geometric collision checkers are typically non-differentiable, while workspace-based implicit distance models are hindered by the highly nonlinear workspace--configuration mapping and often suffer from poor convergence; moreover, self-collision and environment collision are commonly handled as separate constraints. We propose Configuration-Space Signed Distance Field-Net (CSSDF-Net), which learns a continuous signed distance field directly in configuration space to provide joint-space distance and gradient queries under a unified geometric notion of safety. To enable zero-shot generalization without environment-specific retraining, we introduce a spatial-hashing-based data generation pipeline that encodes robot-centric geometric priors and supports efficient retrieval of risk configurations for arbitrary obstacle point sets. The learned distance field is integrated into safety-constrained trajectory optimization and receding-horizon MPC, enabling both offline planning and online reactive avoidance. Experiments on a planar arm and a 7-DoF manipulator demonstrate stable gradients, effective collision avoidance in static and dynamic scenes, and practical inference latency for large-scale point-cloud queries, supporting deployment in previously unseen environments.