Differentiable Optimization Layered Safety-Critical Control for Risk-Aware Navigation via Conformal Prediction

Planning through crowded environments under uncertain obstacle motions remains difficult, as stochastic interactions often induce overly conservative behavior or reduced efficiency. To address this challenge, we propose an end-to-end risk adaptation framework for crowd navigation under obstacle-motion uncertainty modeled by a Gaussian mixture model. The framework combines reinforcement learning~(RL) with a differentiable quadratic-program safety layer based on Conditional Value-at-Risk~(CVaR) barrier functions, jointly learning nominal control input, risk level, and safety margin and enforcing explicit probabilistic safety constraints. This design enables context-aware adaptation, promoting efficient behavior while invoking caution only when necessary. We conduct extensive evaluations in dynamic, uncertain, and crowded environments across varying obstacle densities and robot models, and further assess generalization under three out-of-distribution cases. Comparisons across optimization-based, RL-based, and integrated RL and optimization methods are provided, and the proposed method is shown to deliver the strongest overall performance in safety, efficiency, and generalization under uncertainty.

Safe navigation in dynamic and uncertain environments often relies on accurate estimation of, or assumptions about, the true underlying uncertainty. However, accurately characterizing the true uncertainty distribution is often difficult due to limited data or imperfect information. An incorrect understanding of the uncertainty and its associated risk may lead to dangerous decisions even under high levels of risk aversion. To address this issue, we propose a risk-aware model predictive control (RA-MPC) framework that incorporates prediction sets to guarantee risk control below a user-specified threshold without requiring assumptions about the underlying uncertainty distribution. To generate the prediction sets, we develop a distribution-free risk quantification framework that extends conformal risk control (CRC) to general spectral risk measures. We then show that incorporating the prediction sets into the MPC framework provides statistical safety guarantees in terms of spectral risk constraint satisfaction even under uncertainty misspecification. We validate the proposed framework in simulated vehicle obstacle avoidance scenarios, demonstrating improved safety and reduced solve time compared to a baseline RA-MPC framework.

Safe and efficient robot navigation in crowds requires anticipating pedestrian motion despite uncertain and potentially shifting prediction errors. Existing reactive methods can produce oscillatory behavior, while predictive planners often treat forecasts as exact or rely on restrictive error models. Incorporating conservative uncertainty sets as hard constraints can also render model predictive control (MPC) infeasible. We propose \textit{CoCoNav}, a crowd-navigation framework that combines online conformal calibration with runtime-certified planning. A horizon-specific conformal proportional--integral controller adapts trajectory-error bounds to regulate long-run empirical coverage, enabling the framework to respond to changing prediction errors. A \textit{relax-then-verify} planner preserves solver feasibility by generating nominal trajectories with soft-constrained MPC and separately certifying them, together with contingency maneuvers, against the calibrated bounds before execution. Simulations and quadruped experiments show that CoCoNav achieves a favorable balance among collision avoidance, task success, and navigation efficiency relative to the evaluated baselines.