Safety-Critical Contextual Control via Online Riemannian Optimization with World Models

Many safety-critical control problems are modeled as risk-sensitive partially observable Markov decision processes, where the controller must make decisions from incomplete observations while balancing task performance against safety risk. Although belief-space planning provides a principled solution, maintaining and planning over beliefs can be computationally costly and sensitive to model specification in practical domains. We propose a lightweight risk-gated reinforcement learning approximation for risk-sensitive control under partial observability. The method constructs a compact finite-history proxy state and learns an action-conditioned predictor of near-term safety violation. This predicted candidate-action risk is used in two complementary ways: as a risk penalty during value learning, and as a decision-time gate that interpolates between optimistic and conservative ensemble value estimates. As a result, low-risk actions are evaluated closer to reward-seeking estimates, while high-risk actions are evaluated more conservatively. We evaluate the approach in two safety-critical partially observable domains: automated glucose regulation and safety-constrained navigation. Across adult and adolescent glucose-control cohorts, the method improves overall glycemic tradeoffs and substantially reduces runtime relative to a belief-space planning baseline. On Safety-Gym navigation benchmarks, it achieves a more favorable reward-cost balance than unconstrained RL and several standard safe-RL baselines. These results suggest that action-conditioned near-term risk can provide an effective local signal for approximate risk-sensitive POMDP control when full belief-space planning is impractical.

Sampling-based model predictive control methods handle nonlinear dynamics and complex cost landscapes through Monte Carlo rollouts, yet typically employ fixed constraint penalties that do not adapt to model-plant mismatch. This paper proposes Residual-Conservative Model Predictive Path Integral Control (RC-MPPI), a sampling-based MPC framework that modulates safety conservatism online using the prediction-execution residual. RC-MPPI combines three coupled mechanisms: residual-dependent constraint tightening, adaptive safety-cost shaping, and residual-adaptive sampling modulation through exploration contraction and temperature relaxation. The temperature adaptation reflects a key insight: when the model is inaccurate, rollout cost evaluations become unreliable, and increasing temperature reduces overcommitment to apparent cost rankings. Under Lipschitz dynamics and sub-Gaussian disturbances, we derive probabilistic bounds on constraint violation and show that the joint effect of the adaptive mechanisms reduces violation probability as the residual grows. A rollout-cost uncertainty analysis further shows that model-plant mismatch perturbs MPPI importance weights in proportion to residual magnitude and inversely with temperature, providing theoretical justification for residual-adaptive temperature relaxation. Simulations on an LTI point-mass system and a planar 2R manipulator show improved safety margin, success rate, and control efficiency compared with vanilla MPPI under significant model-plant mismatch.

Many safety-critical control systems operate under latent uncertainty that sensors cannot resolve at decision time. Such uncertainty, arising from unknown physical properties, disturbances, or unobserved geometry, affects dynamics, task feasibility, and safety margins. Standard methods optimize expected performance and offer limited protection against rare but severe outcomes, while robust formulations treat uncertainty conservatively without exploiting its probabilistic structure. We consider systems with measured state and an unknown, time-invariant parameter represented by a belief distribution. We propose a risk-sensitive belief-space Model Predictive Path Integral (MPPI) controller that plans under this belief, regularizes performance using Conditional Value-at-Risk (CVaR), and imposes a CVaR constraint on a trajectory safety margin over the horizon. For the exact risk-constrained formulation underlying this controller, we establish three properties: (1) the CVaR constraint implies a probabilistic safety guarantee, (2) the controller recovers the risk-neutral optimum as the objective risk weight tends to zero, and (3) a union-bound argument extends the per-horizon guarantee to cumulative safety over repeated solves. In contact-rich MuJoCo simulations of vision-guided dexterous stowing, where a manipulator inserts a grasped object into an occupied slot with pose uncertainty exceeding prescribed lateral clearance requirements, our method achieves 82% success with zero contact violations at high risk aversion, compared with 55% and 50% for a risk-neutral configuration and a chance-constrained baseline, both of which incur nonzero exterior contact forces. Project page: https://clintonenwerem.com/belief-cvar-mppi/.