Risk-Constrained Belief-Space Optimization for Safe Control under Latent Uncertainty

Many safety-critical control systems must operate under latent uncertainty that sensors cannot directly resolve at decision time. Such uncertainty, arising from unknown physical properties, exogenous disturbances, or unobserved environment geometry, influences 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 partially observed dynamical systems whose dynamics, costs, and safety constraints depend on a latent parameter maintained as a belief distribution, and propose a risk-sensitive belief-space Model Predictive Path Integral (MPPI) control framework that plans under this belief while enforcing a Conditional Value-at-Risk (CVaR) constraint on a trajectory safety margin over the receding horizon. The resulting controller optimizes a risk-regularized performance objective while explicitly constraining the tail risk of safety violations induced by latent parameter variability. We establish three properties of the resulting risk-constrained controller: (1) the CVaR constraint implies a probabilistic safety guarantee, (2) the controller recovers the risk-neutral optimum as the risk weight in the objective tends to zero, and (3) a union-bound argument extends the per-horizon guarantee to cumulative safety over repeated solves. In physics-based simulations of a vision-guided dexterous stowing task in which a grasped object must be inserted 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 to 55% and 50% for a risk-neutral configuration and a chance-constrained baseline, both of which incur nonzero exterior contact forces.