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.

Robust Stochastic Shortest-Path Planning via Risk-Sensitive Incremental Sampling

With the pervasiveness of Stochastic Shortest-Path (SSP) problems in high-risk industries, such as last-mile autonomous delivery and supply chain management, robust planning algorithms are crucial for ensuring successful task completion while mitigating hazardous outcomes. Mainstream chance-constrained incremental sampling techniques for solving SSP problems tend to be overly conservative and typically do not consider the likelihood of undesirable tail events. We propose an alternative risk-aware approach inspired by the asymptotically-optimal Rapidly-Exploring Random Trees (RRT*) planning algorithm, which selects nodes along path segments with minimal Conditional Value-at-Risk (CVaR). Our motivation rests on the step-wise coherence of the CVaR risk measure and the optimal substructure of the SSP problem. Thus, optimizing with respect to the CVaR at each sampling iteration necessarily leads to an optimal path in the limit of the sample size. We validate our approach via numerical path planning experiments in a two-dimensional grid world with obstacles and stochastic path-segment lengths. Our simulation results show that incorporating risk into the tree growth process yields paths with lengths that are significantly less sensitive to variations in the noise parameter, or equivalently, paths that are more robust to environmental uncertainty. Algorithmic analyses reveal similar query time and memory space complexity to the baseline RRT* procedure, with only a marginal increase in processing time. This increase is offset by significantly lower noise sensitivity and reduced planner failure rates.

Safe Collective Control under Noisy Inputs and Competing Constraints via Non-Smooth Barrier Functions

We consider the problem of safely coordinating ensembles of identical autonomous agents to conduct complex missions with conflicting safety requirements and under noisy control inputs. Using non-smooth control barrier functions (CBFs) and stochastic model-predictive control as springboards and by adopting an extrinsic approach where the ensemble is treated as a unified dynamic entity, we devise a method to synthesize safety-aware control inputs for uncertain collectives, drawing upon recent developments in Boolean CBF composition and extensions of CBFs to stochastic systems. Specifically, we approximate the combined CBF by a smooth function and solve a stochastic optimization problem, with agent-level forcing terms restricted to the resulting affine subspace of safe control inputs. For the smoothing step, we employ a polynomial approximation scheme, providing evidence for its advantage in generating more conservative yet sufficiently-filtered control signals than the smoother but more aggressive equivalents realized via an approximation technique based on the log-sum-exp function. To further demonstrate the utility of the proposed method, we present bounds for the expected value of the CBF approximation error, along with results from simulations of a single-integrator collective under velocity perturbations, comparing these results with those obtained using a naive state-feedback controller lacking safety filters.