Ensuring safety in real-world robotic systems is often challenging due to unmodeled disturbances and noisy sensors. To account for such stochastic uncertainties, many robotic systems leverage probabilistic state estimators such as Kalman filters to obtain a robot's belief, i.e. a probability distribution over possible states. We propose belief control barrier functions (BCBFs) to enable risk-aware control, leveraging all information provided by state estimators. This allows robots to stay in predefined safety regions with desired confidence under these stochastic uncertainties. BCBFs are general and can be applied to a variety of robots that use extended Kalman filters as state estimator. We demonstrate BCBFs on a quadrotor that is exposed to external disturbances and varying sensing conditions. Our results show improved safety compared to traditional state-based approaches while allowing control frequencies of up to 1 kHz.

This paper addresses the problem of safety-critical control of autonomous robots, considering the ubiquitous uncertainties arising from unmodeled dynamics and noisy sensors. To take into account these uncertainties, probabilistic state estimators are often deployed to obtain a belief over possible states. Namely, Particle Filters (PFs) can handle arbitrary non-Gaussian distributions in the robot's state. In this work, we define the belief state and belief dynamics for continuous-discrete PFs and construct safe sets in the underlying belief space. We design a controller that provably keeps the robot's belief state within this safe set. As a result, we ensure that the risk of the unknown robot's state violating a safety specification, such as avoiding a dangerous area, is bounded. We provide an open-source implementation as a ROS2 package and evaluate the solution in simulations and hardware experiments involving high-dimensional belief spaces.

Partially Observable Markov Decision Processes(POMDPs) provide a principled framework for robot decisionmaking under uncertainty. Solving reach-avoid POMDPs, however, requires coordinating three distinct behaviors: goal reaching, safety, and active information gathering to reduce uncertainty. Existing online POMDP solvers attempt to address all three within a single belief tree search, but this unified approach struggles with the conflicting time scales inherent to these objectives. We propose a layered, certificate-based control architecture that operates directly in belief space, decoupling goal reaching, information gathering, and safety into modular components. We introduce Belief Control Lyapunov Functions(BCLFs) that formalize information gathering as a Lyapunov convergence problem in belief space, and show how they can be learned via reinforcement learning. For safety, we develop Belief Control Barrier Functions (BCBFs) that leverage conformal prediction to provide probabilistic safety guarantees over finite horizons. The resulting control synthesis reduces to lightweight quadratic programs solvable in real time, even for non-Gaussian belief representations with dimension > 104. Experiments in simulation and on a space-robotics platform1 demonstrate real-time performance and improved safety and task success compared to state-of-the-art constrained POMDP solvers.

Robots deployed in dynamic environments must remain safe even when key physical parameters are uncertain or change over time. We propose Parameter-Robust Model Predictive Path Integral (PRMPPI) control, a framework that integrates online parameter learning with probabilistic safety constraints. PRMPPI maintains a particle-based belief over parameters via Stein Variational Gradient Descent, evaluates safety constraints using Conformal Prediction, and optimizes both a nominal performance-driven and a safety-focused backup trajectory in parallel. This yields a controller that is cautious at first, improves performance as parameters are learned, and ensures safety throughout. Simulation and hardware experiments demonstrate higher success rates, lower tracking error, and more accurate parameter estimates than baselines.

Useful robot control algorithms should not only achieve performance objectives but also adhere to hard safety constraints. Control Barrier Functions (CBFs) have been developed to provably ensure system safety through forward invariance. However, they often unnecessarily sacrifice performance for safety since they are purely reactive. Receding horizon control (RHC), on the other hand, consider planned trajectories to account for the future evolution of a system. This work provides a new perspective on safety-critical control by introducing Forward Invariance in Trajectory Spaces (FITS). We lift the problem of safe RHC into the trajectory space and describe the evolution of planned trajectories as a controlled dynamical system. Safety constraints defined over states can be converted into sets in the trajectory space which we render forward invariant via a CBF framework. We derive an efficient quadratic program (QP) to synthesize trajectories that provably satisfy safety constraints. Our experiments support that FITS improves the adherence to safety specifications without sacrificing performance over alternative CBF and NMPC methods.

Control invariant sets play an important role in safety-critical control and find broad application in numerous fields such as obstacle avoidance for mobile robots. However, finding valid control invariant sets of dynamical systems under input limitations is notoriously difficult. We present an approach to safely expand an initial set while always guaranteeing that the set is control invariant. Specifically, we define an expansion law for the boundary of a set and check for control invariance using Linear Programs (LPs). To verify control invariance on a continuous domain, we leverage recently proposed Lipschitz constants of LPs to transform the problem of continuous verification into a finite number of LPs. Using concepts from differentiable optimization, we derive the safe expansion law of the control invariant set and show how it can be interpreted as a second invariance problem in the space of possible boundaries. Finally, we show how the obtained set can be used to obtain a minimally invasive safety filter in a Control Barrier Function (CBF) framework. Our work is supported by theoretical results as well as numerical examples.