Staggered Integral Online Conformal Prediction for Safe Dynamics Adaptation with Multi-Step Coverage Guarantees

Safety-critical control of uncertain, adaptive systems often relies on conservative, worst-case uncertainty bounds that limit closed-loop performance. Online conformal prediction is a powerful data-driven method for quantifying uncertainty when truth values of predicted outputs are revealed online; however, for systems that adapt the dynamics without measurements of the state derivatives, standard online conformal prediction is insufficient to quantify the model uncertainty. We propose Staggered Integral Online Conformal Prediction (SI-OCP), an algorithm utilizing an integral score function to quantify the lumped effect of disturbance and learning error. This approach provides long-run coverage guarantees, resulting in long-run safety when synthesized with safety-critical controllers, including robust tube model predictive control. Finally, we validate the proposed approach through a numerical simulation of an all-layer deep neural network (DNN) adaptive quadcopter using robust tube MPC, highlighting the applicability of our method to complex learning parameterizations and control strategies.

Backup-Based Safety Filters: A Comparative Review of Backup CBF, Model Predictive Shielding, and gatekeeper

This paper revisits three backup-based safety filters -- Backup Control Barrier Functions (Backup CBF), Model Predictive Shielding (MPS), and gatekeeper -- through a unified comparative framework. Using a common safety-filter abstraction and shared notation, we make explicit both their common backup-policy structure and their key algorithmic differences. We compare the three methods through their filter-inactive sets, i.e., the states where the nominal policy is left unchanged. In particular, we show that MPS is a special case of gatekeeper, and we further relate gatekeeper to the interior of the Backup CBF inactive set within the implicit safe set. This unified view also highlights a key source of conservatism in backup-based safety filters: safety is often evaluated through the feasibility of a backup maneuver, rather than through the nominal policy's continued safe execution. The paper is intended as a compact tutorial and review that clarifies the theoretical connections and differences among these methods.

Provably Safe Stein Variational Clarity-Aware Informative Planning

Autonomous robots are increasingly deployed for information-gathering tasks in environments that vary across space and time. Planning informative and safe trajectories in such settings is challenging because information decays when regions are not revisited. Most existing planners model information as static or uniformly decaying, ignoring environments where the decay rate varies spatially; those that model non-uniform decay often overlook how it evolves along the robot's motion, and almost all treat safety as a soft penalty. In this paper, we address these challenges. We model uncertainty in the environment using clarity, a normalized representation of differential entropy from our earlier work that captures how information improves through new measurements and decays over time when regions are not revisited. Building on this, we present Stein Variational Clarity-Aware Informative Planning, a framework that embeds clarity dynamics within trajectory optimization and enforces safety through a low-level filtering mechanism based on our earlier gatekeeper framework for safety verification. The planner performs Bayesian inference-based learning via Stein variational inference, refining a distribution over informative trajectories while filtering each nominal Stein informative trajectory to ensure safety. Hardware experiments and simulations across environments with varying decay rates and obstacles demonstrate consistent safety and reduced information deficits.

Beyond Collision Cones: Dynamic Obstacle Avoidance for Nonholonomic Robots via Dynamic Parabolic Control Barrier Functions

Control Barrier Functions (CBFs) are a powerful tool for ensuring the safety of autonomous systems, yet applying them to nonholonomic robots in cluttered, dynamic environments remains an open challenge. State-of-the-art methods often rely on collision-cone or velocity-obstacle constraints which, by only considering the angle of the relative velocity, are inherently conservative and can render the CBF-based quadratic program infeasible, particularly in dense scenarios. To address this issue, we propose a Dynamic Parabolic Control Barrier Function (DPCBF) that defines the safe set using a parabolic boundary. The parabola's vertex and curvature dynamically adapt based on both the distance to an obstacle and the magnitude of the relative velocity, creating a less restrictive safety constraint. We prove that the proposed DPCBF is valid for a kinematic bicycle model subject to input constraints. Extensive comparative simulations demonstrate that our DPCBF-based controller significantly enhances navigation success rates and QP feasibility compared to baseline methods. Our approach successfully navigates through dense environments with up to 100 dynamic obstacles, scenarios where collision cone-based methods fail due to infeasibility.

Online Safety under Multiple Constraints and Input Bounds using gatekeeper: Theory and Applications

This letter presents an approach to guarantee online safety of a cyber-physical system under multiple state and input constraints. Our proposed framework, called gatekeeper, recursively guarantees the existence of an infinite-horizon trajectory that satisfies all constraints and system dynamics. Such trajectory is constructed using a backup controller, which we define formally in this paper. gatekeeper relies on a small number of verifiable assumptions, and is computationally efficient since it requires optimization over a single scalar variable. We make two primary contributions in this letter. (A) First, we develop the theory of gatekeeper: we derive a sub-optimality bound relative to a full nonlinear trajectory optimization problem, and show how this can be used in runtime to validate performance. This also informs the design of the backup controllers and sets. (B) Second, we demonstrate in detail an application of gatekeeper for multi-agent formation flight, where each Dubins agent must avoid multiple obstacles and weapons engagement zones, both of which are nonlinear, nonconvex constraints.

BR-MPPI: Barrier Rate guided MPPI for Enforcing Multiple Inequality Constraints with Learned Signed Distance Field

Model Predictive Path Integral (MPPI) controller is used to solve unconstrained optimal control problems and Control Barrier Function (CBF) is a tool to impose strict inequality constraints, a.k.a, barrier constraints. In this work, we propose an integration of these two methods that employ CBF-like conditions to guide the control sampling procedure of MPPI. CBFs provide an inequality constraint restricting the rate of change of barrier functions by a classK function of the barrier itself. We instead impose the CBF condition as an equality constraint by choosing a parametric linear classK function and treating this parameter as a state in an augmented system. The time derivative of this parameter acts as an additional control input that is designed by MPPI. A cost function is further designed to reignite Nagumo's theorem at the boundary of the safe set by promoting specific values of classK parameter to enforce safety. Our problem formulation results in an MPPI subject to multiple state and control-dependent equality constraints which are non-trivial to satisfy with randomly sampled control inputs. We therefore also introduce state transformations and control projection operations, inspired by the literature on path planning for manifolds, to resolve the aforementioned issue. We show empirically through simulations and experiments on quadrotor that our proposed algorithm exhibits better sampled efficiency and enhanced capability to operate closer to the safe set boundary over vanilla MPPI.

Adaptive Ergodic Search with Energy-Aware Scheduling for Persistent Multi-Robot Missions

Autonomous robots are increasingly deployed for long-term information-gathering tasks, which pose two key challenges: planning informative trajectories in environments that evolve across space and time, and ensuring persistent operation under energy constraints. This paper presents a unified framework, mEclares, that addresses both challenges through adaptive ergodic search and energy-aware scheduling in multi-robot systems. Our contributions are two-fold: (1) we model real-world variability using stochastic spatiotemporal environments, where the underlying information evolves unpredictably due to process uncertainty. To guide exploration, we construct a target information spatial distribution (TISD) based on clarity, a metric that captures the decay of information in the absence of observations and highlights regions of high uncertainty; and (2) we introduce Robustmesch (Rmesch), an online scheduling method that enables persistent operation by coordinating rechargeable robots sharing a single mobile charging station. Unlike prior work, our approach avoids reliance on preplanned schedules, static or dedicated charging stations, and simplified robot dynamics. Instead, the scheduler supports general nonlinear models, accounts for uncertainty in the estimated position of the charging station, and handles central node failures. The proposed framework is validated through real-world hardware experiments, and feasibility guarantees are provided under specific assumptions.

Constraint Selection in Optimization-Based Controllers

Human-machine collaboration often involves constrained optimization problems for decision-making processes. However, when the machine is a dynamical system with a continuously evolving state, infeasibility due to multiple conflicting constraints can lead to dangerous outcomes. In this work, we propose a heuristic-based method that resolves infeasibility at every time step by selectively disregarding a subset of soft constraints based on the past values of the Lagrange multipliers. Compared to existing approaches, our method requires the solution of a smaller optimization problem to determine feasibility, resulting in significantly faster computation. Through a series of simulations, we demonstrate that our algorithm achieves performance comparable to state-of-the-art methods while offering improved computational efficiency.

Certifiably-Correct Mapping for Safe Navigation Despite Odometry Drift

Accurate perception, state estimation and mapping are essential for safe robotic navigation as planners and controllers rely on these components for safety-critical decisions. However, existing mapping approaches often assume perfect pose estimates, an unrealistic assumption that can lead to incorrect obstacle maps and therefore collisions. This paper introduces a framework for certifiably-correct mapping that ensures that the obstacle map correctly classifies obstacle-free regions despite the odometry drift in vision-based localization systems (VIO}/SLAM). By deflating the safe region based on the incremental odometry error at each timestep, we ensure that the map remains accurate and reliable locally around the robot, even as the overall odometry error with respect to the inertial frame grows unbounded. Our contributions include two approaches to modify popular obstacle mapping paradigms, (I) Safe Flight Corridors, and (II) Signed Distance Fields. We formally prove the correctness of both methods, and describe how they integrate with existing planning and control modules. Simulations using the Replica dataset highlight the efficacy of our methods compared to state-of-the-art techniques. Real-world experiments with a robotic rover show that, while baseline methods result in collisions with previously mapped obstacles, the proposed framework enables the rover to safely stop before potential collisions.

Enabling Safety for Aerial Robots: Planning and Control Architectures

Ensuring safe autonomy is crucial for deploying aerial robots in real-world applications. However, safety is a multifaceted challenge that must be addressed from multiple perspectives, including navigation in dynamic environments, operation under resource constraints, and robustness against adversarial attacks and uncertainties. In this paper, we present the authors' recent work that tackles some of these challenges and highlights key aspects that must be considered to enhance the safety and performance of autonomous aerial systems. All presented approaches are validated through hardware experiments.