Distributed Model-Based Diffusion For Scalable Multi-Robot Trajectory Optimization

Trajectory optimization for multi-robot systems remains a critical challenge, particularly when navigating highly non-convex, non-linear, and non-differentiable environments. While Model-Based Diffusion (MBD) has recently emerged as a promising sampling-based optimization paradigm for single-robot trajectory generation, extending it to multi-robot systems results in a centralized, high-dimensional inference problem that (i) suffers from poor sample efficiency due to the curse of dimensionality and (ii) requires global access to all robots' dynamics, constraints, and objectives. To address this, we propose Distributed Model-Based Diffusion (DMBD), a distributed server-robot framework that decomposes the reverse diffusion process into local conditional reverse diffusion processes. This decomposition enables each robot to iteratively perform denoising independently within its own control subspace while conditioning on the current trajectory estimates of the other robots that are aggregated and broadcast by the server. Extensive simulations in goal swapping, multi-floor coverage, parking, and rush-hour scenarios demonstrate that DMBD achieves strong scalability, solving many challenging coordination tasks in sub-seconds and significantly outperforming existing baselines.

Stochastic Multi-Objective Kinodynamic Planning Against Adversaries

This paper addresses multi-objective kinodynamic planning in environments with stochastic hybrid adversaries that probabilistically transition to adversarial modes based on the ego state. The goal is to construct the Pareto-front of paths that trade off execution cost and the probability of safety constraint violation (risk). Existing chance-constrained planners evaluate risk over open-loop trajectories, yielding overly conservative solutions that fail to account for ego-agent reactivity. To address this limitation, we shift the planning space to sequences of closed-loop policies, and integrate sample-based risk evaluation directly into tree construction via Monte-Carlo particle rollouts. We first introduce Stochastic Multi-Objective RRT (SMO-RRT), for which we prove probabilistic completeness, followed by Stochastic Multi-Objective Stable Sparse RRT (SMO-SST), which leverages selective pruning to improve numerical performance at the cost of completeness. For both algorithms, we derive a finite-sample bound on the probability of chance constraint violation for systems with non-Gaussian, state-dependent uncertainty, enabling probabilistically safe planning in a broad class of environments applicable to multi-agent systems, social navigation, and autonomous driving.

SEAMLiS: Visibility-Aware Safety for Perception-Limited Multi-Robot Exploration

Autonomous exploration in unknown environments is typically driven by informative frontiers, viewpoints, or trajectories, while local safety controllers avoid obstacles represented in the current map. Under finite sensing range and limited field of view, this separation can be unsafe: an exploration stack may plan optimistically through unobserved space and steer the sensor toward information gain rather than along the direction of motion, causing hidden obstacles to be detected too late for bounded-actuation avoidance. This paper presents SEAMLiS (Safe Exploration for Autonomous Multi-Robot Systems Under Limited Sensing), a modular execution-layer safety framework for decentralized multi-robot exploration. SEAMLiS preserves the upstream exploration stack, including the goal allocator and local planner, and enforces safety at the execution layer through perception-aware attitude and positional filters. A gatekeeper-based attitude filter switches between a visibility-promoting yaw policy and a velocity-tracking backup policy to preserve visibility of the critical known-free/unknown boundary with sufficient braking margin. A Control Barrier Function (CBF)-based positional filter then avoids known obstacles, newly detected obstacles, and other robots. We provide sufficient collision-avoidance conditions and validate the framework in randomized simulation, Isaac Sim, and Crazyflie hardware experiments. Results show collision-free exploration across tested single- and multi-robot settings while retaining much of the efficiency of visibility-promoting yaw control.

Reinforcement Learning for Risk Adaptation via Differentiable CVaR Barrier Functions

Planning through crowded environments under uncertain obstacle motions remains difficult, as stochastic interactions often induce overly conservative behavior or reduced efficiency. To address this challenge, we propose an end-to-end risk adaptation framework for crowd navigation under obstacle-motion uncertainty modeled by a Gaussian mixture model. The framework combines reinforcement learning~(RL) with a differentiable quadratic-program safety layer based on Conditional Value-at-Risk~(CVaR) barrier functions, jointly learning nominal control input, risk level, and safety margin and enforcing explicit probabilistic safety constraints. This design enables context-aware adaptation, promoting efficient behavior while invoking caution only when necessary. We conduct extensive evaluations in dynamic, uncertain, and crowded environments across varying obstacle densities and robot models, and further assess generalization under three out-of-distribution cases. Comparisons across optimization-based, RL-based, and integrated RL and optimization methods are provided, and the proposed method is shown to deliver the strongest overall performance in safety, efficiency, and generalization under uncertainty.

Distributionally Robust Safety Under Arbitrary Uncertainties: A Safety Filtering Approach

In this work, we study how to ensure probabilistic safety for nonlinear systems under distributional ambiguity. Our approach builds on a backup-based safety filtering framework that switches between a high-performance nominal policy and a certified backup policy to ensure safety. To handle arbitrary uncertainties from ambiguous distributions, i.e., where the distribution is not of specific structure and the true distribution is unknown, we adopt a distributionally robust (DR) formulation using Wasserstein ambiguity sets. Rather than solving a high-dimensional DR trajectory optimization problem online, we exploit the structure of backup-based safety filtering to reduce safety certification to a one-dimensional search over the switching time between nominal and backup policies. We then develop a sampling-based certification procedure with finite-sample guarantees, where empirical failure probabilities are compared against a Wasserstein-inflated threshold. We validate our method through simulations across three systems, from a Dubins vehicle to a high-speed racing car and a fighter jet, demonstrating the broad applicability and computational efficiency.

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.