arXiv subjects

Samuel Coogan

Publications and source records attributed to Samuel Coogan.

At least 19 recordsLinked to original sources

arXiv2026

Online, Reachability-Aware, Sampling-Based Motion Planning

Sampling-Based Model-Predictive Control (MPC) algorithms are a flexible class of controllers used for navigation on a wide range of robotic systems. Historically, such approaches have lacked hard safety guarantees, a shortcoming which we remedy in this work by computing guaranteed reachable-set overapproximations online with a fast, interval-based pipeline. We show that our method achieves similar performance to a state-of-the-art reachability-based planner without the need for the expensive pre-computation step, and can be scaled to systems that are infeasible using existing approaches. Finally, we demonstrate that our technique reduces safety violations by over 99% in a racing simulation and successfully controls a model racecar on real hardware experiments without crashes.

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arXiv2026

Safe, Real-Time Active Model Discrimination and Fault Diagnosis for Nonlinear Systems via Differentiable Reachability

We present a safe, real-time algorithm for active fault diagnosis and model discrimination for uncertain continuous-time nonlinear systems with process and measurement disturbances. Given a finite set of candidate models representing nominal and faulty modes, including actuator and sensor faults, we formulate an output-feedback, time-varying policy optimization problem that (i) robustly enforces state-input safety constraints over a finite horizon and (ii) drives the system to produce sampled measurements consistent with at most one model, enabling deterministic diagnosis. To solve this problem in real time, we develop a tractable approximation using interval over-approximations of reachable state and output sets, and encode diagnosability via a differentiable objective that penalizes overlap between the reachable output sets of possible models. The resulting optimization is solved efficiently online with gradient-based methods using JAX and differentiable reachability primitives. We evaluate our method on sensor and actuator fault diagnosis (up to 11 fault modes) in several high-dimensional nonlinear robotic systems, including a simulated quadrotor and fighter-jet model, a hardware differential-drive robot, and quadrupedal navigation. Across these case studies, our approach achieves reliable model discrimination in under 50 ms, outperforming baselines in discrimination success rate and speed while providing formal safety guarantees.

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arXiv2026

Merging model-based control with multi-agent reinforcement learning for multi-agent cooperative teaming strategies

In this work, we propose a framework that combines multi-agent reinforcement learning (MARL) with model-based control to achieve safe, dynamically feasible actions in cooperative multi-agent tasks. Multi-agent reinforcement learning provides the advantage of learning cooperative policies for multi-agent teams from discrete non-differentiable rewards in a long planning horizon. Model-predictive control is robust and offers safe, dynamically feasible actions in a fast replanning framework for short horizons. We propose an algorithm that extends actor-critic model predictive control for MARL which we refer to as multi-agent actor-critic model predictive control (MA-AC-MPC). We demonstrate the capabilities of this algorithm by applying it to a multi-agent pursuit-evasion scenario. Specifically, we compare the evader team's strategy using the MA-AC-MPC model and a multi-layer perceptron model (MA-AC-MLP). The pursuer team uses augmented proportional navigation as it is accepted as an advanced adversarial control law. We also provide an example with a heterogeneous environment where a drone and omni-wheeled rover cooperate to achieve repeatable and successful landing with 100% success rate in hardware for MA-AC-MPC compared to 60% for MA-AC-MLP. We demonstrate the robustness of the proposed MA-AC-MPC algorithm in hardware for both environments.

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arXiv2026

Make Your VLA More Robust Without More Data By Interleaving Motion Planning

Vision-Language-Action (VLA) models have shown remarkable progress for mobile manipulation, but their performance on long-horizon tasks remains poor. These tasks are especially challenging because (1) progress toward high-level goals must be maintained across extended sequences of spatially distributed subtasks, and (2) early execution errors compound rapidly over the task horizon. These challenges persist despite finetuning on large human teleoperated mobile manipulation data, indicating that more data alone may not resolve the problem. To address these challenges, we propose MPVI: Motion Planner / VLA Interleaving, a framework that integrates model-based motion planning with VLAs to improve robustness without further training. The proposed integration enables localization and navigation to distant or occluded target objects through cluttered scenes using open-vocabulary object detection, frontier exploration and motion planning. However, such integration is non-trivial, requiring reliable switching between modules; we show one way forward via VLM-based completion checking with proprioceptive triggers. We evaluate our approach on the BEHAVIOR-1K benchmark and demonstrate 113% improvement in task progress over a top end-to-end VLA baseline. Additional details are available at the project page: https://mpvi.netlify.app/.

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arXiv2026

Over-Approximating Minimizer Sets of Constrained Convex Programs with Parametric Uncertainty via Reachability Analysis

We study the set of solutions to a parameterized, strongly convex optimization problem whose cost depends on uncertain, bounded parameters. We compute a certified outer approximation of the corresponding set of optimizers, using convergence properties of the projected gradient descent (PGD) algorithm for convex programs. Concretely, by treating the cost parameter as constant but unknown, we interpret the PGD iterates as an uncertain dynamical system and analyze its forward reachable sets. Since PGD converges exponentially to the unique optimizer for each fixed parameter, these reachable sets provide outer approximations of the optimizer set, with an explicit error bound that decays exponentially with the iteration count. We apply system-level synthesis (SLS) on the PGD dynamics to optimize the step-size sequence and obtain reachable-set over-approximations. Our method outperforms existing baselines in over-approximating, with low conservativeness, the minimizer sets of convex programs with uncertain costs and high-dimensional decision variables.

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arXiv2026

Output Feedback Backup Control Barrier Functions: Safety Guarantees Under Input Bounds and State Estimation Error

Guaranteeing the safety of controllers is vital for real-world applications, but is markedly difficult when the states are not perfectly known and when the control inputs are bounded. Backup control barrier functions (bCBFs) use predictions of the flow under a prescribed controller to achieve safety in the presence of bounded inputs and perfect state information. However, when only an estimate of the true state is known, this flow may not be precisely computed, as the initial condition is unknown. Furthermore, the true flow evolves using feedback from the estimated state, thus introducing coupling between known and unknown flows. To address these challenges, we propose a technique that leverages an uncertainty envelope centered around the estimated flow and show that ensuring the safety of this envelope guarantees that the true state satisfies the safety constraints. Additionally, we show that in the presence of state uncertainty, using the resulting Output Feedback Backup Control Barrier Functions (O-bCBFs), there always exists a feasible control input that can guarantee the safety of the true state, even in the presence of input constraints.

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arXiv2026

Differentiable Invariant Sets for Hybrid Limit Cycles with Application to Legged Robots

For hybrid systems exhibiting periodic behavior, analyzing the invariant set containing the limit cycle is a natural way to study the robustness of the closed-loop system. However, computing these sets can be computationally expensive, especially when applied to contact-rich cyber-physical systems such as legged robots. In this work, we extend existing methods for overapproximating reachable sets of continuous systems using parametric embeddings to compute a forward-invariant set around the nominal trajectory of a simplified model of a bipedal robot. Our three-step approach (i) computes an overapproximating reachable set around the nominal continuous flow, (ii) catalogs intersections with the guard surface, and (iii) passes these intersections through the reset map. If the overapproximated reachable set after one step is a strict subset of the initial set, we formally verify a forward invariant set for this hybrid periodic orbit. We verify this condition on the bipedal walker model numerically using immrax, a JAX-based library for parametric reachable set computation, and use it within a bi-level optimization framework to design a tracking controller that maximizes the size of the invariant set.

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arXiv2026

Learning Certified Neural Network Controllers Using Contraction and Interval Analysis

We present a novel framework that jointly trains a neural network controller and a neural Riemannian metric with rigorous closed-loop contraction guarantees using formal bound propagation. Directly bounding the symmetric Riemannian contraction linear matrix inequality causes unnecessary overconservativeness due to poor dependency management. Instead, we analyze an asymmetric matrix function $G$, where $2^n$ GPU-parallelized corner checks of its interval hull verify that an entire interval subset $X$ is a contraction region in a single shot. This eliminates the sample complexity problems encountered with previous Lipschitz-based guarantees. Additionally, for control-affine systems under a Killing field assumption, our method produces an explicit tracking controller capable of exponentially stabilizing any dynamically feasible trajectory using just two forward inferences of the learned policy. Using JAX and \immrax{} for linear bound propagation, we apply this approach to a full 10-state quadrotor model. In $<$10 minutes of post-JIT training, we simultaneously learn a control policy $\pi$, a neural contraction metric $\Theta$, and a verified 10-dimensional contraction region $X$.

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arXiv2026

RTD-RAX: Fast, Safe Trajectory Planning for Systems under Unknown Disturbances

Reachability-based Trajectory Design (RTD) is a provably safe, real-time trajectory planning framework that combines offline reachable-set computation with online trajectory optimization. However, standard RTD implementations suffer from two key limitations: conservatism induced by worst-case reachable-set overapproximations, and an inability to account for real-time disturbances during execution. This paper presents RTD-RAX, a runtime-assurance extension of RTD that utilizes a non-conservative RTD formulation to rapidly generate goal-directed candidate trajectories, and utilizes mixed monotone reachability for fast, disturbance-aware online safety certification. When proposed trajectories fail safety certification under real-time uncertainty, a repair procedure finds nearby safe trajectories that preserve progress toward the goal while guaranteeing safety under real-time disturbances.

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arXiv2025

Adaptive Obstacle-Aware Task Assignment and Planning for Heterogeneous Robot Teaming

Multi-Agent Task Assignment and Planning (MATP) has attracted growing attention but remains challenging in terms of scalability, spatial reasoning, and adaptability in obstacle-rich environments. To address these challenges, we propose OATH - Adaptive Obstacle-Aware Task Assignment and Planning for Heterogeneous Robot Teaming - which advances MATP by introducing a novel obstacle-aware strategy for task assignment. First, we develop an adaptive Halton sequence map, the first known application of Halton sampling with obstacle-aware adaptation in MATP, which adjusts sampling density based on obstacle distribution. Second, we propose a cluster-auction-selection framework that integrates obstacle-aware clustering with weighted auctions and intra-cluster task selection. These mechanisms jointly enable effective coordination among heterogeneous robots while maintaining scalability and suboptimal allocation performance. In addition, our framework leverages an LLM to interpret human instructions and directly guide the planner in real time. We validate OATH in both NVIDIA Isaac Sim and real-world hardware experiments using TurtleBot platforms, demonstrating substantial improvements in task assignment quality, scalability, adaptability to dynamic changes, and overall execution performance compared to state-of-the-art MATP baselines. A project website is available at https://llm-oath.github.io/.

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arXiv2025

Efficient Norm-Based Reachable Sets via Iterative Dynamic Programming

In this work, we present a numerical optimal control framework for reachable set computation using \emph{normotopes}, a new set representation as a norm ball with a shaping matrix. In reachable set computations, we expect to continuously vary the shape matrix as a function of time. Incorporating the shape dynamics as an input, we build a \emph{controlled embedding system} using a linear differential inclusion overapproximating the dynamics of the system, where a single forward simulation of this embedding system always provides an overapproximating reachable set of the system, no matter the choice of \emph{hypercontrol}. By iteratively solving a linear quadratic approximation of the nonlinear optimal hypercontrol problem, we synthesize less conservative final reachable sets, providing a natural tradeoff between runtime and accuracy. Terminating our algorithm at any point always returns a valid reachable set overapproximation.

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arXiv2025

Ask, Reason, Assist: Robot Collaboration via Natural Language and Temporal Logic

Increased robot deployment, such as in warehousing, has revealed a need for collaboration among heterogeneous robot teams to resolve unforeseen conflicts. To this end, we propose a peer-to-peer coordination protocol that enables robots to request and provide help without a central task allocator. The process begins when a robot detects a conflict and uses a Large Language Model (LLM) to decide whether external assistance is required. If so, it crafts and broadcasts a natural language (NL) help request. Potential helper robots reason over the request and respond with offers of assistance, including information about the effect on their ongoing tasks. Helper reasoning is implemented via an LLM grounded in Signal Temporal Logic (STL) using a Backus-Naur Form (BNF) grammar, ensuring syntactically valid NL-to-STL translations, which are then solved as a Mixed Integer Linear Program (MILP). Finally, the requester robot selects a helper by reasoning over the expected increase in system-level total task completion time. We evaluated our framework through experiments comparing different helper-selection strategies and found that considering multiple offers allows the requester to minimize added makespan. Our approach significantly outperforms heuristics such as selecting the nearest available candidate helper robot, and achieves performance comparable to a centralized "Oracle" baseline but without heavy information demands.

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arXiv2025

linrax: A JAX Compatible, Simplex Method Linear Program Solver

We present linrax, the first simplex based linear program (LP) solver compatible with the JAX ecosystem. In many control algorithms, LPs are often automatically generated and frequently solved either offline or online in the control loop. This motivates the design of linrax, which is especially suited for compilation into a complex JAX-based pipeline as a subroutine. We discuss the challenges associated with implementing a general purpose LP solver under strict design requirements from JAX. Notably, we can solve general problems which may include dependent constraints-something not possible with existing JAX-compatible LP solvers that use first-order techniques and may fail to converge. We demonstrate the utility of linrax through several examples, including a robust control synthesis pipeline for a nonlinear vehicle model using automatic differentiation through a LP-based reachable set framework.

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arXiv2025

Automatic and Scalable Safety Verification using Interval Reachability with Subspace Sampling

Interval refinement is a technique for reducing the conservatism of traditional interval based reachability methods by lifting the system to a higher dimension using new auxiliary variables and exploiting the introduced structure through a refinement procedure. We present a novel, efficiently scaling, automatic refinement strategy based on a subspace sampling argument and motivated by reducing the number of interval operations through sparsity. Unlike previous methods, we guarantee that refined bounds shrink as additional auxiliary variables are added. This additionally encourages automation of the lifting phase by allowing larger groups of auxiliary variables to be considered. We implement our strategy in JAX, a high-performance computational toolkit for Python and demonstrate its efficacy on several examples, including regulating a multi-agent platoon to the origin while avoiding an obstacle.

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arXiv2025

Lightweight Tracking Control for Computationally Constrained Aerial Systems with the Newton-Raphson Method

We investigate the performance of a lightweight tracking controller, based on a flow version of the Newton-Raphson method, applied to a miniature blimp and a mid-size quadrotor. This tracking technique admits theoretical performance guarantees for certain classes of systems and has been successfully applied in simulation studies and on mobile robots with simplified motion models. We evaluate the technique through real-world flight experiments on aerial hardware platforms subject to realistic deployment and onboard computational constraints. The technique's performance is assessed in comparison with established baseline control frameworks of feedback linearization for the blimp, and nonlinear model predictive control for both the quadrotor and the blimp. The performance metrics under consideration are (i) root mean square error of flight trajectories with respect to target trajectories, (ii) algorithms' computation times, and (iii) CPU energy consumption associated with the control algorithms. The experimental findings show that the Newton-Raphson-based tracking controller achieves competitive or superior tracking performance to the baseline methods with substantially reduced computation time and energy expenditure.

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arXiv2025

Accelerating Signal-Temporal-Logic-Based Task and Motion Planning of Bipedal Navigation using Benders Decomposition

Task and motion planning under Signal Temporal Logic constraints is known to be NP-hard. A common class of approaches formulates these hybrid problems, which involve discrete task scheduling and continuous motion planning, as mixed-integer programs (MIP). However, in applications for bipedal locomotion, introduction of non-convex constraints such as kinematic reachability and footstep rotation exacerbates the computational complexity of MIPs. In this work, we present a method based on Benders Decomposition to address scenarios where solving the entire monolithic optimization problem is prohibitively intractable. Benders Decomposition proposes an iterative cutting-plane technique that partitions the problem into a master problem to prototype a plan that meets the task specification, and a series of subproblems for kinematics and dynamics feasibility checks. Our experiments demonstrate that this method achieves faster planning compared to alternative algorithms for solving the resulting optimization program with nonlinear constraints.

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arXiv2025

Seeing, Saying, Solving: An LLM-to-TL Framework for Cooperative Robots

Increased robot deployment, such as in warehousing, has revealed a need for seamless collaboration among heterogeneous robot teams to resolve unforeseen conflicts. To address this challenge, we propose a novel, decentralized framework for robots to request and provide help. The framework begins with robots detecting conflicts using a Vision Language Model (VLM), then reasoning over whether help is needed. If so, it crafts and broadcasts a natural language (NL) help request using a Large Language Model (LLM). Potential helper robots reason over the request and offer help (if able), along with information about impact to their current tasks. Helper reasoning is implemented via an LLM grounded in Signal Temporal Logic (STL) using a Backus-Naur Form (BNF) grammar to guarantee syntactically valid NL-to-STL translations, which are then solved as a Mixed Integer Linear Program (MILP). Finally, the requester robot chooses a helper by reasoning over impact on the overall system. We evaluate our system via experiments considering different strategies for choosing a helper, and find that a requester robot can minimize overall time impact on the system by considering multiple help offers versus simple heuristics (e.g., selecting the nearest robot to help).

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arXiv2025

Parametric Reachable Sets Via Controlled Dynamical Embeddings

In this work, we propose a new framework for reachable set computation through continuous evolution of a set of parameters and offsets which define a parametope, through the intersection of constraints. This results in a dynamical approach towards nonlinear reachability analysis: a single trajectory of an embedding system provides a parametope reachable set for the original system, and uncertainties are accounted for through continuous parameter evolution. This is dual to most existing computational strategies, which define sets through some combination of generator vectors, and usually discretize the system dynamics. We show how, under some regularity assumptions of the dynamics and the set considered, any desired parameter evolution can be accommodated as long as the offset dynamics are set accordingly, providing a virtual "control input" for reachable set computation. In a special case of the theory, we demonstrate how closing the loop for the parameter dynamics using the adjoint of the linearization results in a desirable first-order cancellation of the original system dynamics. Using interval arithmetic in JAX, we demonstrate the efficiency and utility of reachable parametope computation through two numerical examples.

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