arXiv subjects

Jesse B. Hoagg

Publications and source records attributed to Jesse B. Hoagg.

At least 19 recordsLinked to original sources

arXiv2026

Predicted-Flow Control Barrier Functions for Real-Time Safe Optimal Control

Control barrier functions (CBFs) provide real-time safety guarantees through pointwise conditions on the state. However, synthesizing a valid CBF is difficult and the resulting controllers are myopic. To address myopia, this article introduces predicted-flow control barrier functions (P-CBFs), which generalize the CBF from a function of the current state to a functional of a predicted flow under a parametrized control plan over a finite prediction horizon. For safety, a P-CBF can certify that the predicted flow is in a safe set over the entire prediction horizon. However, candidate P-CBFs suffer from the same challenge as candidate CBFs, namely, control constraints make it difficult to guarantee that the P-CBF is valid. This article resolves this challenge by introducing a terminal candidate P-CBF requiring that the predicted flow end in a backup safe set at the terminal time, and a planning-time shift that modulates the prediction horizon, providing an additional degree of freedom to ensure feasibility. The real-time control and the evolution of the control-plan parameter and planning-time shift are determined jointly by a single convex optimization that is guaranteed to be feasible and renders the associated safe set forward invariant. The resulting safe optimal flow control provides a safety certificate over the entire prediction horizon and unifies finite-horizon integral-cost optimization with safety certification. This optimization reduces to a quadratic program (QP) if the control constraints are a convex polytope. The QP implementation, termed FlowBarrier, is validated on a nonholonomic ground robot navigating a dense environment. FlowBarrier is compared to nonlinear model predictive control and two CBF-based safety filter methods across 100 trials, where FlowBarrier achieves the highest goal-reaching rate, zero safety violations, and the lowest computation time.

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arXiv2026

Geometric Conditions for Lossless Convexification in Linear Optimal Control with Discrete-Valued Inputs: Real-Time Implementation for Spacecraft Rendezvous

Optimal control problems with discrete-valued inputs are inherently challenging due to their mixed-integer nature, rendering them generally intractable for real-time, safety-critical aerospace applications. Lossless convexification offers a powerful alternative by reformulating these mixed-integer programs into computationally efficient convex programs. This paper develops a lossless convexification framework for the optimal control of linear time-varying systems with discrete-valued inputs. We extend existing theoretical results by demonstrating that system normality is preserved when reformulating Lagrange-form problems into Mayer-form via an epigraph transformation. Furthermore, we establish that under simple geometric conditions on the input set, the solution to the relaxed convex problem strictly satisfies the original non-convex input constraints. This framework enables the real-time computation of optimal discrete-valued controls without resorting to mixed-integer optimization. The proposed algorithm is validated on a spacecraft rendezvous maneuver utilizing discrete-valued reaction thrusters in an elliptical orbit. Numerical results from Monte Carlo simulations confirm that the algorithm consistently yields exact discrete-valued control inputs with computational timelines compatible with safety-critical, on-board applications.

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arXiv2026

Receding-Horizon Nonlinear Optimal Control With Safety Constraints Using Constrained Approximate Dynamic Programming

We present a receding-horizon optimal control for nonlinear continuous-time systems subject to state constraints. The cost is a quadratic finite-horizon integral. The key enabling technique is a new constrained approximate dynamic programming (C-ADP) approach for finite-horizon nonlinear optimal control with constraints that are affine in the control. The C-ADP approach is intuitive because it uses a quadratic approximation of the cost-to-go function at each backward step. This method yields a sequence of analytic closed-form optimal control functions, which have identical structure and where parameters are obtained from 2 Riccati-like difference equations. This C-ADP method is well suited for real-time implementation. Thus, we use the C-ADP approach in combination with control barrier functions to obtain a continuous-time receding-horizon optimal control that is farsighted in the sense that it optimizes the integral cost subject to state constraints along the entire prediction horizon. Lastly, receding-horizon C-ADP control is demonstrated in simulation of a nonholonomic ground robot subject to velocity and no-collision constraints. We compare performance with 3 other approaches.

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arXiv2026

Safe Landing on Small Celestial Bodies with Gravitational Uncertainty Using Disturbance Estimation and Control Barrier Functions

Soft landing on small celestial bodies (SCBs) poses unique challenges, as gravitational models poorly characterize the higher-order gravitational effects of SCBs. Existing control approaches lack guarantees for safety under gravitational uncertainty. This paper proposes a three-stage control architecture that combines disturbance estimation, trajectory tracking, and safety enforcement. An extended high-gain observer estimates gravitational disturbances online, a feedback-linearizing controller tracks a reference trajectory, and a minimum-intervention quadratic program enforces state and input constraints while remaining close to the nominal control. The proposed approach enables aggressive yet safe maneuvers despite gravitational uncertainty. Numerical simulations demonstrate the effectiveness of the controller in achieving soft-landing on irregularly shaped SCBs, highlighting its potential for autonomous SCB missions.

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arXiv2026

Experimental Demonstration of a Decentralized Electromagnetic Formation Flying Control Using Alternating Magnetic Field Forces

Electromagnetic formation flying (EMFF) is challenging due to the complex coupling between the electromagnetic fields generated by each satellite in the formation. To address this challenge, this article uses alternating magnetic field forces (AMFF) to decouple the electromagnetic forces between each pair of satellites. The key idea of AMFF is that a pair of alternating (e.g., sinusoidal) magnetic moments results in a nonzero time-averaged interaction force if and only if those alternating magnetic moments have the same frequency. Hence, the approach in this article is to drive each satellite's electromagnetic actuation system with a sum of sinusoids, where each frequency is common to only a pair of satellites. Then, the amplitudes of each sinusoid are modulated (i.e., controlled) to achieve the desired forces between each pair of satellites. The main contribution of this article is an experimental demonstration of 3-satellite decentralized closed-loop EMFF using AMFF. To the authors' knowledge, this is the first demonstration of AMFF with at least 3 satellites in open or closed loop. This is noteworthy because the coupling challenges of EMFF are only present with more than 2 satellites, and thus, a formation of at least 3 is necessary to evaluate the effectiveness of AMFF. The experiments are conducted on a ground-based testbed consisting of 3 electromagnetically actuated satellites on linear air tracks. The closed-loop experiments demonstrate decentralized EMFF with AMFF where the maximum steady-state formation error is less than $\pm $0.01 m and the settling time is less than 30 s. These experiments validate the decoupling of intersatellite forces through frequency-multiplexed AMFF. The closed-loop experimental results are compared with the behavior of numerical simulations.

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arXiv2025

Electromagnetic Formation Flying Using Alternating Magnetic Field Forces and Control Barrier Functions for State and Input Constraints

This article presents a feedback control algorithm for electromagnetic formation flying with constraints on the satellites' states and control inputs. The algorithm combines several key techniques. First, we use alternating magnetic field forces to decouple the electromagnetic forces between each pair of satellites in the formation. Each satellite's electromagnetic actuation system is driven by a sum of amplitude-modulated sinusoids, where amplitudes are controlled in order to prescribe the time-averaged force between each pair of satellites. Next, the desired time-averaged force is computed from a optimal control that satisfies state constraints (i.e., no collisions and an upper limit on intersatellite speeds) and input constraints (i.e., not exceeding satellite's apparent power capability). The optimal time-averaged force is computed using a single relaxed control barrier function that is obtained by composing multiple control barrier functions that are designed to enforce each state and input constraint. Finally, we demonstrate the satellite formation control method in numerical simulations.

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arXiv2025

Control Barrier Functions With Real-Time Gaussian Process Modeling

We present an approach for satisfying state constraints in systems with nonparametric uncertainty by estimating this uncertainty with a real-time-update Gaussian process (GP) model. Notably, new data is incorporated into the model in real time as it is obtained and select old data is removed from the model. This update process helps improve the model estimate while keeping the model size (memory required) and computational complexity fixed. We present a recursive formulation for the model update, which reduces time complexity of the update from O(p3) to O(p2), where p is the number of data used. The GP model includes a computable upper bound on the model error. Together, the model and upper bound are used to construct a control-barrier-function (CBF) constraint that guarantees state constraints are satisfied.

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arXiv2025

Time-Varying Soft-Maximum Barrier Functions for Safety in Unmapped and Dynamic Environments

We present a closed-form optimal feedback control method that ensures safety in an a prior unknown and potentially dynamic environment. This article considers the scenario where local perception data (e.g., LiDAR) is obtained periodically, and this data can be used to construct a local control barrier function (CBF) that models a local set that is safe for a period of time into the future. Then, we use a smooth time-varying soft-maximum function to compose the N most recently obtained local CBFs into a single barrier function that models an approximate union of the N most recently obtained local sets. This composite barrier function is used in a constrained quadratic optimization, which is solved in closed form to obtain a safe-and-optimal feedback control. We also apply the time-varying soft-maximum barrier function control to 2 robotic systems (nonholonomic ground robot with nonnegligible inertia, and quadrotor robot), where the objective is to navigate an a priori unknown environment safely and reach a target destination. In these applications, we present a simple approach to generate local CBFs from periodically obtained perception data.

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arXiv2025

Safe Navigation in Unmapped Environments for Robotic Systems with Input Constraints

This paper presents an approach for navigation and control in unmapped environments under input and state constraints using a composite control barrier function (CBF). We consider the scenario where real-time perception feedback (e.g., LiDAR) is used online to construct a local CBF that models local state constraints (e.g., local safety constraints such as obstacles) in the a priori unmapped environment. The approach employs a soft-maximum function to synthesize a single time-varying CBF from the N most recently obtained local CBFs. Next, the input constraints are transformed into controller-state constraints through the use of control dynamics. Then, we use a soft-minimum function to compose the input constraints with the time-varying CBF that models the a priori unmapped environment. This composition yields a single relaxed CBF, which is used in a constrained optimization to obtain an optimal control that satisfies the state and input constraints. The approach is validated through simulations of a nonholonomic ground robot that is equipped with LiDAR and navigates an unmapped environment. The robot successfully navigates the environment while avoiding the a priori unmapped obstacles and satisfying both speed and input constraints.

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arXiv2024

Electromagnetic Formation Flying with State and Input Constraints Using Alternating Magnetic Field Forces

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arXiv2024

Adaptive Control Barrier Functions with Vanishing Conservativeness Under Persistency of Excitation

This article presents a closed-form adaptive controlbarrier-function (CBF) approach for satisfying state constraints in systems with parametric uncertainty. This approach uses a sampled-data recursive-least-squares algorithm to estimate the unknown model parameters and construct a nonincreasing upper bound on the norm of the estimation error. Together, this estimate and upper bound are used to construct a CBF-based constraint that has nonincreasing conservativeness. Furthermore, if a persistency of excitation condition is satisfied, then the CBFbased constraint has vanishing conservativeness in the sense that the CBF-based constraint converges to the ideal constraint corresponding to the case where the uncertainty is known. In addition, the approach incorporates a monotonically improving estimate of the unknown model parameters thus, this estimate can be effectively incorporated into a desired control law. We demonstrate constraint satisfaction and performance using 2 two numerical examples, namely, a nonlinear pendulum and a nonholonomic robot.

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arXiv2024

Guaranteed-Safe MPPI Through Composite Control Barrier Functions for Efficient Sampling in Multi-Constrained Robotic Systems

We present a new guaranteed-safe model predictive path integral (GS-MPPI) control algorithm that enhances sample efficiency in nonlinear systems with multiple safety constraints. The approach use a composite control barrier function (CBF) along with MPPI to ensure all sampled trajectories are provably safe. We first construct a single CBF constraint from multiple safety constraints with potentially differing relative degrees, using it to create a safe closed-form control law. This safe control is then integrated into the system dynamics, allowing MPPI to optimize over exclusively safe trajectories. The method not only improves computational efficiency but also addresses the myopic behavior often associated with CBFs by incorporating long-term performance considerations. We demonstrate the algorithm's effectiveness through simulations of a nonholonomic ground robot subject to position and speed constraints, showcasing safety and performance.

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arXiv2024

Soft-Minimum and Soft-Maximum Barrier Functions for Safety with Actuation Constraints

This paper presents two new control approaches for guaranteed safety (remaining in a safe set) subject to actuator constraints (the control is in a convex polytope). The control signals are computed using real-time optimization, including linear and quadratic programs subject to affine constraints, which are shown to be feasible. The first control method relies on a soft-minimum barrier function that is constructed using a finite-time-horizon prediction of the system trajectories under a known backup control. The main result shows that the control is continuous and satisfies the actuator constraints, and a subset of the safe set is forward invariant under the control. Next, we extend this method to allow from multiple backup controls. This second approach relies on a combined soft-maximum/soft-minimum barrier function, and it has properties similar to the first. We demonstrate these controls on numerical simulations of an inverted pendulum and a nonholonomic ground robot.

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arXiv2024

A Closed-Form Control for Safety Under Input Constraints Using a Composition of Control Barrier Functions

We present a closed-form optimal control that satisfies both safety constraints (i.e., state constraints) and input constraints (e.g., actuator limits) using a composition of multiple control barrier functions (CBFs). This main contribution is obtained through the combination of several ideas. First, we present a method for constructing a single relaxed control barrier function (R-CBF) from multiple CBFs, which can have different relative degrees. The construction relies on a log-sum-exponential soft-minimum function and yields an R-CBF whose zero-superlevel set is a subset of the intersection of the zero-superlevel sets of all CBFs used in the composition. Next, we use the soft-minimum R-CBF to construct a closed-form control that is optimal with respect to a quadratic cost subject to the safety constraints. Finally, we use the soft-minimum R-CBF to develop a closed-form optimal control that not only guarantees safety but also respects input constraints. The key elements in developing this novel control include: the introduction of the control dynamics, which allow the input constraints to be transformed into controller-state constraints; the use of the soft-minimum R-CBF to compose multiple safety and input CBFs, which have different relative degrees; and the development of a desired surrogate control (i.e., a desired input to the control dynamics). We demonstrate these new control approaches in simulation on a nonholonomic ground robot.

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arXiv2024

Time-Varying Soft-Maximum Control Barrier Functions for Safety in an A Priori Unknown Environment

This paper presents a time-varying soft-maximum composite control barrier function (CBF) that can be used to ensure safety in an a priori unknown environment, where local perception information regarding the safe set is periodically obtained. We consider the scenario where the periodically obtained perception feedback can be used to construct a local CBF that models a local subset of the unknown safe set. Then, we use a novel smooth time-varying soft-maximum function to compose the N most recently obtained local CBFs into a single CBF. This composite CBF models an approximate union of the N most recently obtained local subsets of the safe set. Notably, this composite CBF can have arbitrary relative degree r. Next, this composite CBF is used as a rth-order CBF constraint in a real-time optimization to determine a control that minimizes a quadratic cost while guaranteeing that the state stays in a time-varying subset of the unknown safe set. We also present an application of the time-varying soft-maximum composite CBF method to a nonholonomic ground robot with nonnegligible inertia. In this application, we present a simple approach to generate the local CBFs from the periodically obtained perception data.

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arXiv2024

Composition of Control Barrier Functions With Differing Relative Degrees for Safety Under Input Constraints

This paper presents a new approach for guaranteed safety subject to input constraints (e.g., actuator limits) using a composition of multiple control barrier functions (CBFs). First, we present a method for constructing a single CBF from multiple CBFs, which can have different relative degrees. This construction relies on a soft minimum function and yields a CBF whose $0$-superlevel set is a subset of the union of the $0$-superlevel sets of all the CBFs used in the construction. Next, we extend the approach to systems with input constraints. Specifically, we introduce control dynamics that allow us to express the input constraints as CBFs in the closed-loop state (i.e., the state of the system and the controller). The CBFs constructed from input constraints do not have the same relative degree as the safety constraints. Thus, the composite soft-minimum CBF construction is used to combine the input-constraint CBFs with the safety-constraint CBFs. Finally, we present a feasible real-time-optimization control that guarantees that the state remains in the $0$-superlevel set of the composite soft-minimum CBF. We demonstrate these approaches on a nonholonomic ground robot example.

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arXiv2023

Control Barrier Function Based UAV Safety Controller in Autonomous Airborne Tracking and Following Systems

Safe operations of UAVs are of paramount importance for various mission-critical and safety-critical UAV applications. In context of airborne target tracking and following, UAVs need to track a flying target avoiding collision and also closely follow its trajectory. The safety situation becomes critical and more complex when the flying target is non-cooperative and has erratic movements. This paper proposes a method for collision avoidance in an autonomous fast moving dynamic quadrotor UAV tracking and following another target UAV. This is achieved by designing a safety controller that minimally modifies the control input from a trajectory tracking controller and guarantees safety. This method enables pairing our proposed safety controller with already existing flight controllers. Our safety controller uses a control barrier function based quadratic program (CBF-QP) to produce an optimal control input enabling safe operation while also follow the trajectory of the target closely. We implement our solution on AirSim simulator over PX4 flight controller and with numerical results, we validate our approach through several simulation experiments with multiple scenarios and trajectories.

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arXiv2023

Soft-Minimum Barrier Functions for Safety-Critical Control Subject to Actuation Constraints

This paper presents a new control approach for guaranteed safety (remaining in a safe set) subject to actuator constraints (the control is in a convex polytope). The control signals are computed using real-time optimization, including linear and quadratic programs subject to affine constraints, which are shown to be feasible. The control method relies on a new soft-minimum barrier function that is constructed using a finite-time-horizon prediction of the system trajectories under a known backup control. The main result shows that: (i) the control is continuous and satisfies the actuator constraints, and (ii) a subset of the safe set is forward invariant under the control. We also demonstrate this control on numerical simulations of an inverted pendulum and a double-integrator ground robot.

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