Jesse B. Hoagg

Amirsaeid Safari, Jesse B. Hoagg

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.

Mohammadreza Kamaldar, Jesse B. Hoagg

This paper presents an adaptive harmonic steady-state (AHSS) controller, which addresses the problem of rejecting sinusoids with known frequencies that act on a completely unknown multi-input multi-output linear time-invariant system. We analyze the stability and closed-loop performance of AHSS for single-input single-output systems. In this case, we show that AHSS asymptotically rejects disturbances.

Sumit S. Kamat, Ajin Sunny, T. Michael Seigler et al.

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.

Felipe Arenas-Uribe, Hasan A. Poonawala, Jesse B. Hoagg

Optimal control problems with discrete-valued inputs are challenging due to the mixed-integer nature of the resulting optimization problems, which are generally intractable for real-time, safety-critical applications. Lossless convexification offers an alternative by reformulating mixed-integer programs as convex programs that can be solved efficiently. This paper develops a lossless convexification for optimal control problems of linear systems. We extend existing results by showing that system normality is preserved when reformulating Lagrange-form problems into Mayer-form via an epigraph transformation, and under simple geometric conditions on the input set the solution to the relaxed convex problem is the solution to the original non-convex problem. These results enable real-time computation of optimal discrete-valued controls without resorting to mixed-integer optimization. Numerical results from Monte Carlo simulations confirm that the proposed algorithm consistently yields discrete-valued control inputs with computation times compatible with safety-critical real-time applications.

Ricardo Gutierrez, Jesse B. Hoagg

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.

Felipe Arenas-Uribe, T. Michael Seigler, Jesse B. Hoagg

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.