arXiv subjects

Sean B. Andersson

Publications and source records attributed to Sean B. Andersson.

At least 19 recordsLinked to original sources

arXiv2025

Double-Helix based Real-Time Single Particle Tracking

In Real-Time, Feedback-Driven Single Particle Tracking methods, measurements of the emission intensity from a labeled, nanometer-scale particle are used in a feedback loop to track the motion of the particle as it moves inside its native environment, including within living cells. In this work, we take advantage of Point Spread Function (PSF) engineering techniques that encode the axial position of the particle into the shape of the PSF in the focal plane to eliminate the need for out-of-focal-plane measurements, reducing the complexity of implementation and decreasing the overall measurement time of the control loop. Specifically, we used the Double Helix PSF (DH-PSF) in which a single fluorescent source gives rise to two lobes in the image plane with the lobes rotating in the plane as the particle moves along the optical axis. We designed simple estimators of the relative error between the particle and the tracker, and a simple proportional feedback controller to regulate that error to zero. We explored the efficacy of the approach through simulation studies, demonstrating the tracking of fast-moving particles (with diffusion coefficients up to 10 {μ\text{m}^2/\text{s}}) over long time periods (multiple seconds).

physics.optics↗

arXiv2025

Multi-agent Robust and Optimal Policy Learning for Data Harvesting

We consider the problem of using multiple agents to harvest data from a collection of sensor nodes (targets) scattered across a two-dimensional environment. These targets transmit their data to the agents that move in the space above them, and our goal is for the agents to collect data from the targets as efficiently as possible while moving to their final destinations. The agents are assumed to have a continuous control action, and we leverage reinforcement learning, specifically Proximal Policy Optimization (PPO) with Lagrangian Penalty (LP), to identify highly effective solutions. Additionally, we enhance the controller's robustness by incorporating regularization at each state to smooth the learned policy. We conduct a series of simulations to demonstrate our approach and validate its performance and robustness.

eess.SY↗

arXiv2025

Robust Behavior Cloning Via Global Lipschitz Regularization

Behavior Cloning (BC) is an effective imitation learning technique and has even been adopted in some safety-critical domains such as autonomous vehicles. BC trains a policy to mimic the behavior of an expert by using a dataset composed of only state-action pairs demonstrated by the expert, without any additional interaction with the environment. However, During deployment, the policy observations may contain measurement errors or adversarial disturbances. Since the observations may deviate from the true states, they can mislead the agent into making sub-optimal actions. In this work, we use a global Lipschitz regularization approach to enhance the robustness of the learned policy network. We then show that the resulting global Lipschitz property provides a robustness certificate to the policy with respect to different bounded norm perturbations. Then, we propose a way to construct a Lipschitz neural network that ensures the policy robustness. We empirically validate our theory across various environments in Gymnasium. Keywords: Robust Reinforcement Learning; Behavior Cloning; Lipschitz Neural Network

cs.LG↗

arXiv2025

Online Trajectory Optimization for Persistent Monitoring Problems in Partitioned Environments

We consider the problem of using an autonomous agent to persistently monitor a collection of dynamic targets distributed in an environment. We generalize existing work by allowing the agent's dynamics to vary throughout the environment, leading to a hybrid dynamical system. This introduces an additional layer of complexity towards the planning portion of the problem: we must not only identify in which order to visit the points of interest, but also in which order to traverse the regions. We design an offline high-level sequence planner together with an online trajectory optimizer realizing the computed visiting sequence. We provide numerical experiments to illustrate the performance of our approach.

math.OC↗

arXiv2025

Regularization by Neural Style Transfer for MRI Field-Transfer Reconstruction with Limited Data

Recent advances in MRI reconstruction have demonstrated remarkable success through deep learning-based models. However, most existing methods rely heavily on large-scale, task-specific datasets, making reconstruction in data-limited settings a critical yet underexplored challenge. While regularization by denoising (RED) leverages denoisers as priors for reconstruction, we propose Regularization by Neural Style Transfer (RNST), a novel framework that integrates a neural style transfer (NST) engine with a denoiser to enable magnetic field-transfer reconstruction. RNST generates high-field-quality images from low-field inputs without requiring paired training data, leveraging style priors to address limited-data settings. Our experiment results demonstrate RNST's ability to reconstruct high-quality images across diverse anatomical planes (axial, coronal, sagittal) and noise levels, achieving superior clarity, contrast, and structural fidelity compared to lower-field references. Crucially, RNST maintains robustness even when style and content images lack exact alignment, broadening its applicability in clinical environments where precise reference matches are unavailable. By combining the strengths of NST and denoising, RNST offers a scalable, data-efficient solution for MRI field-transfer reconstruction, demonstrating significant potential for resource-limited settings.

cs.CV↗

arXiv2024

BoxMap: Efficient Structural Mapping and Navigation

While humans can successfully navigate using abstractions, ignoring details that are irrelevant to the task at hand, most existing robotic applications require the maintenance of a detailed environment representation which consumes a significant amount of sensing, computing, and storage. These issues are particularly important in a resource-constrained setting with limited power budget. Deep learning methods can learn from prior experience to abstract knowledge of unknown environments, and use it to execute tasks (e.g., frontier exploration, object search, or scene understanding) more efficiently. We propose BoxMap, a Detection-Transformer-based architecture that takes advantage of the structure of the sensed partial environment to update a topological graph of the environment as a set of semantic entities (e.g. rooms and doors) and their relations (e.g. connectivity). These predictions from low-level measurements can then be leveraged to achieve high-level goals with lower computational costs than methods based on detailed representations. As an example application, we consider a robot equipped with a 2-D laser scanner tasked with exploring a residential building. Our BoxMap representation scales quadratically with the number of rooms (with a small constant), resulting in significant savings over a full geometric map. Moreover, our high-level topological representation results in 30.9% shorter trajectories in the exploration task with respect to a standard method.

cs.RO↗

arXiv2024

Lyapunov Neural Network with Region of Attraction Search

Deep learning methods have been widely used in robotic applications, making learning-enabled control design for complex nonlinear systems a promising direction. Although deep reinforcement learning methods have demonstrated impressive empirical performance, they lack the stability guarantees that are important in safety-critical situations. One way to provide these guarantees is to learn Lyapunov certificates alongside control policies. There are three related problems: 1) verify that a given Lyapunov function candidate satisfies the conditions for a given controller on a region, 2) find a valid Lyapunov function and controller on a given region, and 3) find a valid Lyapunov function and a controller such that the region of attraction is as large as possible. Previous work has shown that if the dynamics are piecewise linear, it is possible to solve problems 1) and 2) by solving a Mixed-Integer Linear Program (MILP). In this work, we build upon this method by proposing a Lyapunov neural network that considers monotonicity over half spaces in different directions. We 1) propose a specific choice of Lyapunov function architecture that ensures non-negativity and a unique global minimum by construction, and 2) show that this can be leveraged to find the controller and Lyapunov certificates faster and with a larger valid region by maximizing the size of a square inscribed in a given level set. We apply our method to a 2D inverted pendulum, unicycle path following, a 3-D feedback system, and a 4-D cart pole system, and demonstrate it can shorten the training time by half compared to the baseline, as well as find a larger ROA.

eess.SY↗

arXiv2024

A Fisher Information based Receding Horizon Control Method for Signal Strength Model Estimation

This paper considers the problem of localizing a set of nodes in a wireless sensor network when both their positions and the parameters of the communication model are unknown. We assume that a single agent moves through the environment, taking measurements of the Received Signal Strength (RSS), and seek a controller that optimizes a performance metric based on the Fisher Information Matrix (FIM). We develop a receding horizon (RH) approach that alternates between estimating the parameter values (using a maximum likelihood estimator) and determining where to move so as to maximally inform the estimation problem. The receding horizon controller solves a multi-stage look ahead problem to determine the next control to be applied, executes the move, collects the next measurement, and then re-estimates the parameters before repeating the sequence. We consider both a Dynamic Programming (DP) approach to solving the optimal control problem at each step, and a simplified heuristic based on a pruning algorithm that significantly reduces the computational complexity. We also consider a modified cost function that seeks to balance the information acquired about each of the parameters to ensure the controller does not focus on a single value in its optimization. These approaches are compared against two baselines, one based on a purely random trajectory and one on a greedy control solution. The simulations indicate our RH schemes outperform the baselines, while the pruning algorithm produces significant reductions in computation time with little effect on overall performance.

eess.SY↗

arXiv2023

A Bilevel Optimization Scheme for Persistent Monitoring

In this paper we study an infinite-horizon persistent monitoring problem in a two-dimensional mission space containing a finite number of statically placed targets, at each of which we assume a constant rate of uncertainty accumulation. Equipped with a sensor of finite range, the agent is capable of reducing the uncertainty of nearby targets. We derive a steady-state minimum time periodic trajectory over which each of the target uncertainties is driven down to zero during each visit. A hierarchical decomposition leads to purely local optimal control problems, coupled via boundary conditions. We optimize both the local trajectory segments as well as the boundary conditions in an on-line bilevel optimization scheme.

math.OC↗

arXiv2022

Optimal Persistent Monitoring of Mobile Targets in One Dimension

This work shows the existence of optimal control laws for persistent monitoring of mobile targets in a one-dimensional mission space and derives explicit solutions. The underlying performance metric consists of minimizing the total uncertainty accumulated over a finite mission time. We first demonstrate that the corresponding optimal control problem can be reduced to a finite-dimensional optimization problem, and then establish existence of an optimal solution. Motivated by this result, we construct a parametric reformulation for which an event based gradient descent method is utilized with the goal of deriving (locally optimal) solutions. We additionally provide a more practical parameterization that has attractive properties such as simplicity, flexibility, and robustness. Both parameterizations are validated through simulation.

math.OC↗

arXiv2022

Real-Time Feedback-Driven Single-Particle Tracking: A Survey and Perspective

Real-time feedback-driven single-particle tracking (RT-FD-SPT) is a class of techniques in the field of single-particle tracking that uses feedback control to keep a particle of interest in a detection volume. These methods provide high spatiotemporal resolution on particle dynamics and allow for concurrent spectroscopic measurements. This review article begins with a survey of existing techniques and of applications where RT-FD-SPT has played an important role. We then systematically discuss each of the core components of RT-FD-SPT in order to develop an understanding of the trade-offs that must be made in algorithm design and to create a clear picture of the important differences, advantages, and drawbacks of existing approaches. These components are feedback tracking and control, ranging from simple proportional-integral-derivative control to advanced nonlinear techniques, estimation to determine particle location from the measured data, including both online and offline algorithms, and techniques for calibrating and characterizing different RT-FD-SPT methods. We then introduce a collection of metrics for RT-FD-SPT to help guide experimentalists in selecting a method for their particular application and to help reveal where there are gaps in the techniques that represent opportunities for further development. Finally, we conclude with a discussion on future perspectives in the field.

physics.chem-ph↗

arXiv2022

Bearing-Based Formation Control with Optimal Motion Trajectory

Bearing-based distributed formation control is attractive because it can be implemented using vision-based measurements to achieve a desired formation. Gradient-descent-based controllers using bearing measurements have been shown to have many beneficial characteristics, such as global convergence, applicability to different graph topologies and workspaces of arbitrary dimension, and some flexibility in the choice of the cost. In practice, however, such controllers typically yield convoluted paths from their initial location to the final position in the formation. In this paper we propose a novel procedure to optimize gradient-descent-based bearing-based formation controllers to obtain shorter paths. Our approach is based on the parameterization of the cost function and, by extension, of the controller. We form and solve a nonlinear optimization problem with the sum of path lengths of the agent trajectories as the objective and subject to the original equilibria and global convergence conditions for formation control. Our simulation shows that the parameters can be optimized from a very small number of training samples (1 to 7) to straighten the trajectory by around 16% for a large number of random initial conditions for bearing-only formation. However, in the absence of any range information, the scale of the formation is not fixed and this optimization may lead to an undesired compression of the formation size. Including range measurements avoids this issue and leads to further trajectories straightening by 66%.

eess.SY↗

arXiv2022

Minimax Multi-Agent Persistent Monitoring of a Network System

We investigate the problem of optimally observing a finite set of targets using a mobile agent over an infinite time horizon. The agent is tasked to move in a network-constrained structure to gather information so as to minimize the worst-case uncertainty about the internal states of the targets. To do this, the agent has to decide its sequence of target-visits and the corresponding dwell-times at each visited target. For a given visiting sequence, we prove that in an optimal dwelling time allocation the peak uncertainty is the same among all the targets. This allows us to formulate the optimization of dwelling times as a resource allocation problem and to solve it using a novel efficient algorithm. Next, we optimize the visiting sequence using a greedy exploration process, using heuristics inspired by others developed in the context of the traveling salesman problem. Numerical results are included to illustrate the contributions.

eess.SY↗

arXiv2021

A Semidefinite Programming Approach to Discrete-time Infinite Horizon Persistent Monitoring

We investigate the problem of persistent monitoring, where a mobile agent has to survey multiple targets in an environment in order to estimate their internal states. These internal states evolve with linear stochastic dynamics and the agent can observe them with a linear observation model. However, the signal to noise ratio is a monotonically decreasing function of the distance between the agent and the target. The goal is to minimize the uncertainty in the state estimates over the infinite horizon. We show that, for a periodic trajectory with fixed cycle length, the problem can be formulated as a set of semidefinite programs. We design a scheme that leverages the spatial configuration of the targets to guide the search over this set of optimization problems in order to provide efficient trajectories. Results are compared to a state of the art approach and we obtain improvements of up to 91% in terms of cost in a simple scenario, with much lower computational time.

eess.SY↗

arXiv2020

Optimal Minimax Mobile Sensor Scheduling Over a Network

We investigate the problem of monitoring multiple targets using a single mobile sensor, with the goal of minimizing the maximum estimation error among all the targets over long time horizons. The sensor can move in a network-constrained structure, where it has to plan which targets to visit and for how long to dwell at each node. We prove that in an optimal observation time allocation, the peak uncertainty is the same among all the targets. By further restricting the agent policy to only visit each target once every cycle, we develop a scheme to optimize the agent's behavior that is significantly simpler computationally when compared to previous approaches for similar problems.

eess.SY↗

arXiv2020

Multi-Agent Persistent Monitoring of Targets with Uncertain States

We address the problem of persistent monitoring, where a finite set of mobile agents has to persistently visit a finite set of targets. Each of these targets has an internal state that evolves with linear stochastic dynamics. The agents can observe these states, and the observation quality is a function of the distance between the agent and a given target. The goal is then to minimize the mean squared estimation error of these target states. We approach the problem from an infinite horizon perspective, where we prove that, under some natural assumptions, the covariance matrix of each target converges to a limit cycle. The goal, therefore, becomes to minimize the steady state uncertainty. Assuming that the trajectory is parameterized, we provide tools for computing the steady state cost gradient. We show that, in one-dimensional (1D) environments with bounded control and non-overlapping targets, when an optimal control exists it can be represented using a finite number of parameters. We also propose an efficient parameterization of the agent trajectories for multidimensional settings using Fourier curves. Simulation results show the efficacy of the proposed technique in 1D, 2D and 3D scenarios.

eess.SY↗

arXiv2020

Simultaneous Localization and Parameter Estimation for Single Particle Tracking via Sigma Points based EM

Single Particle Tracking (SPT) is a powerful class of tools for analyzing the dynamics of individual biological macromolecules moving inside living cells. The acquired data is typically in the form of a sequence of camera images that are then post-processed to reveal details about the motion. In this work, we develop an algorithm for jointly estimating both particle trajectory and motion model parameters from the data. Our approach uses Expectation Maximization (EM) combined with an Unscented Kalman filter (UKF) and an Unscented Rauch-Tung-Striebel smoother (URTSS), allowing us to use an accurate, nonlinear model of the observations acquired by the camera. Due to the shot noise characteristics of the photon generation process, this model uses a Poisson distribution to capture the measurement noise inherent in imaging. In order to apply a UKF, we first must transform the measurements into a model with additive Gaussian noise. We consider two approaches, one based on variance stabilizing transformations (where we compare the Anscombe and Freeman-Tukey transforms) and one on a Gaussian approximation to the Poisson distribution. Through simulations, we demonstrate efficacy of the approach and explore the differences among these measurement transformations.

q-bio.BM↗

arXiv2019

Optimal Periodic Multi-Agent Persistent Monitoring of a Finite Set of Targets with Uncertain States

We investigate the problem of persistently monitoring a finite set of targets with internal states that evolve with linear stochastic dynamics using a finite set of mobile agents. We approach the problem from the infinite-horizon perspective, looking for periodic movement schedules for the agents. Under linear dynamics and some standard assumptions on the noise distribution, the optimal estimator is a Kalman-Bucy filter and the mean estimation error is a function of its covariance matrix, which evolves as a differential Riccati equation. It is shown that when the agents are constrained to move only over a line and they can see at most one target at a time, the movement policy that minimizes the mean estimation error over time is such that the agent is always either moving with maximum speed or dwelling at a fixed position. This type of trajectory can be fully defined by a finite set of parameters. For periodic trajectories, under some observability conditions, the estimation error converges to a steady state condition and the stochastic gradient estimate of the cost with respect to the trajectory parameters of each agent and the global period can be explicitly computed using Infinitesimal Perturbation Analysis. A gradient-descent approach is used to compute locally optimal parameters. This approach allows us to deal with a very long persistent monitoring horizon using a small number of parameters.

eess.SY↗