Roberto Tron

Dawei Zhang, Nuo Chen, Shuo Liu et al.

We propose an online monocular perception-to-control framework that embeds semantic risk into the distance field used by Control Barrier Function (CBF)-based safe navigation and teleoperation. Many perception-based safety filters assign the same distance-based safety margin to all mapped obstacles or use semantics only as a downstream controller adjustment, rather than encoding semantic risk in the spatial representation. Our framework instead reasons online about obstacle geometry and class-dependent risk by embedding semantic information directly into the Euclidean Signed Distance Field (ESDF). This design encodes semantic risk before control optimization, so high-risk objects exert a larger spatial influence in the safety field while retaining efficient ESDF queries at runtime. Specifically, a foundation-model-based SLAM front end reconstructs dense 3-D geometry from monocular RGB video, while per-frame semantic segmentation provides pixel-level class labels that are fused into the reconstructed geometry. The resulting geometric-semantic representation is then converted into an ESDF, where semantic labels identify safety-relevant regions and impose class-dependent inflation before field computation. The semantic-aware ESDF provides the local distance values and spatial derivatives required by the CBF controller, while class-dependent gains further regulate the controller response. Extensive simulation and hardware experiments demonstrate online operation at 10--20 Hz and semantic-aware safe behavior in both teleoperation and autonomous navigation.

Danyang Li, Mingyu Cai, Cristian-Ioan Vasile et al.

Machine learning techniques using neural networks have achieved promising success for time-series data classification. However, the models that they produce are challenging to verify and interpret. In this paper, we propose an explainable neural-symbolic framework for the classification of time-series behaviors. In particular, we use an expressive formal language, namely Signal Temporal Logic (STL), to constrain the search of the computation graph for a neural network. We design a novel time function and sparse softmax function to improve the soundness and precision of the neural-STL framework. As a result, we can efficiently learn a compact STL formula for the classification of time-series data through off-the-shelf gradient-based tools. We demonstrate the computational efficiency, compactness, and interpretability of the proposed method through driving scenarios and naval surveillance case studies, compared with state-of-the-art baselines.

Marc Mitjans, David M. Levine, Louis N. Awad et al.

We tackle the problem of tracking the human lower body as an initial step toward an automatic motion assessment system for clinical mobility evaluation, using a multimodal system that combines Inertial Measurement Unit (IMU) data, RGB images, and point cloud depth measurements. This system applies the factor graph representation to an optimization problem that provides 3-D skeleton joint estimations. In this paper, we focus on improving the temporal consistency of the estimated human trajectories to greatly extend the range of operability of the depth sensor. More specifically, we introduce a new factor graph factor based on Koopman theory that embeds the nonlinear dynamics of several lower-limb movement activities. This factor performs a two-step process: first, a custom activity recognition module based on spatial temporal graph convolutional networks recognizes the walking activity; then, a Koopman pose prediction of the subsequent skeleton is used as an a priori estimation to drive the optimization problem toward more consistent results. We tested the performance of this module on datasets composed of multiple clinical lowerlimb mobility tests, and we show that our approach reduces outliers on the skeleton form by almost 1 m, while preserving natural walking trajectories at depths up to more than 10 m.

Xinhuan Sang, Adam Rozman, Sheryl Grace et al.

We present a quadrotor dynamics Gaussian Process (GP) with gradient information that achieves real-time inference via state-space partitioning and approximation, and that includes aerodynamic effects using data from mid-fidelity potential flow simulations. While traditional GP-based approaches provide reliable Bayesian predictions with uncertainty quantification, they are computationally expensive and thus unsuitable for real-time simulations. To address this challenge, we integrate gradient information to improve accuracy and introduce a novel partitioning and approximation strategy to reduce online computational cost. In particular, for the latter, we associate a local GP with each non-overlapping region; by splitting the training data into local near and far subsets, and by using Schur complements, we show that a large part of the matrix inversions required for inference can be performed offline, enabling real-time inference at frequencies above 30 Hz on standard desktop hardware. To generate a training dataset that captures aerodynamic effects, such as rotor-rotor interactions and apparent wind direction, we use the CHARM code, which is a mid-fidelity aerodynamic solver. It is applied to the SUI Endurance quadrotor to predict force and torque, along with noise at three specified locations. The derivative information is obtained via finite differences. Experimental results demonstrate that the proposed partitioned GP with gradient conditioning achieves higher accuracy than standard partitioned GPs without gradient information, while greatly reducing computational time. This framework provides an efficient foundation for real-time aerodynamic prediction and control algorithms in complex and unsteady environments.

Liangting Wu, Roberto Tron

Inverse kinematics (IK) is central to robot control and motion planning, yet its nonlinear kinematic mapping makes it inherently nonconvex and particularly challenging under complex constraints. We present IKSPARK (Inverse Kinematics using Semidefinite Programming And RanK minimization), an obstacle-aware IK solver for robots with diverse morphologies, including open and closed kinematic chains with spherical, revolute, and prismatic joints. Our formulation expresses IK as a semidefinite programming (SDP) problem with additional rank-1 constraints on symmetric matrices with fixed traces. IKSPARK first solves the relaxed SDP, whose infeasibility certifies infeasibility of the original IK problem, and then recovers a rank-1 solution using iterative rank-minimization methods with proven local convergence. Obstacle avoidance is handled through a convexified formulation of mixed-integer constraints. Extensive experiments show that IKSPARK computes highly accurate solutions across various kinematic structures and constrained environments without post-processing. In obstacle-rich settings, especially fixed workcell environments, IKSPARK achieves substantially higher success rates than traditional nonlinear optimization methods.

Yixuan Wang, Danyang Li, Matthew Cleaveland et al.

Signal Temporal Logic (STL) inference learns interpretable logical rules for temporal behaviors in dynamical systems. To ensure the correctness of learned STL formulas, recent approaches have incorporated conformal prediction as a statistical tool for uncertainty quantification. However, most existing methods rely on the assumption that calibration and testing data are identically distributed and exchangeable, an assumption that is frequently violated in real-world settings. This paper proposes a conformalized STL inference framework that explicitly addresses covariate shift between training and deployment trajectories dataset. From a technical standpoint, the approach first employs a template-free, differentiable STL inference method to learn an initial model, and subsequently refines it using a limited deployment side dataset to promote distribution alignment. To provide validity guarantees under distribution shift, the framework estimates the likelihood ratio between training and deployment distributions and integrates it into an STL-robustness-based weighted conformal prediction scheme. Experimental results on trajectory datasets demonstrate that the proposed framework preserves the interpretability of STL formulas while significantly improving symbolic learning reliability at deployment time.

Xinhuan Sang, Abdelrahman Abdelgawad, Roberto Tron

As autonomous robots move into complex, dynamic real-world environments, they must learn to navigate safely in real time, yet anticipating all possible behaviors is infeasible. We propose a composable, model-free reinforcement learning method that learns a value function and an optimal policy for each individual environment element (e.g., goal or obstacle) and composes them online to achieve goal reaching and collision avoidance. Assuming unknown nonlinear dynamics that evolve in continuous time and are input-affine, we derive a continuous-time Hamilton-Jacobi-Bellman (HJB) equation for the value function and show that the corresponding advantage function is quadratic in the action and optimal policy. Based on this structure, we introduce a model-free actor-critic algorithm that learns policies and value functions for static or moving obstacles using gradient descent. We then compose multiple reach/avoid models via a quadratically constrained quadratic program (QCQP), yielding formal obstacle-avoidance guarantees in terms of value-function level sets, providing a model-free alternative to CLF/CBF-based controllers. Simulations demonstrate improved performance over a PPO baseline applied to a discrete-time approximation.

Danyang Li, Mingyu Cai, Cristian-Ioan Vasile et al.

There has been a growing interest in extracting formal descriptions of the system behaviors from data. Signal Temporal Logic (STL) is an expressive formal language used to describe spatial-temporal properties with interpretability. This paper introduces TLINet, a neural-symbolic framework for learning STL formulas. The computation in TLINet is differentiable, enabling the usage of off-the-shelf gradient-based tools during the learning process. In contrast to existing approaches, we introduce approximation methods for max operator designed specifically for temporal logic-based gradient techniques, ensuring the correctness of STL satisfaction evaluation. Our framework not only learns the structure but also the parameters of STL formulas, allowing flexible combinations of operators and various logical structures. We validate TLINet against state-of-the-art baselines, demonstrating that our approach outperforms these baselines in terms of interpretability, compactness, rich expressibility, and computational efficiency.

Wenliang Liu, Danyang Li, Erfan Aasi et al.

Imitation learning methods have demonstrated considerable success in teaching autonomous systems complex tasks through expert demonstrations. However, a limitation of these methods is their lack of interpretability, particularly in understanding the specific task the learning agent aims to accomplish. In this paper, we propose a novel imitation learning method that combines Signal Temporal Logic (STL) inference and control synthesis, enabling the explicit representation of the task as an STL formula. This approach not only provides a clear understanding of the task but also supports the integration of human knowledge and allows for adaptation to out-of-distribution scenarios by manually adjusting the STL formulas and fine-tuning the policy. We employ a Generative Adversarial Network (GAN)-inspired approach to train both the inference and policy networks, effectively narrowing the gap between expert and learned policies. The efficiency of our algorithm is demonstrated through simulations, showcasing its practical applicability and adaptability.

Xiaoshan Lin, Roberto Tron

This work addresses the problem of multi-robot coordination under unknown robot transition models, ensuring that tasks specified by Time Window Temporal Logic are satisfied with user-defined probability thresholds. We present a bi-level framework that integrates (i) high-level task allocation, where tasks are assigned based on the robots' estimated task completion probabilities and expected rewards, and (ii) low-level distributed policy learning and execution, where robots independently optimize auxiliary rewards while fulfilling their assigned tasks. To handle uncertainty in robot dynamics, our approach leverages real-time task execution data to iteratively refine expected task completion probabilities and rewards, enabling adaptive task allocation without explicit robot transition models. We theoretically validate the proposed algorithm, demonstrating that the task assignments meet the desired probability thresholds with high confidence. Finally, we demonstrate the effectiveness of our framework through comprehensive simulations.

Ahmad Ahmad, Mehdi Kermanshah, Kevin Leahy et al.

In this paper, we tackle the challenging problem of delayed rewards in reinforcement learning (RL). While Proximal Policy Optimization (PPO) has emerged as a leading Policy Gradient method, its performance can degrade under delayed rewards. We introduce two key enhancements to PPO: a hybrid policy architecture that combines an offline policy (trained on expert demonstrations) with an online PPO policy, and a reward shaping mechanism using Time Window Temporal Logic (TWTL). The hybrid architecture leverages offline data throughout training while maintaining PPO's theoretical guarantees. Building on the monotonic improvement framework of Trust Region Policy Optimization (TRPO), we prove that our approach ensures improvement over both the offline policy and previous iterations, with a bounded performance gap of $(2ςγα^2)/(1-γ)^2$, where $α$ is the mixing parameter, $γ$ is the discount factor, and $ς$ bounds the expected advantage. Additionally, we prove that our TWTL-based reward shaping preserves the optimal policy of the original problem. TWTL enables formal translation of temporal objectives into immediate feedback signals that guide learning. We demonstrate the effectiveness of our approach through extensive experiments on an inverted pendulum and a lunar lander environments, showing improvements in both learning speed and final performance compared to standard PPO and offline-only approaches.

Danyang Li, Roberto Tron

Time-series data can represent the behaviors of autonomous systems, such as drones and self-driving cars. The task of binary and multi-class classification for time-series data has become a prominent area of research. Neural networks represent a popular approach to classifying data; However, they lack interpretability, which poses a significant challenge in extracting meaningful information from them. Signal Temporal Logic (STL) is a formalism that describes the properties of timed behaviors. We propose a method that combines all of the above: neural networks that represent STL specifications for multi-class classification of time-series data. We offer two key contributions: 1) We introduce a notion of margin for multi-class classification, and 2) we introduce STL-based attributes for enhancing the interpretability of the results. We evaluate our method on two datasets and compare it with state-of-the-art baselines.

Danyang Li, Yixuan Wang, Matthew Cleaveland et al.

Signal Temporal Logic (STL) inference seeks to extract human-interpretable rules from time-series data, but existing methods lack formal confidence guarantees for the inferred rules. Conformal prediction (CP) is a technique that can provide statistical correctness guarantees, but is typically applied as a post-training wrapper without improving model learning. Instead, we introduce an end-to-end differentiable CP framework for STL inference that enhances both reliability and interpretability of the resulting formulas. We introduce a robustness-based nonconformity score, embed a smooth CP layer directly into training, and employ a new loss function that simultaneously optimizes inference accuracy and CP prediction sets with a single term. Following training, an exact CP procedure delivers statistical guarantees for the learned STL formulas. Experiments on benchmark time-series tasks show that our approach reduces uncertainty in predictions (i.e., it achieves high coverage while reducing prediction set size), and improves accuracy (i.e., the number of misclassifications when using a fixed threshold) over state-of-the-art baselines.

Khizar Anjum, Parul Pandey, Vidyasagar Sadhu et al.

Most applications in autonomous navigation using mounted cameras rely on the construction and processing of geometric 3D point clouds, which is an expensive process. However, there is another simpler way to make a space navigable quickly: to use semantic information (e.g., traffic signs) to guide the agent. However, detecting and acting on semantic information involves Computer Vision~(CV) algorithms such as object detection, which themselves are demanding for agents such as aerial drones with limited onboard resources. To solve this problem, we introduce a novel Markov Decision Process~(MDP) framework to reduce the workload of these CV approaches. We apply our proposed framework to both feature-based and neural-network-based object-detection tasks, using open-loop and closed-loop simulations as well as hardware-in-the-loop emulations. These holistic tests show significant benefits in energy consumption and speed with only a limited loss in accuracy compared to models based on static features and neural networks.

Mahroo Bahreinian, Marc Mitjans, Roberto Tron

We propose a novel approach for sampling-based and control-based motion planning that combines a representation of the environment obtained via a modified version of optimal Rapidly-exploring Random Trees (RRT*), with landmark-based output-feedback controllers obtained via Control Lyapunov Functions, Control Barrier Functions, and robust Linear Programming. Our solution inherits many benefits of RRT*-like algorithms, such as the ability to implicitly handle arbitrarily complex obstacles, and asymptotic optimality. Additionally, it extends planning beyond the discrete nominal paths, as feedback controllers can correct deviations from such paths, and are robust to discrepancies between the map used for planning and the real environment. We test our algorithms first in simulations and then in experiments, testing the robustness of the approach to practical conditions, such as deformations of the environment, mismatches in the dynamical model of the robot, and measurements acquired with a camera with a limited field of view.

Dawei Zhang, Roberto Tron

We present a novel haptic teleoperation approach that considers not only the safety but also the stability of a teleoperation system. Specifically, we build upon previous work on haptic shared control, which uses control barrier functions (CBFs) to generate a reference haptic feedback that informs the human operator on the internal state of the system, helping them to safely navigate the robot without taking away their control authority. Crucially, in this approach the force rendered to the user is not directly reflected in the motion of the robot (which is still directly controlled by the user); however, previous work in the area neglected to consider the feedback loop through the user, possibly resulting in unstable closed trajectories. In this paper we introduce a differential constraint on the rendered force that makes the system finite-gain $L_2$ stable; the constraint results in a Quadratically Constrained Quadratic Program (QCQP), for which we provide a closed-form solution. Our constraint is related to but less restrictive than the typical passivity constraint used in previous literature. We conducted an experimental simulation in which a human operator flies a UAV near an obstacle to evaluate the proposed method.

Dawei Zhang, Roberto Tron, Rebecca P. Khurshid

Shared autonomy teleoperation can guarantee safety, but does so by reducing the human operator's control authority, which can lead to reduced levels of human-robot agreement and user satisfaction. This paper presents a novel haptic shared autonomy teleoperation paradigm that uses haptic feedback to inform the user about the inner state of a shared autonomy paradigm, while still guaranteeing safety. This differs from haptic shared control, which uses haptic feedback to inform the user's actions, but gives the human operator full control over the robot's actions. We conducted a user study in which twelve users flew a simulated UAV in a search-and-rescue task with no assistance or assistance provided by haptic shared control, shared autonomy, or haptic shared autonomy. All assistive teleoperation methods use control barrier functions to find a control command that is both safe and as close as possible to the human-generated control command. For assistive teleoperation conditions with haptic feedback, we apply a force to the user that is proportional to the difference between the human-generated control and the safe control. We find that haptic shared autonomy improves the user's task performance and satisfaction. We also find that haptic feedback in assistive teleoperation can improve the user's situational awareness. Finally, results show that adding haptic feedback to shared-autonomy teleoperation can improve human-robot agreement.

Arman Karimian, Ziqi Yang, Roberto Tron

This paper introduces a novel and distributed method for detecting inter-map loop closure outliers in simultaneous localization and mapping (SLAM). The proposed algorithm does not rely on a good initialization and can handle more than two maps at a time. In multi-robot SLAM applications, maps made by different agents have nonidentical spatial frames of reference which makes initialization very difficult in the presence of outliers. This paper presents a probabilistic approach for detecting incorrect orientation measurements prior to pose graph optimization by checking the geometric consistency of rotation measurements. Expectation-Maximization is used to fine-tune the model parameters. As ancillary contributions, a new approximate discrete inference procedure is presented which uses evidence on loops in a graph and is based on optimization (Alternate Direction Method of Multipliers). This method yields superior results compared to Belief Propagation and has convergence guarantees. Simulation and experimental results are presented that evaluate the performance of the outlier detection method and the inference algorithm on synthetic and real-world data.

Zachary Serlin, Guang Yang, Brandon Sookraj et al.

In this work we consider the multi-image object matching problem, extend a centralized solution of the problem to a distributed solution, and present an experimental application of the centralized solution. Multi-image feature matching is a keystone of many applications, including simultaneous localization and mapping, homography, object detection, and structure from motion. We first review the QuickMatch algorithm for multi-image feature matching. We then present a scheme for distributing sets of features across computational units (agents) that largely preserves feature match quality and minimizes communication between agents (avoiding, in particular, the need of flooding all data to all agents). Finally, we show how QuickMatch performs on an object matching test with low quality images. The centralized QuickMatch algorithm is compared to other standard matching algorithms, while the Distributed QuickMatch algorithm is compared to the centralized algorithm in terms of preservation of match consistency. The presented experiment shows that QuickMatch matches features across a large number of images and features in larger numbers and more accurately than standard techniques.

Mahroo Bahreinian, Erfan Aasi, Roberto Tron

We propose a novel approach for navigating in polygonal environments by synthesizing controllers that take as input relative displacement measurements with respect to a set of landmarks. Our algorithm is based on solving a sequence of robust min-max Linear Programming problems on the elements of a cell decomposition of the environment. The optimization problems are formulated using linear Control Lyapunov Function (CLF) and Control Barrier Function (CBF) constraints, to provide stability and safety guarantees, respectively. The inner maximization problem ensures that these constraints are met by all the points in each cell, while the outer minimization problem balances the different constraints in a robust way. We show that the min-max optimization problems can be solved efficiently by transforming it into regular linear programming via the dualization of the inner maximization problem. We test our algorithm to agents with first and second-order integrator dynamics, although our approach is in principle applicable to any system with piecewise linear dynamics. Through our theoretical results and simulations, we show that the resulting controllers: are optimal (with respect to the criterion used in the formulation), are applicable to linear systems of any order, are robust to changes to the start location (since they do not rely on a single nominal path), and to significant deformations of the environment.

Guang Yang, Bee Vang, Zachary Serlin et al.

Robot motion planning is central to real-world autonomous applications, such as self-driving cars, persistence surveillance, and robotic arm manipulation. One challenge in motion planning is generating control signals for nonlinear systems that result in obstacle free paths through dynamic environments. In this paper, we propose Control Barrier Function guided Rapidly-exploring Random Trees (CBF-RRT), a sampling-based motion planning algorithm for continuous-time nonlinear systems in dynamic environments. The algorithm focuses on two objectives: efficiently generating feasible controls that steer the system toward a goal region, and handling environments with dynamical obstacles in continuous time. We formulate the control synthesis problem as a Quadratic Program (QP) that enforces Control Barrier Function (CBF) constraints to achieve obstacle avoidance. Additionally, CBF-RRT does not require nearest neighbor or collision checks when sampling, which greatly reduce the run-time overhead when compared to standard RRT variants.

Roberto Tron

We consider the problem of reconstructing a 3-D scene from a moving camera with high frame rate using the affine projection model. This problem is traditionally known as Affine Structure from Motion (Affine SfM), and can be solved using an elegant low-rank factorization formulation. In this paper, we assume that an accelerometer and gyro are rigidly mounted with the camera, so that synchronized linear acceleration and angular velocity measurements are available together with the image measurements. We extend the standard Affine SfM algorithm to integrate these measurements through the use of image derivatives.

Nikolay A. Atanasov, Roberto Tron, Victor M. Preciado et al.

This paper addresses the problem of collaborative tracking of dynamic targets in wireless sensor networks. A novel distributed linear estimator, which is a version of a distributed Kalman filter, is derived. We prove that the filter is mean square consistent in the case of static target estimation. When large sensor networks are deployed, it is common that the sensors do not have good knowledge of their locations, which affects the target estimation procedure. Unlike most existing approaches for target tracking, we investigate the performance of our filter when the sensor poses need to be estimated by an auxiliary localization procedure. The sensors are localized via a distributed Jacobi algorithm from noisy relative measurements. We prove strong convergence guarantees for the localization method and in turn for the joint localization and target estimation approach. The performance of our algorithms is demonstrated in simulation on environmental monitoring and target tracking tasks.

Dheeraj Singaraju, Ehsan Elhamifar, Roberto Tron et al.

Recent results in Compressive Sensing have shown that, under certain conditions, the solution to an underdetermined system of linear equations with sparsity-based regularization can be accurately recovered by solving convex relaxations of the original problem. In this work, we present a novel primal-dual analysis on a class of sparsity minimization problems. We show that the Lagrangian bidual (i.e., the Lagrangian dual of the Lagrangian dual) of the sparsity minimization problems can be used to derive interesting convex relaxations: the bidual of the $\ell_0$-minimization problem is the $\ell_1$-minimization problem; and the bidual of the $\ell_{0,1}$-minimization problem for enforcing group sparsity on structured data is the $\ell_{1,\infty}$-minimization problem. The analysis provides a means to compute per-instance non-trivial lower bounds on the (group) sparsity of the desired solutions. In a real-world application, the bidual relaxation improves the performance of a sparsity-based classification framework applied to robust face recognition.