arXiv subjects

Calin Belta

Publications and source records attributed to Calin Belta.

At least 37 records · Page 2Linked to original sources

arXiv2025

Safety-Aware Reinforcement Learning for Control via Risk-Sensitive Action-Value Iteration and Quantile Regression

Mainstream approximate action-value iteration reinforcement learning (RL) algorithms suffer from overestimation bias, leading to suboptimal policies in high-variance stochastic environments. Quantile-based action-value iteration methods reduce this bias by learning a distribution of the expected cost-to-go using quantile regression. However, ensuring that the learned policy satisfies safety constraints remains a challenge when these constraints are not explicitly integrated into the RL framework. Existing methods often require complex neural architectures or manual tradeoffs due to combined cost functions. To address this, we propose a risk-regularized quantile-based algorithm integrating Conditional Value-at-Risk (CVaR) to enforce safety without complex architectures. We also provide theoretical guarantees on the contraction properties of the risk-sensitive distributional Bellman operator in Wasserstein space, ensuring convergence to a unique cost distribution. Simulations of a mobile robot in a dynamic reach-avoid task show that our approach leads to more goal successes, fewer collisions, and better safety-performance trade-offs than risk-neutral methods.

cs.LG↗

arXiv2025

Control Barrier Functions via Minkowski Operations for Safe Navigation among Polytopic Sets

Safely navigating around obstacles while respecting the dynamics, control, and geometry of the underlying system is a key challenge in robotics. Control Barrier Functions (CBFs) generate safe control policies by considering system dynamics and geometry when calculating safe forward-invariant sets. Existing CBF-based methods often rely on conservative shape approximations, like spheres or ellipsoids, which have explicit and differentiable distance functions. In this paper, we propose an optimization-defined CBF that directly considers the exact Signed Distance Function (SDF) between a polytopic robot and polytopic obstacles. Inspired by the Gilbert-Johnson-Keerthi (GJK) algorithm, we formulate both (i) minimum distance and (ii) penetration depth between polytopic sets as convex optimization problems in the space of Minkowski difference operations (the MD-space). Convenient geometric properties of the MD-space enable the derivatives of implicit SDF between two polytopes to be computed via differentiable optimization. We demonstrate the proposed framework in three scenarios including pure translation, initialization inside an unsafe set, and multi-obstacle avoidance. These three scenarios highlight the generation of a non-conservative maneuver, a recovery after starting in collision, and the consideration of multiple obstacles via pairwise CBF constraint, respectively.

cs.RO↗

arXiv2025

STL-based Optimization of Biomolecular Neural Networks for Regression and Control

Biomolecular Neural Networks (BNNs), artificial neural networks with biologically synthesizable architectures, achieve universal function approximation capabilities beyond simple biological circuits. However, training BNNs remains challenging due to the lack of target data. To address this, we propose leveraging Signal Temporal Logic (STL) specifications to define training objectives for BNNs. We build on the quantitative semantics of STL, enabling gradient-based optimization of the BNN weights, and introduce a learning algorithm that enables BNNs to perform regression and control tasks in biological systems. Specifically, we investigate two regression problems in which we train BNNs to act as reporters of dysregulated states, and a feedback control problem in which we train the BNN in closed-loop with a chronic disease model, learning to reduce inflammation while avoiding adverse responses to external infections. Our numerical experiments demonstrate that STL-based learning can solve the investigated regression and control tasks efficiently.

cs.LG↗

arXiv2025

Interpretable Imitation Learning via Generative Adversarial STL Inference and Control

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.

cs.LG↗

arXiv2025

SPLASH! Sample-efficient Preference-based inverse reinforcement learning for Long-horizon Adversarial tasks from Suboptimal Hierarchical demonstrations

Inverse Reinforcement Learning (IRL) presents a powerful paradigm for learning complex robotic tasks from human demonstrations. However, most approaches make the assumption that expert demonstrations are available, which is often not the case. Those that allow for suboptimality in the demonstrations are not designed for long-horizon goals or adversarial tasks. Many desirable robot capabilities fall into one or both of these categories, thus highlighting a critical shortcoming in the ability of IRL to produce field-ready robotic agents. We introduce Sample-efficient Preference-based inverse reinforcement learning for Long-horizon Adversarial tasks from Suboptimal Hierarchical demonstrations (SPLASH), which advances the state-of-the-art in learning from suboptimal demonstrations to long-horizon and adversarial settings. We empirically validate SPLASH on a maritime capture-the-flag task in simulation, and demonstrate real-world applicability with sim-to-real translation experiments on autonomous unmanned surface vehicles. We show that our proposed methods allow SPLASH to significantly outperform the state-of-the-art in reward learning from suboptimal demonstrations.

cs.LG↗

arXiv2024

Accelerating Proximal Policy Optimization Learning Using Task Prediction for Solving Environments with Delayed Rewards

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.

cs.LG↗

arXiv2024

Learning Biomolecular Models using Signal Temporal Logic

Modeling dynamical biological systems is key for understanding, predicting, and controlling complex biological behaviors. Traditional methods for identifying governing equations, such as ordinary differential equations (ODEs), typically require extensive quantitative data, which is often scarce in biological systems due to experimental limitations. To address this challenge, we introduce an approach that determines biomolecular models from qualitative system behaviors expressed as Signal Temporal Logic (STL) statements, which are naturally suited to translate expert knowledge into computationally tractable specifications. Our method represents the biological network as a graph, where edges represent interactions between species, and uses a genetic algorithm to identify the graph. To infer the parameters of the ODEs modeling the interactions, we propose a gradient-based algorithm. On a numerical example, we evaluate two loss functions using STL robustness and analyze different initialization techniques to improve the convergence of the approach.

q-bio.MN↗

arXiv2024

Model Predictive Control for Magnetically-Actuated Cellbots

This paper presents a control framework for magnetically actuated cellbots, which combines Model Predictive Control (MPC) with Gaussian Processes (GPs) as a disturbance estimator for precise trajectory tracking. To address the challenges posed by unmodeled dynamics, we integrate data-driven modeling with model-based control to accurately track desired trajectories using relatively small data. To the best of our knowledge, this is the first work to integrate data-driven modeling with model-based control for the magnetic actuation of cellbots. The GP effectively learns and predicts unmodeled disturbances, providing uncertainty bounds as well. We validate our method through experiments with cellbots, demonstrating improved trajectory tracking accuracy.

cs.RO↗

arXiv2024

Capability Augmentation for Heterogeneous Dynamic Teaming with Temporal Logic Tasks

This paper considers how heterogeneous multi-agent teams can leverage their different capabilities to mutually improve individual agent performance. We present Capability-Augmenting Tasks (CATs), which encode how agents can augment their capabilities based on interactions with other teammates. Our framework integrates CAT into the semantics of Metric Temporal Logic (MTL), which defines individual spatio-temporal tasks for all agents. A centralized Mixed-Integer Program (MIP) is used to synthesize trajectories for all agents. We compare the expressivity of our approach to a baseline of Capability Temporal Logic Plus (CaTL+). Case studies demonstrate that our approach allows for simpler specifications and improves individual performance when agents leverage the capabilities of their teammates.

eess.SY↗

arXiv2024

Uncertainty Quantification for Recursive Estimation in Adaptive Safety-Critical Control

In this paper, we present a framework for online parameter estimation and uncertainty quantification in the context of adaptive safety-critical control. The key insight enabling our approach is that the parameter estimate generated by the continuous-time recursive least squares (RLS) algorithm at any point in time is an affine transformation of the initial parameter estimate. This property allows for parameterizing such estimates using objects that are closed under affine transformation, such as zonotopes, and enables the efficient propagation of such set-based estimates as time progresses. We illustrate how such an approach facilitates the synthesis of safety-critical controllers for systems with parametric uncertainty and additive disturbances using control barrier functions, and demonstrate the utility of our approach through illustrative examples.

eess.SY↗

arXiv2023

Control-Based Planning over Probability Mass Function Measurements via Robust Linear Programming

We propose an approach to synthesize linear feedback controllers for linear systems in polygonal environments. Our method focuses on designing a robust controller that can account for uncertainty in measurements. Its inputs are provided by a perception module that generates probability mass functions (PMFs) for predefined landmarks in the environment, such as distinguishable geometric features. We formulate an optimization problem with Control Lyapunov Function (CLF) and Control Barrier Function (CBF) constraints to derive a stable and safe controller. Using the strong duality of linear programs (LPs) and robust optimization, we convert the optimization problem to a linear program that can be efficiently solved offline. At a high level, our approach partially combines perception, planning, and real-time control into a single design problem. An additional advantage of our method is the ability to produce controllers capable of exhibiting nonlinear behavior while relying solely on an offline LP for control synthesis.

eess.SY↗

arXiv2023

LQR-CBF-RRT*: Safe and Optimal Motion Planning

We present LQR-CBF-RRT*, an incremental sampling-based algorithm for offline motion planning. Our framework leverages the strength of Control Barrier Functions (CBFs) and Linear Quadratic Regulators (LQR) to generate safety-critical and optimal trajectories for a robot with dynamics described by an affine control system. CBFs are used for safety guarantees, while LQRs are employed for optimal control synthesis during edge extensions. Popular CBF-based formulations for safety critical control require solving Quadratic Programs (QPs), which can be computationally expensive. Moreover, LQR-based controllers require repetitive applications of first-order Taylor approximations for nonlinear systems, which can also create an additional computational burden. To improve the motion planning efficiency, we verify the satisfaction of the CBF constraints directly in edge extension to avoid the burden of solving the QPs. We store computed optimal LQR gain matrices in a hash table to avoid re-computation during the local linearization of the rewiring procedure. Lastly, we utilize the Cross-Entropy Method for importance sampling to improve sampling efficiency. Our results show that the proposed planner surpasses its counterparts in computational efficiency and performs well in an experimental setup.

cs.RO↗

arXiv2023

Learning a Tracking Controller for Rolling $μ$bots

Micron-scale robots ($μ$bots) have recently shown great promise for emerging medical applications. Accurate controlling $μ$bots, while critical to their successful deployment, is challenging. In this work, we consider the problem of tracking a reference trajectory using a $μ$bot in the presence of disturbances and uncertainty. The disturbances primarily come from Brownian motion and other environmental phenomena, while the uncertainty originates from errors in the model parameters. We model the $μ$bot as an uncertain unicycle that is controlled by a global magnetic field. To compensate for disturbances and uncertainties, we develop a nonlinear mismatch controller. We define the model mismatch error as the difference between our model's predicted velocity and the actual velocity of the $μ$bot. We employ a Gaussian Process to learn the model mismatch error as a function of the applied control input. Then we use a least-squares minimization to select a control action that minimizes the difference between the actual velocity of the $μ$bot and a reference velocity. We demonstrate the online performance of our joint learning and control algorithm in simulation, where our approach accurately learns the model mismatch and improves tracking performance. We also validate our approach in an experiment and show that certain error metrics are reduced by up to $40\%$.

cs.RO↗

arXiv2023

Robustness Measures and Monitors for Time Window Temporal Logic

Temporal logics (TLs) have been widely used to formalize interpretable tasks for cyber-physical systems. Time Window Temporal Logic (TWTL) has been recently proposed as a specification language for dynamical systems. In particular, it can easily express robotic tasks, and it allows for efficient, automata-based verification and synthesis of control policies for such systems. In this paper, we define two quantitative semantics for this logic, and two corresponding monitoring algorithms, which allow for real-time quantification of satisfaction of formulas by trajectories of discrete-time systems. We demonstrate the new semantics and their runtime monitors on numerical examples.

cs.FL↗

arXiv2023

Robust Multi-Agent Coordination from CaTL+ Specifications

We consider the problem of controlling a heterogeneous multi-agent system required to satisfy temporal logic requirements. Capability Temporal Logic (CaTL) was recently proposed to formalize such specifications for deploying a team of autonomous agents with different capabilities and cooperation requirements. In this paper, we extend CaTL to a new logic CaTL+, which is more expressive than CaTL and has semantics over a continuous workspace shared by all agents. We define two novel robustness metrics for CaTL+: the traditional robustness and the exponential robustness. The latter is sound, differentiable almost everywhere and eliminates masking, which is one of the main limitations of the traditional robustness metric. We formulate a control synthesis problem to maximize CaTL+ robustness and propose a two-step optimization method to solve this problem. Simulation results are included to illustrate the increased expressivity of CaTL+ and the efficacy of the proposed control synthesis approach.

eess.SY↗

arXiv2023

Learning Robust and Correct Controllers from Signal Temporal Logic Specifications Using BarrierNet

In this paper, we consider the problem of learning a neural network controller for a system required to satisfy a Signal Temporal Logic (STL) specification. We exploit STL quantitative semantics to define a notion of robust satisfaction. Guaranteeing the correctness of a neural network controller, i.e., ensuring the satisfaction of the specification by the controlled system, is a difficult problem that received a lot of attention recently. We provide a general procedure to construct a set of trainable High Order Control Barrier Functions (HOCBFs) enforcing the satisfaction of formulas in a fragment of STL. We use the BarrierNet, implemented by a differentiable Quadratic Program (dQP) with HOCBF constraints, as the last layer of the neural network controller, to guarantee the satisfaction of the STL formulas. We train the HOCBFs together with other neural network parameters to further improve the robustness of the controller. Simulation results demonstrate that our approach ensures satisfaction and outperforms existing algorithms.

eess.SY↗

arXiv2023

Modular Adaptive Safety-Critical Control

This paper presents an adaptive control approach for uncertain nonlinear systems subject to safety constraints that allows for modularity in the selection of the parameter estimation algorithm. Such modularity is achieved by unifying the concepts of input-to-state stability (ISS) and input-to-state safety (ISSf) via control Lyapunov functions (CLFs) and control barrier functions (CBFs), respectively. In particular, we propose a class of exponential ISS-CLFs and ISSf high order CBFs that can be combined with a general class of parameter estimation algorithms akin to those found in the literature on concurrent learning adaptive control. We demonstrate that the unification of ISS and ISSf in an adaptive control setting allows for maintaining a single set of parameter estimates for both the CLF and CBF that can be generated by a class of update laws satisfying a few general properties. The modularity of our approach is demonstrated via numerical examples by comparing performance in terms of stability and safety across different parameter estimation algorithms.

eess.SY↗

arXiv2023

Safe Model-based Control from Signal Temporal Logic Specifications Using Recurrent Neural Networks

We propose a policy search approach to learn controllers from specifications given as Signal Temporal Logic (STL) formulae. The system model, which is unknown but assumed to be an affine control system, is learned together with the control policy. The model is implemented as two feedforward neural networks (FNNs) - one for the drift, and one for the control directions. To capture the history dependency of STL specifications, we use a recurrent neural network (RNN) to implement the control policy. In contrast to prevalent model-free methods, the learning approach proposed here takes advantage of the learned model and is more efficient. We use control barrier functions (CBFs) with the learned model to improve the safety of the system. We validate our algorithm via simulations and experiments. The results show that our approach can satisfy the given specification within very few system runs, and can be used for on-line control.

eess.SY↗