About

Calin Belta is the Brendan Iribe Endowed Professor of Electrical and Computer Engineering and Computer Science at the University of Maryland, College Park. He is also affiliated with the Institute of Systems Research (ISR) and the Maryland Robotics Center (MRC). His research focuses on dynamics and control theory, with particular emphasis on cyber-physical systems, formal methods, and applications to robotics and systems biology. His work involves the development and application of control strategies and formal verification techniques to complex systems, including robotics and biological systems. He earned his PhD from the University of Pennsylvania in 2003. Throughout his career, he has received notable awards such as the 2008 AFOSR Young Investigator Award, the 2005 NSF CAREER Award, and the 2017 IEEE TCNS Outstanding Paper Award. He is recognized as a Fellow of the IEEE and serves as a Distinguished Lecturer of the IEEE CSS. His contributions have significantly advanced the understanding and application of control and formal methods in cyber-physical systems, robotics, and systems biology.

Research topics

• Computer Science
• Artificial Intelligence
• Mathematical optimization
• Mathematics
• Engineering

Selected publications

• Ternary Logic Encodings of Temporal Behavior Trees with Application to Control Synthesis

  arXiv (Cornell University) · 2026-04-13

  articleOpen accessSenior author

  Behavior Trees (BTs) provide designers an intuitive graphical interface to construct long-horizon plans for autonomous systems. To ensure their correctness and safety, rigorous formal models and verification techniques are essential. Temporal BTs (TBTs) offer a promising approach by leveraging existing temporal logic formalisms to specify and verify the executions of BTs. However, this analysis is currently limited to offline post hoc analysis and trace repair. In this paper, we reformulate TBTs using a ternary-valued Signal Temporal Logic (STL) amenable for control synthesis. Ternary logic introduces a third truth value \textit{Unknown}, formally capturing cases where a trajectory has neither fully satisfied or dissatisfied a specification. We propose mixed-integer linear encodings for partial trajectory STL and TBTs over ternary logic allowing for correct-by-construction control strategies for linear dynamical systems via mixed-integer optimization. We demonstrate the utility of our framework by solving optimal control problems.

  PublisherOA PDF

• Ternary Logic Encodings of Temporal Behavior Trees with Application to Control Synthesis

  arXiv (Cornell University) · 2026-04-13

  preprintOpen accessSenior author

  Behavior Trees (BTs) provide designers an intuitive graphical interface to construct long-horizon plans for autonomous systems. To ensure their correctness and safety, rigorous formal models and verification techniques are essential. Temporal BTs (TBTs) offer a promising approach by leveraging existing temporal logic formalisms to specify and verify the executions of BTs. However, this analysis is currently limited to offline post hoc analysis and trace repair. In this paper, we reformulate TBTs using a ternary-valued Signal Temporal Logic (STL) amenable for control synthesis. Ternary logic introduces a third truth value \textit{Unknown}, formally capturing cases where a trajectory has neither fully satisfied or dissatisfied a specification. We propose mixed-integer linear encodings for partial trajectory STL and TBTs over ternary logic allowing for correct-by-construction control strategies for linear dynamical systems via mixed-integer optimization. We demonstrate the utility of our framework by solving optimal control problems.

  PublisherDOI

• Event-Triggered Adaptive Taylor-Lagrange Control for Safety-Critical Systems

  arXiv (Cornell University) · 2026-04-01

  preprintOpen accessSenior author

  This paper studies safety-critical control for nonlinear systems under sampled-data implementations of the controller. The recently proposed Taylor--Lagrange Control (TLC) method provides rigorous safety guarantees but relies on a fixed discretization-related parameter, which can lead to infeasibility or unsafety in the presence of input constraints and inter-sampling effects. To address these limitations, we propose an adaptive Taylor--Lagrange Control (aTLC) framework with an event-triggered implementation, where the discretization-related parameter defines the discretization time scale and is selected online as state-dependent rather than fixed. This enables the controller to dynamically balance feasibility and safety by adjusting the effective time scale of the Taylor expansion. The resulting controller is implemented as a sequence of Quadratic Programs (QPs) with input constraints. We further introduce a selection rule to choose the discretization-related parameter from a finite candidate set, favoring feasible inputs and improved safety. Simulation results on an adaptive cruise control (ACC) problem demonstrate that the proposed approach improves feasibility, guarantees safety, and achieves smoother control actions compared to TLC while requiring a single automatically tuned parameter.

  PublisherDOI

• Long-Horizon Geometry-Aware Navigation among Polytopes via MILP-MPC and Minkowski-Based CBFs

  ArXiv.org · 2026-03-31

  articleOpen accessSenior author

  Autonomous navigation in complex, non-convex environments remains challenging when robot dynamics, control limits, and exact robot geometry must all be taken into account. In this paper, we propose a hierarchical planning and control framework that bridges long-horizon guidance and geometry-aware safety guarantees for a polytopic robot navigating among polytopic obstacles. At the high level, Mixed-Integer Linear Programming (MILP) is embedded within a Model Predictive Control (MPC) framework to generate a nominal trajectory around polytopic obstacles while modeling the robot as a point mass for computational tractability. At the low level, we employ a control barrier function (CBF) based on the exact signed distance in the Minkowski-difference space as a safety filter to explicitly enforce the geometric constraints of the robot shape, and further extend its formulation to a high-order CBF (HOCBF). We demonstrate the proposed framework in U-shaped and maze-like environments under single- and double-integrator dynamics. The results show that the proposed architecture mitigates the topology-induced local-minimum behavior of purely reactive CBF-based navigation while enabling safe, real-time, geometry-aware navigation.

  PublisherOA PDF

• Iterative Convex Optimization with Control Barrier Functions for Obstacle Avoidance among Polytopes

  Open MIND · 2026-03-06

  preprintSenior author

  Obstacle avoidance of polytopic obstacles by polytopic robots is a challenging problem in optimization-based control and trajectory planning. Many existing methods rely on smooth geometric approximations, such as hyperspheres or ellipsoids, which allow differentiable distance expressions but distort the true geometry and restrict the feasible set. Other approaches integrate exact polytope distances into nonlinear model predictive control (MPC), resulting in nonconvex programs that limit real-time performance. In this paper, we construct linear discrete-time control barrier function (DCBF) constraints by deriving supporting hyperplanes from exact closest-point computations between convex polytopes. We then propose a novel iterative convex MPC-DCBF framework, where local linearization of system dynamics and robot geometry ensures convexity of the finite-horizon optimization at each iteration. The resulting formulation reduces computational complexity and enables fast online implementation for safety-critical control and trajectory planning of general nonlinear dynamics. The framework extends to multi-robot and three-dimensional environments. Numerical experiments demonstrate collision-free navigation in cluttered maze scenarios with millisecond-level solve times.

  DOI

• Learning for feasible and safe control with control barrier functions: A tutorial

  Cybernetics and Intelligence · 2026-03-01

  articleOpen access

  The Control Barrier Function (CBF) method is becoming a popular tool that transforms nonlinear constrained optimal control problems into a sequence of Quadratic Programs (QPs). In this tutorial paper, we show how to employ machine learning techniques to ensure the feasibility of these QPs, which is a challenging problem, especially for high relative degree constraints where High Order CBFs (HOCBFs) are employed. We present two complementary learning approaches: (i) param-eter learning for regular unsafe sets; (ii) sampling learning for irregular unsafe sets, where “regularity” of an unsafe set is formally defined in terms of the dependence of QP feasibility on initial system conditions. The first approach compensates for the myopic nature of the QP-based approach by parame-terizing the HOCBFs and using machine learning techniques to select parameters that maximize a feasibility robustness metric related to system performance. This feasibility robustness metric measures the extent to which QP feasibility is maintained in the presence of time-varying and unknown unsafe sets. The sampling learning approach addresses “irregular” unsafe sets in which the problem feasibility heavily depends on the initial conditions. This approach learns a new feasibility constraint that guarantees the QP feasibility, and it is then enforced by another HOCBF added to the QPs. The accuracy of the learned feasibility constraint can be recursively improved by the proposed recurrent training algorithm. We demonstrate the advantages of the proposed learning approaches to constrained optimal control problems with specific focus on a robot control problem and on autonomous driving in an unknown environment.

  PublisherOA PDFDOI

• Event-Triggered Adaptive Taylor-Lagrange Control for Safety-Critical Systems

  ArXiv.org · 2026-04-01

  articleOpen accessSenior author

  This paper studies safety-critical control for nonlinear systems under sampled-data implementations of the controller. The recently proposed Taylor--Lagrange Control (TLC) method provides rigorous safety guarantees but relies on a fixed discretization-related parameter, which can lead to infeasibility or unsafety in the presence of input constraints and inter-sampling effects. To address these limitations, we propose an adaptive Taylor--Lagrange Control (aTLC) framework with an event-triggered implementation, where the discretization-related parameter defines the discretization time scale and is selected online as state-dependent rather than fixed. This enables the controller to dynamically balance feasibility and safety by adjusting the effective time scale of the Taylor expansion. The resulting controller is implemented as a sequence of Quadratic Programs (QPs) with input constraints. We further introduce a selection rule to choose the discretization-related parameter from a finite candidate set, favoring feasible inputs and improved safety. Simulation results on an adaptive cruise control (ACC) problem demonstrate that the proposed approach improves feasibility, guarantees safety, and achieves smoother control actions compared to TLC while requiring a single automatically tuned parameter.

  PublisherOA PDF

• Risk-Constrained Belief-Space Optimization for Safe Control under Latent Uncertainty

  arXiv (Cornell University) · 2026-04-04

  articleOpen accessSenior author

  Many safety-critical control systems must operate under latent uncertainty that sensors cannot directly resolve at decision time. Such uncertainty, arising from unknown physical properties, exogenous disturbances, or unobserved environment geometry, influences dynamics, task feasibility, and safety margins. Standard methods optimize expected performance and offer limited protection against rare but severe outcomes, while robust formulations treat uncertainty conservatively without exploiting its probabilistic structure. We consider partially observed dynamical systems whose dynamics, costs, and safety constraints depend on a latent parameter maintained as a belief distribution, and propose a risk-sensitive belief-space Model Predictive Path Integral (MPPI) control framework that plans under this belief while enforcing a Conditional Value-at-Risk (CVaR) constraint on a trajectory safety margin over the receding horizon. The resulting controller optimizes a risk-regularized performance objective while explicitly constraining the tail risk of safety violations induced by latent parameter variability. We establish three properties of the resulting risk-constrained controller: (1) the CVaR constraint implies a probabilistic safety guarantee, (2) the controller recovers the risk-neutral optimum as the risk weight in the objective tends to zero, and (3) a union-bound argument extends the per-horizon guarantee to cumulative safety over repeated solves. In physics-based simulations of a vision-guided dexterous stowing task in which a grasped object must be inserted into an occupied slot with pose uncertainty exceeding prescribed lateral clearance requirements, our method achieves 82% success with zero contact violations at high risk aversion, compared to 55% and 50% for a risk-neutral configuration and a chance-constrained baseline, both of which incur nonzero exterior contact forces.

  PublisherOA PDF

• Variational Neural Belief Parameterizations for Robust Dexterous Grasping under Multimodal Uncertainty

  arXiv (Cornell University) · 2026-04-28

  preprintOpen accessSenior author

  Contact variability, sensing uncertainty, and external disturbances make grasp execution stochastic. Expected-quality objectives ignore tail outcomes and often select grasps that fail under adverse contact realizations. Risk-sensitive POMDPs address this failure mode, but many use particle-filter beliefs that scale poorly, obstruct gradient-based optimization, and estimate Conditional Value-at-Risk (CVaR) with high-variance approximations. We instead formulate grasp acquisition as variational inference over latent contact parameters and object pose, representing the belief with a differentiable Gaussian mixture. We use Gumbel-Softmax component selection and location-scale reparameterization to express samples as smooth functions of the belief parameters, enabling pathwise gradients through a differentiable CVaR surrogate for direct optimization of tail robustness. In simulation, our variational neural belief improves robust grasp success under contact-parameter uncertainty and exogenous force perturbations while reducing planning time by roughly an order of magnitude relative to particle-filter model-predictive control. On a serial-chain robot arm with a multifingered hand, we validate grasp-and-lift success under object-pose uncertainty against a Gaussian baseline. Both methods succeed on the tested perturbations, but our controller terminates in fewer steps and less wall-clock time while achieving a higher tactile grasp-quality proxy. Our learned belief also calibrates risk more accurately, keeping mean absolute calibration error below 0.14 across tested simulation regimes, compared with 0.58 for a Cross-Entropy Method planner.

  PublisherDOI

• Learning from Imperfect Demonstrations via Temporal Behavior Tree-Guided Trajectory Repair

  arXiv (Cornell University) · 2026-04-05

  articleOpen accessSenior author

  Learning robot control policies from demonstrations is a powerful paradigm, yet real-world data is often suboptimal, noisy, or otherwise imperfect, posing significant challenges for imitation and reinforcement learning. In this work, we present a formal framework that leverages Temporal Behavior Trees (TBT), an extension of Signal Temporal Logic (STL) with Behavior Tree semantics, to repair suboptimal trajectories prior to their use in downstream policy learning. Given demonstrations that violate a TBT specification, a model-based repair algorithm corrects trajectory segments to satisfy the formal constraints, yielding a dataset that is both logically consistent and interpretable. The repaired trajectories are then used to extract potential functions that shape the reward signal for reinforcement learning, guiding the agent toward task-consistent regions of the state space without requiring knowledge of the agent's kinematic model. We demonstrate the effectiveness of this framework on discrete grid-world navigation and continuous single and multi-agent reach-avoid tasks, highlighting its potential for data-efficient robot learning in settings where high-quality demonstrations cannot be assumed.

  PublisherOA PDF

Recent grants

• CPS: Frontier: Collaborative Research: BioCPS for Engineering Living Cells

  NSF · $1.9M · 2015–2021

• Collaborative Research: The Dynamics of the Innate Immune Systems: A Study of the Toll-like Receptors (TLR) Network

  NSF · $143k · 2011–2014

• Combining Optimality and Correctness in Control Systems

  NSF · $350k · 2014–2019

• S&AS: INT: COLLAB: Autonomy as a Service

  NSF · $235k · 2017–2021

• NRI: FND: A Formal Methods Approach to Safe, Composable, and Distributed Reinforcement Learning for co-Robots

  NSF · $548k · 2020–2024

Frequent coauthors

• Cristian-Ioan Vasile

  Lehigh University

  54 shared

• Wei Xiao

  Massachusetts Institute of Technology

  47 shared

• Christos G. Cassandras

  41 shared

• Xu Chu Ding

  Hartford Financial Services (United States)

  40 shared

• Ebru Aydın Göl

  Middle East Technical University

  38 shared

• Boyan Yordanov

  37 shared

• Sadra Sadraddini

  37 shared

• Noushin Mehdipour

  Boston University

  27 shared

Awards & honors

• 2008 AFOSR Young Investigator Award
• 2005 National Science Foundation CAREER Award
• 2017 IEEE TCNS Outstanding Paper Award