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- Marius Kloetzer, Calin Belta
- IEEE Trans. Automat. Contr.
- 2008

We consider the following problem: given a linear system and a linear temporal logic (LTL) formula over a set of linear predicates in its state variables, find a feedback control law with polyhedral bounds and a set of initial states so that all trajectories of the closed loop system satisfy the formula. Our solution to this problem consists of three main… (More)

- Calin Belta, Vijay R. Kumar
- IEEE Transactions on Robotics
- 2004

This paper addresses the general problem of controlling a large number of robots required to move as a group. We propose an abstraction based on the definition of a map from the configuration space Q of the robots to a lower dimensional manifold A, whose dimension is independent of the number of robots. In this paper, we focus on planar fully actuated… (More)

- Calin Belta, Volkan Isler, George J. Pappas
- IEEE Transactions on Robotics
- 2005

In this paper, we present a computational framework for automatic generation of provably correct control laws for planar robots in polygonal environments. Using polygon triangulation and discrete abstractions, we map continuous motion planning and control problems, specified in terms of triangles, to computationally inexpensive problems on… (More)

- Grégory Batt, Boyan Yordanov, Ron Weiss, Calin Belta
- Bioinformatics
- 2007

MOTIVATION
The goal of synthetic biology is to design and construct biological systems that present a desired behavior. The construction of synthetic gene networks implementing simple functions has demonstrated the feasibility of this approach. However, the design of these networks is difficult, notably because existing techniques and tools are not adapted… (More)

- Calin Belta, Luc C. G. J. M. Habets
- IEEE Trans. Automat. Contr.
- 2006

In this paper, we focus on a particular class of nonlinear affine control systems of the form _ = ( ) + , where the drift is a multi-affine vector field (i.e., affine in each state component), the control distribution is constant, and the control is constrained to a convex set. For such a system, we first derive necessary and sufficient conditions for the… (More)

- Calin Belta, Antonio Bicchi, Magnus Egerstedt, Emilio Frazzoli, Eric Klavins, George J. Pappas
- IEEE Robotics & Automation Magazine
- 2007

In this paper, different research trends that use symbolic techniques for robot motion planning and control are illustrated. As it often happens in new research areas, contributions to this topic started at about the same time by different groups with different emphasis, approaches, and notation. This article tries to describe a framework in which many of… (More)

- Rajeev Alur, Calin Belta, Franjo Ivancic
- HSCC
- 2001

In a biological cell, cellular functions and the genetic regulatory apparatus are implemented and controlled by a network of chemical reactions in which regulatory proteins can control genes that produce other regulators, which in turn control other genes. Further, the feedback pathways appear to incorporate switches that result in changes in the dynamic… (More)

- Stephen L. Smith, Jana Tumova, Calin Belta, Daniela Rus
- I. J. Robotics Res.
- 2011

In this paper we present a method for automatically generating optimal robot paths satisfying high level mission specifications. The motion of the robot in the environment is modeled as a weighted transition system. The mission is specified by an arbitrary linear temporal logic (LTL) formula over propositions satisfied at the regions of a partitioned… (More)

- Calin Belta, Vijay R. Kumar
- IEEE Trans. Robotics and Automation
- 2002

This paper develops a method for generating smooth trajectories for a moving rigid body with specified boundary conditions. Our method involves two key steps: 1) the generation of optimal trajectories in ( ), a subgroup of the affine group in IR and 2) the projection of the trajectories onto (3), the Lie group of rigid body displacements. The overall… (More)

- Boyan Yordanov, Calin Belta
- CDC
- 2009

We present a computational framework for automatic synthesis of a feedback control strategy for a discrete-time piecewise affine (PWA) system from a specification given as a linear temporal logic (LTL) formula over an arbitrary set of linear predicates in the system’s state variables. Our approach consists of two main steps. First, by defining appropriate… (More)