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61
A fully automated framework for control of linear systems from ltl specifications
 In HSCC, volume 3927 of LNCS
, 2006
"... Abstract. We consider the following problem: given a linear system and an LTL−X 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 ..."
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Cited by 146 (32 self)
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Abstract. We consider the following problem: given a linear system and an LTL−X 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 steps. First, we partition the state space in accordance with the predicates in the formula and construct a transition system over the partition quotient, which captures our capability of designing controllers. Second, using model checking, we determine runs of the transition system satisfying the formula. Third, we generate the control strategy. Illustrative examples are included. 1
TemporalLogicBased Reactive Mission and Motion Planning
, 2009
"... This paper provides a framework to automatically generate a hybrid controller that guarantees that the robot can achieve its task when a robot model, a class of admissible environments, and a highlevel task or behavior for the robot are provided. The desired task specifications, which are expresse ..."
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Cited by 58 (11 self)
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This paper provides a framework to automatically generate a hybrid controller that guarantees that the robot can achieve its task when a robot model, a class of admissible environments, and a highlevel task or behavior for the robot are provided. The desired task specifications, which are expressed in a fragment of linear temporal logic (LTL), can capture complex robot behaviors such as search and rescue, coverage, and collision avoidance. In addition, our framework explicitly captures sensor specifications that depend on the environment with which the robot is interacting, which results in a novel paradigm for sensorbased temporallogicmotion planning. As one robot is part of the environment of another robot, our sensorbased framework very naturally captures multirobot specifications in a decentralized manner. Our computational approach is based on first creating discrete controllers satisfying specific LTL formulas. If feasible, the discrete controller is then used to guide the sensorbased composition of continuous controllers, which results in a hybrid controller satisfying the highlevel specification but only if the environment is admissible.
Discrete abstractions for robot motion planning and control in polygonal environments
 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 ..."
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Cited by 58 (7 self)
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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 finite state transition systems. In this framework, powerful discrete planning algorithms in complex environments can be seamlessly linked to automatic generation of feedback control laws for robots with underactuation constraints and control bounds. We focus on fullyactuated kinematic robots with velocity bounds and (underactuated) unicycles with forward and turning speed bounds.
Temporal logic motion planning for mobile robots
 In Proceedings of the 2005 IEEE International Conference on Robotics and Automation
, 2005
"... Abstract — In this paper, we consider the problem of robot motion planning in order to satisfy formulas expressible in temporal logics. Temporal logics naturally express traditional robot specifications such as reaching a goal or avoiding an obstacle, but also more sophisticated specifications such ..."
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Cited by 53 (10 self)
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Abstract — In this paper, we consider the problem of robot motion planning in order to satisfy formulas expressible in temporal logics. Temporal logics naturally express traditional robot specifications such as reaching a goal or avoiding an obstacle, but also more sophisticated specifications such as sequencing, coverage, or temporal ordering of different tasks. In order to provide computational solutions to this problem, we first construct discrete abstractions of robot motion based on some environmental decomposition. We then generate discrete plans satisfying the temporal logic formula using powerful model checking tools, and finally translate the discrete plans to continuous trajectories using hybrid control. Critical to our approach is providing formal guarantees ensuring that if the discrete plan satisfies the temporal logic formula, then the continuous motion also satisfies the exact same formula. Index Terms — Motion planning, temporal logics, model checking, discrete abstractions, hybrid control. I.
Temporal logic motion planning for dynamic robots,”
 Automatica,
, 2009
"... Abstract In this paper, we address the temporal logic motion planning problem for mobile robots that are modeled by second order dynamics. Temporal logic specifications can capture the usual control specifications such as reachability and invariance as well as more complex specifications like seque ..."
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Cited by 51 (13 self)
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Abstract In this paper, we address the temporal logic motion planning problem for mobile robots that are modeled by second order dynamics. Temporal logic specifications can capture the usual control specifications such as reachability and invariance as well as more complex specifications like sequencing and obstacle avoidance. Our approach consists of three basic steps. First, we design a control law that enables the dynamic model to track a simpler kinematic model with a globally bounded error. Second, we built a robust temporal logic specification that takes into account the tracking errors of the first step. Finally, we solve the new robust temporal logic path planning problem for the kinematic model using automata theory and simple local vector fields. The resulting continuous time trajectory is provably guaranteed to satisfy the initial user specification.
Control of multiaffine systems on rectangles with applications to hybrid biomolecular networks
 In: Proc. CDC’02. (2002
, 2002
"... Given a multiaffine system on an Ædimensional rectangle, the problem of reaching a particular facet, using multiaffine state feedback is studied. Necessary conditions and sufficient conditions for the existence of a solution are derived in terms of linear inequalities on the input vectors at the v ..."
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Cited by 35 (10 self)
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Given a multiaffine system on an Ædimensional rectangle, the problem of reaching a particular facet, using multiaffine state feedback is studied. Necessary conditions and sufficient conditions for the existence of a solution are derived in terms of linear inequalities on the input vectors at the vertices of the rectangle, and a method for constructing a multiaffine state feedback solution is presented. The technique is applied to the control of hybrid models of bioregulatory networks. 1
Reachability analysis of multiaffine systems
 In Hybrid Systems: Computation and Control, LNCS 3927
, 2006
"... Abstract We present a computationally attractive technique to study the reachability of rectangular regions by trajectories of continuous multiaffine systems. The method is iterative. At each step, finer partitions and finite quotients that overapproximate the reachability properties of the initi ..."
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Cited by 31 (4 self)
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Abstract We present a computationally attractive technique to study the reachability of rectangular regions by trajectories of continuous multiaffine systems. The method is iterative. At each step, finer partitions and finite quotients that overapproximate the reachability properties of the initial system are produced. We exploit some convexity properties of multiaffine functions on rectangles to show that the construction of the quotient at each step requires only the evaluation of the vector field at the set of all vertices of all rectangles in the partition and finding the roots of a finite set of scalar affine functions. This methodology can be used for formal analysis of biochemical networks, aircraft and underwater vehicles, where multiaffine models are widely used.
Optimal path planning for surveillance with temporallogic constraints
 The International Journal of Robotics Research
"... 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 pr ..."
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Cited by 22 (7 self)
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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 environment. The mission specification contains an optimizing proposition which must be repeatedly satisfied. The cost function that we seek to minimize is the maximum time between satisfying instances of the optimizing proposition. For every environment model, and for every formula, our method computes a robot path which minimizes the cost function. The problem is motivated by applications in robotic monitoring and data gathering. In this setting, the optimizing proposition is satisfied at all locations where data can be uploaded, and the LTL formula specifies a complex data collection mission. Our method utilizes Büchi automata to produce an automaton (which can be thought of as a graph) whose runs satisfy the temporal logic specification. We then present a graph algorithm which computes a run corresponding to the optimal robot path. We present an implementation for a robot performing data collection in a road network platform. 1
Dealing with nondeterminism in symbolic control,”
 in Proc HSCC, ser. LNCS.
, 2008
"... Abstract. Abstractions (also called symbolic models) are simple descriptions of continuous and hybrid systems that can be used in analysis and control. They are usually constructed in the form of transition systems with finitely many states. Such abstractions offer a very attractive approach to dea ..."
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Cited by 19 (12 self)
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Abstract. Abstractions (also called symbolic models) are simple descriptions of continuous and hybrid systems that can be used in analysis and control. They are usually constructed in the form of transition systems with finitely many states. Such abstractions offer a very attractive approach to deal with complexity, while at the same time allowing for rich specification languages. Recent results show that, through the abstraction process, the resulting transition systems can be nondeterministic (i.e., if an input is applied in a state, several next states are possible). However, the problem of controlling a nondeterministic transition system from a rich specification such as a temporal logic formula is not well understood. In this paper, we develop a control strategy for a nondeterministic transition system from a specification given as a Linear Temporal Logic formula with a deterministic Büchi generator. Our solution is inspired by LTL games on graphs, is complete, and scales polynomially with the size of the Büchi automaton. An example of controlling a linear system from a specification given as a temporal logic formula over the regions of its triangulated state space is included for illustration.
Temporal Logicbased Reactive Mission and Motion Planning
"... Given a robot model, a class of admissible environments and a high level task or behavior for the robot, this paper provides a framework for automatically generating a hybrid controller that guarantees the robot can achieve its task. The desired task specifications, expressed in a fragment of linea ..."
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Cited by 19 (0 self)
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Given a robot model, a class of admissible environments and a high level task or behavior for the robot, this paper provides a framework for automatically generating a hybrid controller that guarantees the robot can achieve its task. The desired task specifications, expressed in a fragment of linear temporal logic, can capture complex robot behaviors such as search and rescue, coverage, and collision avoidance. In addition, our framework explicitly captures sensor specifications that depend on the environment with which the robot is interacting, resulting in a novel paradigm for sensorbased temporal logic motion planning. As one robot is part of the environment of another robot, our sensorbased framework very naturally captures multirobot specifications in a decentralized manner. Our computational approach is based on first creating discrete controllers satisfying specific Linear Temporal Logic formulas. If feasible, the discrete controller is then used to guide the sensorbased composition of continuous controllers, resulting in a hybrid controller satisfying the highlevel specification, but only if the environment is admissible.