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A Quadratic RegulatorBased Heuristic for Rapidly Exploring State Space
, 2010
"... Kinodynamic planning algorithms like RapidlyExploring Randomized Trees (RRTs) hold the promise of finding feasible trajectories for rich dynamical systems with complex, nonconvex constraints. In practice, these algorithms perform very well on configuration space planning, but struggle to grow effi ..."
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Cited by 14 (2 self)
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Kinodynamic planning algorithms like RapidlyExploring Randomized Trees (RRTs) hold the promise of finding feasible trajectories for rich dynamical systems with complex, nonconvex constraints. In practice, these algorithms perform very well on configuration space planning, but struggle to grow
LIBRARIES A Quadratic RegulatorBased Heuristic for Rapidly Exploring State Space
, 2010
"... Kinodynamic planning algorithms like RapidlyExploring Randomized Trees (RRTs) hold the promise of finding feasible trajectories for rich dynamical systems with complex, nonconvex constraints. In practice, these algorithms perform very well on configuration space planning, but struggle to grow effi ..."
Abstract
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integrator and show that an affine quadratic regulator (AQR) design can be used to approximate the exact minimumtime proximity pseudometric at a reasonable computational cost. We demonstrate improved exploration of the state spaces of the double integrator
Symbolic Model Checking: 10^20 States and Beyond
, 1992
"... Many different methods have been devised for automatically verifying finite state systems by examining stategraph models of system behavior. These methods all depend on decision procedures that explicitly represent the state space using a list or a table that grows in proportion to the number of st ..."
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Cited by 758 (41 self)
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Many different methods have been devised for automatically verifying finite state systems by examining stategraph models of system behavior. These methods all depend on decision procedures that explicitly represent the state space using a list or a table that grows in proportion to the number
Impulses and Physiological States in Theoretical Models of Nerve Membrane
 Biophysical Journal
, 1961
"... ABSTRACT Van der Pol's equation for a relaxation oscillator is generalized by the addition of terms to produce a pair of nonlinear differential equations with either a stable singular point or a limit cycle. The resulting "BVP model " has two variables of state, representing excitabi ..."
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Cited by 505 (0 self)
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the 4dimensional HH phase space onto a plane produces a similar diagram which shows the underlying relationship between the two models. Impulse trains occur in the BVP and HH models for a range of constant applied currents which make the singular point representing the resting state unstable.
Spacetime codes for high data rate wireless communication: Performance criterion and code construction
 IEEE TRANS. INFORM. THEORY
, 1998
"... We consider the design of channel codes for improving the data rate and/or the reliability of communications over fading channels using multiple transmit antennas. Data is encoded by a channel code and the encoded data is split into n streams that are simultaneously transmitted using n transmit ant ..."
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Cited by 1782 (28 self)
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are provided for 4 and 8 PSK signal sets with data rates of 2 and 3 bits/symbol, demonstrating excellent performance that is within 2–3 dB of the outage capacity for these channels using only 64 state encoders.
The Theory of Hybrid Automata
, 1996
"... A hybrid automaton is a formal model for a mixed discretecontinuous system. We classify hybrid automata acoording to what questions about their behavior can be answered algorithmically. The classification reveals structure on mixed discretecontinuous state spaces that was previously studied on pur ..."
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Cited by 685 (12 self)
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A hybrid automaton is a formal model for a mixed discretecontinuous system. We classify hybrid automata acoording to what questions about their behavior can be answered algorithmically. The classification reveals structure on mixed discretecontinuous state spaces that was previously studied
Randomized kinodynamic planning
 THE INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH 2001; 20; 378
, 2001
"... This paper presents the first randomized approach to kinodynamic planning (also known as trajectory planning or trajectory design). The task is to determine control inputs to drive a robot from an initial configuration and velocity to a goal configuration and velocity while obeying physically based ..."
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Cited by 626 (35 self)
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dynamical models and avoiding obstacles in the robot’s environment. The authors consider generic systems that express the nonlinear dynamics of a robot in terms of the robot’s highdimensional configuration space. Kinodynamic planning is treated as a motionplanning problem in a higher dimensional state
A Note on the Confinement Problem
, 1973
"... This not explores the problem of confining a program during its execution so that it cannot transmit information to any other program except its caller. A set of examples attempts to stake out the boundaries of the problem. Necessary conditions for a solution are stated and informally justified. ..."
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Cited by 532 (0 self)
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This not explores the problem of confining a program during its execution so that it cannot transmit information to any other program except its caller. A set of examples attempts to stake out the boundaries of the problem. Necessary conditions for a solution are stated and informally justified.
Symbolic Model Checking for Realtime Systems
 INFORMATION AND COMPUTATION
, 1992
"... We describe finitestate programs over realnumbered time in a guardedcommand language with realvalued clocks or, equivalently, as finite automata with realvalued clocks. Model checking answers the question which states of a realtime program satisfy a branchingtime specification (given in an ..."
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Cited by 578 (50 self)
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in an extension of CTL with clock variables). We develop an algorithm that computes this set of states symbolically as a fixpoint of a functional on state predicates, without constructing the state space. For this purpose, we introduce a calculus on computation trees over realnumbered time. Unfortunately
The algorithmic analysis of hybrid systems
 THEORETICAL COMPUTER SCIENCE
, 1995
"... We present a general framework for the formal specification and algorithmic analysis of hybrid systems. A hybrid system consists of a discrete program with an analog environment. We model hybrid systems as nite automata equipped with variables that evolve continuously with time according to dynamica ..."
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Cited by 778 (71 self)
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to linear hybrid systems. In particular, we consider symbolic modelchecking and minimization procedures that are based on the reachability analysis of an infinite state space. The procedures iteratively compute state sets that are definable as unions of convex polyhedra in multidimensional real space. We
Results 1  10
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