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Particle Filters For Infinite (or Large) Dimensional State Spaces  Part 1
 IN IEEE ICASSP
, 2006
"... We propose particle filtering algorithms for tracking on infinite (or large) dimensional state spaces. We consider the general case where state space may not be a vector space, we assume it to be a separable metric space (Polish space). In implementation, any such space is approximated by a finite b ..."
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Cited by 14 (9 self)
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We propose particle filtering algorithms for tracking on infinite (or large) dimensional state spaces. We consider the general case where state space may not be a vector space, we assume it to be a separable metric space (Polish space). In implementation, any such space is approximated by a finite
PARTICLE FILTERS FOR INFINITE (OR LARGE) DIMENSIONAL STATE SPACES PART 1
"... We propose particle filtering algorithms for tracking on infinite (or large) dimensional state spaces. We consider the general case where state space may not be a vector space, we assume it to be a separable metric space (Polish space). In implementation, any such space is approximated by a finite b ..."
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We propose particle filtering algorithms for tracking on infinite (or large) dimensional state spaces. We consider the general case where state space may not be a vector space, we assume it to be a separable metric space (Polish space). In implementation, any such space is approximated by a finite
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
Partitions Of Unity In Sobolev Spaces Over Infinite Dimensional State Spaces
"... We prove some general results on the existence of partitions of unity in Sobolev type spaces on various infinite dimensional manifolds. As special cases we obtain in particular, (continuous) partitions of unity a) in the Malliavin test functions on an abstract Wiener space; b) in the first order Sob ..."
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Cited by 5 (2 self)
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We prove some general results on the existence of partitions of unity in Sobolev type spaces on various infinite dimensional manifolds. As special cases we obtain in particular, (continuous) partitions of unity a) in the Malliavin test functions on an abstract Wiener space; b) in the first order
The particel swarm: Explosion, stability, and convergence in a multidimensional complex space
 IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTION
"... The particle swarm is an algorithm for finding optimal regions of complex search spaces through interaction of individuals in a population of particles. Though the algorithm, which is based on a metaphor of social interaction, has been shown to perform well, researchers have not adequately explained ..."
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Cited by 852 (10 self)
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The particle swarm is an algorithm for finding optimal regions of complex search spaces through interaction of individuals in a population of particles. Though the algorithm, which is based on a metaphor of social interaction, has been shown to perform well, researchers have not adequately
Probabilistic Roadmaps for Path Planning in HighDimensional Configuration Spaces
 IEEE INTERNATIONAL CONFERENCE ON ROBOTICS AND AUTOMATION
, 1996
"... A new motion planning method for robots in static workspaces is presented. This method proceeds in two phases: a learning phase and a query phase. In the learning phase, a probabilistic roadmap is constructed and stored as a graph whose nodes correspond to collisionfree configurations and whose edg ..."
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Cited by 1277 (120 self)
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A new motion planning method for robots in static workspaces is presented. This method proceeds in two phases: a learning phase and a query phase. In the learning phase, a probabilistic roadmap is constructed and stored as a graph whose nodes correspond to collisionfree configurations and whose edges correspond to feasible paths between these configurations. These paths are computed using a simple and fast local planner. In the query phase, any given start and goal configurations of the robot are connected to two nodes of the roadmap; the roadmap is then searched for a path joining these two nodes. The method is general and easy to implement. It can be applied to virtually any type of holonomic robot. It requires selecting certain parameters (e.g., the duration of the learning phase) whose values depend on the scene, that is the robot and its workspace. But these values turn out to be relatively easy to choose, Increased efficiency can also be achieved by tailoring some components of the method (e.g., the local planner) to the considered robots. In this paper the method is applied to planar articulated robots with many degrees of freedom. Experimental results show that path planning can be done in a fraction of a second on a contemporary workstation (=150 MIPS), after learning for relatively short periods of time (a few dozen seconds)
Particle filtering for largedimensional state spaces with multimodal observation likelihoods
 IEEE Transactions on Signal Processing
"... Abstract—We study efficient importance sampling techniques for particle filtering (PF) when either (a) the observation likelihood (OL) is frequently multimodal or heavytailed, or (b) the state space dimension is large or both. When the OL is multimodal, but the state transition pdf (STP) is narrow ..."
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Cited by 5 (0 self)
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Abstract—We study efficient importance sampling techniques for particle filtering (PF) when either (a) the observation likelihood (OL) is frequently multimodal or heavytailed, or (b) the state space dimension is large or both. When the OL is multimodal, but the state transition pdf (STP) is narrow
Actions as spacetime shapes
 IN ICCV
, 2005
"... Human action in video sequences can be seen as silhouettes of a moving torso and protruding limbs undergoing articulated motion. We regard human actions as threedimensional shapes induced by the silhouettes in the spacetime volume. We adopt a recent approach [14] for analyzing 2D shapes and genera ..."
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Cited by 651 (4 self)
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Human action in video sequences can be seen as silhouettes of a moving torso and protruding limbs undergoing articulated motion. We regard human actions as threedimensional shapes induced by the silhouettes in the spacetime volume. We adopt a recent approach [14] for analyzing 2D shapes
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.
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