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Trajectory representation using sequenced linear dynamical systems

K.R. Dixon, P.K. Khosla
2004 IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004  
In this paper we present a novel approach for representing trajectories using sequenced linear dynamical systems.  ...  This method uses a closed-form least-squares procedure to fit a single Linear Dynamical System (LDS) to a simple trajectory.  ...  To address these requirements, we propose a trajectory-representation approach based on sequenced linear dynamical systems.  ... 
doi:10.1109/robot.2004.1308881 dblp:conf/icra/DixonK04a fatcat:v2ftghxc2zhn5gx5sgn4xaioae

Learning States Representations in POMDP [article]

Gabriella Contardo and Ludovic Denoyer and Thierry Artieres and Patrick Gallinari
2014 arXiv   pre-print
We propose to deal with sequential processes where only partial observations are available by learning a latent representation space on which policies may be accurately learned.  ...  The base model we are using is a combination of an L 2 regularized linear decoder with a linear+hyperbolictangent dynamical model.  ...  This unsupervised operation is used to learn the system only once, and may be used to tackle different tasks sharing the same dynamical process.  ... 
arXiv:1312.6042v4 fatcat:jjbvl5wdmzftjmma577altjqru

Bilinear spatiotemporal basis models

Ijaz Akhter, Tomas Simon, Sohaib Khan, Iain Matthews, Yaser Sheikh
2012 ACM Transactions on Graphics  
The principal modes of variation in the spatial geometry of objects are typically modeled using dimensionality reduction techniques, while concurrently, trajectory representations like splines and autoregressive  ...  The model can be interpreted as representing the data as a linear combination of spatiotemporal sequences consisting of shape modes oscillating over time at key frequencies.  ...  Li and colleagues [2009] model marker trajectories as a Linear Dynamical System (LDS) to infer missing markers.  ... 
doi:10.1145/2159516.2159523 fatcat:tacbiwy24jeblc2tetltfhzd3m

Learning Dynamical Systems from Noisy Sensor Measurements using Multiple Shooting [article]

Armand Jordana, Justin Carpentier, Ludovic Righetti
2021 arXiv   pre-print
In this work, we introduce a generic and scalable method based on multiple shooting to learn latent representations of indirectly observed dynamical systems.  ...  very long sequences.  ...  part of the "Investissements d'avenir" program, reference ANR-19-P3IA-0001 (PRAIRIE 3IA Institute), Louis Vuitton ENS Chair on Artificial Intelligence, the European project MEMMO (Grant 780684) and the US  ... 
arXiv:2106.11712v1 fatcat:4mj3vzg5wnev5o7xcsnmyedw6y

Adaptive Sampling of Motion Trajectories for Discrete Task-Based Analysis and Synthesis of Gesture [chapter]

Pierre-François Marteau, Sylvie Gibet
2006 Lecture Notes in Computer Science  
These sequences of samples non uniformly distributed along the trajectory are used as input of our sensory motor system.  ...  We have developed a Dynamic Programming Piecewise Linear Approximation model (DPPLA) that generates the discretization of these 3D Cartesian trajectories.  ...  Our analysis method uses a Dynamic Programming Piecewise Linear Approximation (DPPLA) algorithm that extracts a sequence of multi-dimensional targets from the end-effector trajectory.  ... 
doi:10.1007/11678816_25 fatcat:7xayxvmnhvc6rhjaalrrijsiha

Path Integral Networks: End-to-End Differentiable Optimal Control [article]

Masashi Okada, Luca Rigazio, Takenobu Aoshima
2017 arXiv   pre-print
The network includes both system dynamics and cost models, used for optimal control based planning.  ...  Preliminary experiment results show that PI-Net, trained by imitation learning, can mimic control demonstrations for two simulated problems; a linear system and a pendulum swing-up problem.  ...  the dynamics and a quadratic approximation of the cost model, naturally allowing for non-linear system dynamics and cost models.  ... 
arXiv:1706.09597v1 fatcat:jbdgo2k2nbg45mel6x4fprpsky

Learning Continuous System Dynamics from Irregularly-Sampled Partial Observations [article]

Zijie Huang, Yizhou Sun, Wei Wang
2020 arXiv   pre-print
It can simultaneously learn the embedding of high dimensional trajectories and infer continuous latent system dynamics.  ...  Such dynamics is usually difficult to capture, and understanding and predicting the dynamics based on observed trajectories of objects become a critical research problem in many domains.  ...  This allows us to define object-centric dynamics, which can better capture system dynamics compared to the coarse global system representation. Dynamic Graph Representation.  ... 
arXiv:2011.03880v1 fatcat:t2xpygh7rnhh7iiszd3bfk7joq

Chaotic Invariants for Human Action Recognition

Saad Ali, Arslan Basharat, Mubarak Shah
2007 2007 IEEE 11th International Conference on Computer Vision  
Trajectories of reference joints are used as the representation of the non-linear dynamical system that is generating the action.  ...  The paper introduces an action recognition framework that uses concepts from the theory of chaotic systems to model and analyze nonlinear dynamics of human actions.  ...  , non-linear or stochastic dynamical system.  ... 
doi:10.1109/iccv.2007.4409046 dblp:conf/iccv/AliBS07 fatcat:bxzsz7n6wzemth3kaa6zo53x5q

Gesture Modeling by Hanklet-Based Hidden Markov Model [chapter]

Liliana Lo Presti, Marco La Cascia, Stan Sclaroff, Octavia Camps
2015 Lecture Notes in Computer Science  
We aim at decomposing a gesture into sub-trajectories that are the output of a sequence of atomic linear time invariant (LTI) systems, and we use a Hidden Markov Model to model the transitions from the  ...  well with methods that employ more complex models and feature representations.  ...  Trajectory Representation by Hanklets A trajectory may be represented as the output of a linear time invariant (LTI) system.  ... 
doi:10.1007/978-3-319-16811-1_35 fatcat:fh4y6dmrxzhk5gk7wwo426bkw4

Probabilistic Trajectory Segmentation by Means of Hierarchical Dirichlet Process Switching Linear Dynamical Systems [article]

Maximilian Sieb, Matthias Schultheis, Sebastian Szelag, Rudolf Lioutikov, Jan Peters
2020 arXiv   pre-print
A promising approach is to model the trajectory as being generated by a set of Switching Linear Dynamical Systems and inferring a meaningful segmentation by inspecting the transition points characterized  ...  by the switching dynamics.  ...  Block Sampling of State Sequence x 1:T Conditioned on the mode sequence z 1:T and the set of dynamical parameters θ, the entire system degenerates into a simple linear dynamical system with switching dynamical  ... 
arXiv:1806.06063v3 fatcat:bdyzhdkxubef7efsg7bq4ptsx4

MATS: An Interpretable Trajectory Forecasting Representation for Planning and Control [article]

Boris Ivanovic, Amine Elhafsi, Guy Rosman, Adrien Gaidon, Marco Pavone
2021 arXiv   pre-print
Towards this end, we propose Mixtures of Affine Time-varying Systems (MATS) as an output representation for trajectory forecasting that is more amenable to downstream planning and control use.  ...  Our approach leverages successful ideas from probabilistic trajectory forecasting works to learn dynamical system representations that are well-studied in the planning and control literature.  ...  First, we show that MATS, a linear-affine dynamical structure, is a viable trajectory forecasting representation even for highly non-linear realworld systems.  ... 
arXiv:2009.07517v2 fatcat:6h74htwvqvacxcujc7jyer4zru

Data-Driven Control of Linear Time-Varying Systems

Benita Nortmann, Thulasi Mylvaganam
2020 2020 59th IEEE Conference on Decision and Control (CDC)  
This data-driven system representation is used to classify control laws yielding trajectories which satisfy a certain bound and to solve the linear quadratic regulator problem -both using data-dependent  ...  An identification-free control design strategy for discrete-time linear time-varying systems with unknown dynamics is introduced.  ...  Using this result, the problem of designing feedback controllers such that the closed-loop system trajectories satisfy a certain bound can be recast as a feasibility problem involving data-dependent linear  ... 
doi:10.1109/cdc42340.2020.9303845 fatcat:anwkecyhcvbz5odhnadtxgzvfe

The Behavioral Approach to Linear Parameter-Varying Systems

Roland Toth, Jan C. Willems, Peter S. C. Heuberger, Paul M. J. Van den Hof
2011 IEEE Transactions on Automatic Control  
Therefore, representations used previously to define and specify LPV systems are not equal in terms of dynamics.  ...  Index Terms-Behavioral approach, dynamic dependence, equivalence, linear parameter-varying (LPV).  ...  Driven by the need to address the control of complicated plant dynamics in a linear framework, LPV systems were invented to "embed" nonlinear behaviors into a linear structure enabling the use of convex  ... 
doi:10.1109/tac.2011.2109439 fatcat:xyndvylof5crledlasu5cszjam

Locally time-invariant models of human activities using trajectories on the grassmannian

P. Turaga, R. Chellappa
2009 2009 IEEE Conference on Computer Vision and Pattern Recognition  
To this end, we describe activities as outputs of linear dynamic systems (LDS) whose parameters vary with time, or a Time-Varying Linear Dynamic System (TV-LDS).  ...  We show how trajectories on the Grassmannian can be characterized using appropriate distance metrics and statistical methods that reflect the underlying geometry of the manifold.  ...  We now have a sequence of dynamical systems which defines a trajectory on the space of LDS.  ... 
doi:10.1109/cvprw.2009.5206710 fatcat:nj2vsmmxkvhs3oerben3dg3whe

Locally time-invariant models of human activities using trajectories on the grassmannian

Pavan Turaga, Rama Chellappa
2009 2009 IEEE Conference on Computer Vision and Pattern Recognition  
To this end, we describe activities as outputs of linear dynamic systems (LDS) whose parameters vary with time, or a Time-Varying Linear Dynamic System (TV-LDS).  ...  We show how trajectories on the Grassmannian can be characterized using appropriate distance metrics and statistical methods that reflect the underlying geometry of the manifold.  ...  We now have a sequence of dynamical systems which defines a trajectory on the space of LDS.  ... 
doi:10.1109/cvpr.2009.5206710 dblp:conf/cvpr/TuragaC09 fatcat:nmho4ic4m5gxxkme2tayehm3yq
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