126,262 research outputs found
Safe Learning of Quadrotor Dynamics Using Barrier Certificates
To effectively control complex dynamical systems, accurate nonlinear models
are typically needed. However, these models are not always known. In this
paper, we present a data-driven approach based on Gaussian processes that
learns models of quadrotors operating in partially unknown environments. What
makes this challenging is that if the learning process is not carefully
controlled, the system will go unstable, i.e., the quadcopter will crash. To
this end, barrier certificates are employed for safe learning. The barrier
certificates establish a non-conservative forward invariant safe region, in
which high probability safety guarantees are provided based on the statistics
of the Gaussian Process. A learning controller is designed to efficiently
explore those uncertain states and expand the barrier certified safe region
based on an adaptive sampling scheme. In addition, a recursive Gaussian Process
prediction method is developed to learn the complex quadrotor dynamics in
real-time. Simulation results are provided to demonstrate the effectiveness of
the proposed approach.Comment: Submitted to ICRA 2018, 8 page
On the Geometry of Message Passing Algorithms for Gaussian Reciprocal Processes
Reciprocal processes are acausal generalizations of Markov processes
introduced by Bernstein in 1932. In the literature, a significant amount of
attention has been focused on developing dynamical models for reciprocal
processes. Recently, probabilistic graphical models for reciprocal processes
have been provided. This opens the way to the application of efficient
inference algorithms in the machine learning literature to solve the smoothing
problem for reciprocal processes. Such algorithms are known to converge if the
underlying graph is a tree. This is not the case for a reciprocal process,
whose associated graphical model is a single loop network. The contribution of
this paper is twofold. First, we introduce belief propagation for Gaussian
reciprocal processes. Second, we establish a link between convergence analysis
of belief propagation for Gaussian reciprocal processes and stability theory
for differentially positive systems.Comment: 15 pages; Typos corrected; This paper introduces belief propagation
for Gaussian reciprocal processes and extends the convergence analysis in
arXiv:1603.04419 to the Gaussian cas
Propagation on networks: an exact alternative perspective
By generating the specifics of a network structure only when needed
(on-the-fly), we derive a simple stochastic process that exactly models the
time evolution of susceptible-infectious dynamics on finite-size networks. The
small number of dynamical variables of this birth-death Markov process greatly
simplifies analytical calculations. We show how a dual analytical description,
treating large scale epidemics with a Gaussian approximations and small
outbreaks with a branching process, provides an accurate approximation of the
distribution even for rather small networks. The approach also offers important
computational advantages and generalizes to a vast class of systems.Comment: 8 pages, 4 figure
Double Normalizing Flows: Flexible Bayesian Gaussian Process ODEs Learning
Recently, Gaussian processes have been utilized to model the vector field of
continuous dynamical systems. Bayesian inference for such models
\cite{hegde2022variational} has been extensively studied and has been applied
in tasks such as time series prediction, providing uncertain estimates.
However, previous Gaussian Process Ordinary Differential Equation (ODE) models
may underperform on datasets with non-Gaussian process priors, as their
constrained priors and mean-field posteriors may lack flexibility. To address
this limitation, we incorporate normalizing flows to reparameterize the vector
field of ODEs, resulting in a more flexible and expressive prior distribution.
Additionally, due to the analytically tractable probability density functions
of normalizing flows, we apply them to the posterior inference of GP ODEs,
generating a non-Gaussian posterior. Through these dual applications of
normalizing flows, our model improves accuracy and uncertainty estimates for
Bayesian Gaussian Process ODEs. The effectiveness of our approach is
demonstrated on simulated dynamical systems and real-world human motion data,
including tasks such as time series prediction and missing data recovery.
Experimental results indicate that our proposed method effectively captures
model uncertainty while improving accuracy
Controlled Gaussian Process Dynamical Models with Application to Robotic Cloth Manipulation
Over the last years, robotic cloth manipulation has gained relevance within
the research community. While significant advances have been made in robotic
manipulation of rigid objects, the manipulation of non-rigid objects such as
cloth garments is still a challenging problem. The uncertainty on how cloth
behaves often requires the use of model-based approaches. However, cloth models
have a very high dimensionality. Therefore, it is difficult to find a middle
point between providing a manipulator with a dynamics model of cloth and
working with a state space of tractable dimensionality. For this reason, most
cloth manipulation approaches in literature perform static or quasi-static
manipulation. In this paper, we propose a variation of Gaussian Process
Dynamical Models (GPDMs) to model cloth dynamics in a low-dimensional manifold.
GPDMs project a high-dimensional state space into a smaller dimension latent
space which is capable of keeping the dynamic properties. Using such approach,
we add control variables to the original formulation. In this way, it is
possible to take into account the robot commands exerted on the cloth dynamics.
We call this new version Controlled Gaussian Process Dynamical Model (C-GPDM).
Moreover, we propose an alternative kernel representation for the model,
characterized by a richer parameterization than the one employed in the
majority of previous GPDM realizations. The modeling capacity of our proposal
has been tested in a simulated scenario, where C-GPDM proved to be capable of
generalizing over a considerably wide range of movements and correctly
predicting the cloth oscillations generated by previously unseen sequences of
control actions
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