7,896 research outputs found
Chance-Constrained Trajectory Optimization for Safe Exploration and Learning of Nonlinear Systems
Learning-based control algorithms require data collection with abundant
supervision for training. Safe exploration algorithms ensure the safety of this
data collection process even when only partial knowledge is available. We
present a new approach for optimal motion planning with safe exploration that
integrates chance-constrained stochastic optimal control with dynamics learning
and feedback control. We derive an iterative convex optimization algorithm that
solves an \underline{Info}rmation-cost \underline{S}tochastic
\underline{N}onlinear \underline{O}ptimal \underline{C}ontrol problem
(Info-SNOC). The optimization objective encodes both optimal performance and
exploration for learning, and the safety is incorporated as distributionally
robust chance constraints. The dynamics are predicted from a robust regression
model that is learned from data. The Info-SNOC algorithm is used to compute a
sub-optimal pool of safe motion plans that aid in exploration for learning
unknown residual dynamics under safety constraints. A stable feedback
controller is used to execute the motion plan and collect data for model
learning. We prove the safety of rollout from our exploration method and
reduction in uncertainty over epochs, thereby guaranteeing the consistency of
our learning method. We validate the effectiveness of Info-SNOC by designing
and implementing a pool of safe trajectories for a planar robot. We demonstrate
that our approach has higher success rate in ensuring safety when compared to a
deterministic trajectory optimization approach.Comment: Submitted to RA-L 2020, review-
Sampling-based Approximations with Quantitative Performance for the Probabilistic Reach-Avoid Problem over General Markov Processes
This article deals with stochastic processes endowed with the Markov
(memoryless) property and evolving over general (uncountable) state spaces. The
models further depend on a non-deterministic quantity in the form of a control
input, which can be selected to affect the probabilistic dynamics. We address
the computation of maximal reach-avoid specifications, together with the
synthesis of the corresponding optimal controllers. The reach-avoid
specification deals with assessing the likelihood that any finite-horizon
trajectory of the model enters a given goal set, while avoiding a given set of
undesired states. This article newly provides an approximate computational
scheme for the reach-avoid specification based on the Fitted Value Iteration
algorithm, which hinges on random sample extractions, and gives a-priori
computable formal probabilistic bounds on the error made by the approximation
algorithm: as such, the output of the numerical scheme is quantitatively
assessed and thus meaningful for safety-critical applications. Furthermore, we
provide tighter probabilistic error bounds that are sample-based. The overall
computational scheme is put in relationship with alternative approximation
algorithms in the literature, and finally its performance is practically
assessed over a benchmark case study
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