5,820 research outputs found
MDP Optimal Control under Temporal Logic Constraints
In this paper, we develop a method to automatically generate a control policy
for a dynamical system modeled as a Markov Decision Process (MDP). The control
specification is given as a Linear Temporal Logic (LTL) formula over a set of
propositions defined on the states of the MDP. We synthesize a control policy
such that the MDP satisfies the given specification almost surely, if such a
policy exists. In addition, we designate an "optimizing proposition" to be
repeatedly satisfied, and we formulate a novel optimization criterion in terms
of minimizing the expected cost in between satisfactions of this proposition.
We propose a sufficient condition for a policy to be optimal, and develop a
dynamic programming algorithm that synthesizes a policy that is optimal under
some conditions, and sub-optimal otherwise. This problem is motivated by
robotic applications requiring persistent tasks, such as environmental
monitoring or data gathering, to be performed.Comment: Technical report accompanying the CDC2011 submissio
Control of Probabilistic Systems under Dynamic, Partially Known Environments with Temporal Logic Specifications
We consider the synthesis of control policies for probabilistic systems,
modeled by Markov decision processes, operating in partially known environments
with temporal logic specifications. The environment is modeled by a set of
Markov chains. Each Markov chain describes the behavior of the environment in
each mode. The mode of the environment, however, is not known to the system.
Two control objectives are considered: maximizing the expected probability and
maximizing the worst-case probability that the system satisfies a given
specification
LTL Control in Uncertain Environments with Probabilistic Satisfaction Guarantees
We present a method to generate a robot control strategy that maximizes the
probability to accomplish a task. The task is given as a Linear Temporal Logic
(LTL) formula over a set of properties that can be satisfied at the regions of
a partitioned environment. We assume that the probabilities with which the
properties are satisfied at the regions are known, and the robot can determine
the truth value of a proposition only at the current region. Motivated by
several results on partitioned-based abstractions, we assume that the motion is
performed on a graph. To account for noisy sensors and actuators, we assume
that a control action enables several transitions with known probabilities. We
show that this problem can be reduced to the problem of generating a control
policy for a Markov Decision Process (MDP) such that the probability of
satisfying an LTL formula over its states is maximized. We provide a complete
solution for the latter problem that builds on existing results from
probabilistic model checking. We include an illustrative case study.Comment: Technical Report accompanying IFAC 201
Asymptotically Optimal Sampling-Based Motion Planning Methods
Motion planning is a fundamental problem in autonomous robotics that requires
finding a path to a specified goal that avoids obstacles and takes into account
a robot's limitations and constraints. It is often desirable for this path to
also optimize a cost function, such as path length.
Formal path-quality guarantees for continuously valued search spaces are an
active area of research interest. Recent results have proven that some
sampling-based planning methods probabilistically converge toward the optimal
solution as computational effort approaches infinity. This survey summarizes
the assumptions behind these popular asymptotically optimal techniques and
provides an introduction to the significant ongoing research on this topic.Comment: Posted with permission from the Annual Review of Control, Robotics,
and Autonomous Systems, Volume 4. Copyright 2021 by Annual Reviews,
https://www.annualreviews.org/. 25 pages. 2 figure
Incremental Temporal Logic Synthesis of Control Policies for Robots Interacting with Dynamic Agents
We consider the synthesis of control policies from temporal logic
specifications for robots that interact with multiple dynamic environment
agents. Each environment agent is modeled by a Markov chain whereas the robot
is modeled by a finite transition system (in the deterministic case) or Markov
decision process (in the stochastic case). Existing results in probabilistic
verification are adapted to solve the synthesis problem. To partially address
the state explosion issue, we propose an incremental approach where only a
small subset of environment agents is incorporated in the synthesis procedure
initially and more agents are successively added until we hit the constraints
on computational resources. Our algorithm runs in an anytime fashion where the
probability that the robot satisfies its specification increases as the
algorithm progresses
Trajectory optimization and motion planning for quadrotors in unstructured environments
Trajectory optimization and motion planning for quadrotors in
unstructured environments
Coming out from university labs robots perform tasks usually navigating through
unstructured environment. The realization of autonomous motion in such type of environments
poses a number of challenges compared to highly controlled laboratory
spaces. In unstructured environments robots cannot rely on complete knowledge
of their sorroundings and they have to continously acquire information for decision
making. The challenges presented are a consequence of the high-dimensionality
of the state-space and of the uncertainty introduced by modeling and perception.
This is even more true for aerial-robots that has a complex nonlinear dynamics a can
move freely in 3D-space. To avoid this complexity a robot have to select a small set of
relevant features, reason on a reduced state space and plan trajectories on short-time
horizon. This thesis is a contribution towards the autonomous navigation of aerial
robots (quadrotors) in real-world unstructured scenarios. The first three chapters
present a contribution towards an implementation of Receding Time Horizon Optimal
Control. The optimization problem for a model based trajectory generation in
environments with obstacles is set, using an approach based on variational calculus
and modeling the robots in the SE(3) Lie Group of 3D space transformations. The
fourth chapter explores the problem of using minimal information and sensing to
generate motion towards a goal in an indoor bulding-like scenario. The fifth chapter
investigate the problem of extracting visual features from the environment to
control the motion in an indoor corridor-like scenario. The last chapter deals with
the problem of spatial reasoning and motion planning using atomic proposition in a
multi-robot environments with obstacles
Bayesian model predictive control: Efficient model exploration and regret bounds using posterior sampling
Tight performance specifications in combination with operational constraints
make model predictive control (MPC) the method of choice in various industries.
As the performance of an MPC controller depends on a sufficiently accurate
objective and prediction model of the process, a significant effort in the MPC
design procedure is dedicated to modeling and identification. Driven by the
increasing amount of available system data and advances in the field of machine
learning, data-driven MPC techniques have been developed to facilitate the MPC
controller design. While these methods are able to leverage available data,
they typically do not provide principled mechanisms to automatically trade off
exploitation of available data and exploration to improve and update the
objective and prediction model. To this end, we present a learning-based MPC
formulation using posterior sampling techniques, which provides finite-time
regret bounds on the learning performance while being simple to implement using
off-the-shelf MPC software and algorithms. The performance analysis of the
method is based on posterior sampling theory and its practical efficiency is
illustrated using a numerical example of a highly nonlinear dynamical
car-trailer system
Probabilistically safe vehicle control in a hostile environment
In this paper we present an approach to control a vehicle in a hostile environment with static obstacles and moving adversaries. The vehicle is required to satisfy a mission objective expressed as a temporal logic specification over a set of properties satisfied at regions of a partitioned environment. We model the movements of adversaries in between regions of the environment as Poisson processes. Furthermore, we assume that the time it takes for the vehicle to traverse in between two facets of each region is exponentially distributed, and we obtain the rate of this exponential distribution from a simulator of the environment. We capture the motion of the vehicle and the vehicle updates of adversaries distributions as a Markov Decision Process. Using tools in Probabilistic Computational Tree Logic, we find a control strategy for the vehicle that maximizes the probability of accomplishing the mission objective. We demonstrate our approach with illustrative case studies
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