65 research outputs found
Unified Multi-Rate Control: from Low Level Actuation to High Level Planning
In this paper we present a hierarchical multi-rate control architecture for
nonlinear autonomous systems operating in partially observable environments.
Control objectives are expressed using syntactically co-safe Linear Temporal
Logic (LTL) specifications and the nonlinear system is subject to state and
input constraints. At the highest level of abstraction, we model the
system-environment interaction using a discrete Mixed Observable Markov
Decision Problem (MOMDP), where the environment states are partially observed.
The high level control policy is used to update the constraint sets and cost
function of a Model Predictive Controller (MPC) which plans a reference
trajectory. Afterwards, the MPC planned trajectory is fed to a low-level
high-frequency tracking controller, which leverages Control Barrier Functions
(CBFs) to guarantee bounded tracking errors. Our strategy is based on model
abstractions of increasing complexity and layers running at different
frequencies. We show that the proposed hierarchical multi-rate control
architecture maximizes the probability of satisfying the high-level
specifications while guaranteeing state and input constraint satisfaction.
Finally, we tested the proposed strategy in simulations and experiments on
examples inspired by the Mars exploration mission, where only partial
environment observations are available
Formal Methods for Autonomous Systems
Formal methods refer to rigorous, mathematical approaches to system
development and have played a key role in establishing the correctness of
safety-critical systems. The main building blocks of formal methods are models
and specifications, which are analogous to behaviors and requirements in system
design and give us the means to verify and synthesize system behaviors with
formal guarantees.
This monograph provides a survey of the current state of the art on
applications of formal methods in the autonomous systems domain. We consider
correct-by-construction synthesis under various formulations, including closed
systems, reactive, and probabilistic settings. Beyond synthesizing systems in
known environments, we address the concept of uncertainty and bound the
behavior of systems that employ learning using formal methods. Further, we
examine the synthesis of systems with monitoring, a mitigation technique for
ensuring that once a system deviates from expected behavior, it knows a way of
returning to normalcy. We also show how to overcome some limitations of formal
methods themselves with learning. We conclude with future directions for formal
methods in reinforcement learning, uncertainty, privacy, explainability of
formal methods, and regulation and certification
Formal methods for motion planning and control in dynamic and partially known environments
This thesis is motivated by time and safety critical applications involving the use of autonomous vehicles to accomplish complex tasks in dynamic and partially known environments. We use temporal logic to formally express such complex tasks. Temporal logic specifications generalize the classical notions of stability and reachability widely studied within the control and hybrid systems communities. Given a model describing the motion of a robotic system in an environment and a formal task specification, the aim is to automatically synthesize a control policy that guarantees the satisfaction of the specification. This thesis presents novel control synthesis algorithms
to tackle the problem of motion planning from temporal logic specifications in uncertain environments. For each one of the planning and control synthesis problems addressed in this dissertation, the proposed algorithms are implemented, evaluated, and validated thought experiments and/or simulations.
The first part of this thesis focuses on a mobile robot whose success is measured by the completion of temporal logic tasks within a given period of time. In addition to such time constraints, the planning algorithm must also deal with the uncertainty that arises from the changes in the robot's workspace during task execution. In particular, we consider a robot deployed in a partitioned environment subjected to structural changes such as doors that can open and close. The motion of the robot is modeled
as a continuous time Markov decision process and the robot's mission is expressed as a Continuous Stochastic Logic (CSL) formula. A complete framework to find a control strategy that satisfies a specification given as a CSL formula is introduced.
The second part of this thesis addresses the synthesis of controllers that guarantee the satisfaction of a task specification expressed as a syntactically co-safe Linear Temporal Logic (scLTL) formula. In this case, uncertainty is characterized by the partial knowledge of the robot's environment. Two scenarios are considered. First, a distributed team of robots required to satisfy the specification over a set of service requests occurring at the vertices of a known graph representing the environment is
examined. Second, a single agent motion planning problem from the specification over a set of properties known to be satised at the vertices of the known graph environment is studied. In both cases, we exploit the existence of o-the-shelf model checking and runtime verification tools, the efficiency of graph search algorithms, and the efficacy of exploration techniques to solve the motion planning problem constrained by
the absence of complete information about the environment.
The final part of this thesis extends uncertainty beyond the absence of a complete knowledge of the environment described above by considering a robot equipped with a noisy sensing system. In particular, the robot is tasked with satisfying a scLTL specification over a set of regions of interest known to be present in the environment. In such a case, although the robot is able to measure the properties characterizing such regions of interest, precisely determining the identity of these regions is not feasible. A mixed observability Markov decision process is used to represent the robot's actuation and sensing models. The control synthesis problem from scLTL
formulas is then formulated as a maximum probability reachability problem on this model. The integration of dynamic programming, formal methods, and frontier-based exploration tools allow us to derive an algorithm to solve such a reachability problem
IST Austria Technical Report
We consider partially observable Markov decision processes (POMDPs) with ω-regular conditions specified as parity objectives. The class of ω-regular languages extends regular languages to infinite strings and provides a robust specification language to express all properties used in verification, and parity objectives are canonical forms to express ω-regular conditions. The qualitative analysis problem given a POMDP and a parity objective asks whether there is a strategy to ensure that the objective is satis- fied with probability 1 (resp. positive probability). While the qualitative analysis problems are known to be undecidable even for very special cases of parity objectives, we establish decidability (with optimal complexity) of the qualitative analysis problems for POMDPs with all parity objectives under finite- memory strategies. We establish asymptotically optimal (exponential) memory bounds and EXPTIME- completeness of the qualitative analysis problems under finite-memory strategies for POMDPs with parity objectives
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