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Correctness and Safety in Planning and Control via State-Space Partitions and Barrier Functions

Time: Fri 2023-05-05 14.00

Location: Kollegiesalen, Brinellvägen 8, Stockholm

Video link:

Language: English

Subject area: Applied and Computational Mathematics, Optimization and Systems Theory

Doctoral student: Xiao Tan , Reglerteknik, Division of Decision and Control Systems

Opponent: Professor Samuel Coogan, Georgia Institute of Technology, Atlanta, GA, USA

Supervisor: Professor Dimos V. Dimarogonas, Reglerteknik

QC 20230412


Autonomous systems have become increasingly prevalent in various industries, ranging from household cleaning robots to line inspection drones and copilot vehicles. Ensuring real-time safety is becoming a critical issue when the environment is rapidly changing. Moreover, most of these autonomous systems are still pale in satisfying complex nested temporal logic tasks. Possible solutions to these problems include correct-by-construction and safe-by-construction planning and control algorithms, since they can provide theoretical correctness and safety guarantees for autonomous systems. This thesis proposes several techniques for developing correct- and safe-by-construction planning and control algorithms, exploring both theoretical guarantees and practical implementations. 

One missing component of the existing correct-by-construction algorithms is that abstraction algorithms, which are essential for automaton-based task planning, are largely limited to linear systems associated with polytopic partitionings of the state space. State-space partitioning and control problem for systems on a curved manifold is relatively unexplored. The first part of the thesis is devoted to alleviating this problem. In particular, we consider $SO(3)$ and $\mathbb{S}^2 $, the two most commonly encountered manifolds in mechanical systems, and propose several approaches to address the partitioning and control problem, which in principle could be generalized to other manifolds.

In the second part of the thesis, various theoretical and practical issues related to the emerging control barrier functions (CBFs) approach are investigated. CBFs provides a modular, easy-to-implement framework to render an existing control scheme safe.It is known that CBF for system safety can be viewed as an extension of the classic control Lyapunov function (CLF) approach for system stabilization. Despite their similarity, CBFs have many unique research problems of their own. In this part, we will investigate the construction and theoretical guarantees for high-order constraints, where the asymptotic stability property of the safe set is established. Another result is on the safe stabilization problem using CLF-CBF-induced quadratic programs, where we demonstrate that the undesired equilibrium points of the closed-loop system can be removed given certain easy-to-check conditions. Control design and compatibility issues are also investigated when multiple constraints are present. For multi-agent systems where the safety constraint is coupled, a distributed implementation using only local information is investigated, as well as an experimental validation on a multiple mobile robot platform. Finally, a CBF-based abstraction-free control synthesis scheme is proposed for general nonlinear systems under nested temporal logic tasks with provable correctness guarantees. We demonstrate how these barrier functions are constructed that relate to the temporal logic specifications and system dynamics.