Marius Kloetzer

A Fully Automated Framework for Control of Linear Systems from Temporal Logic Specifications

We consider the following problem: given a linear system and a linear temporal logic (LTL) formula over a set of linear predicates in its state variables, find a feedback control law with polyhedral bounds and a set of initial states so that all trajectories of the closed loop system satisfy the formula. Our solution to this problem consists of three main steps. First, we partition the state space in accordance with the predicates in the formula, and construct a transition system over the partition quotient, which captures our capability of designing controllers. Second, using a procedure resembling model checking, we determine runs of the transition system satisfying the formula. Third, we generate the control strategy. Illustrative examples are included.

Automatic Deployment of Distributed Teams of Robots From Temporal Logic Motion Specifications

We present a computational framework for automatic synthesis of decentralized communication and control strategies for a robotic team from global specifications, which are given as temporal and logic statements about visiting regions of interest in a partitioned environment. We consider a purely discrete scenario, where the robots move among the vertices of a graph. However, by employing recent results on invariance and facet reachability for dynamical systems in environments with polyhedral partitions, the framework from this paper can be directly implemented for robots with continuous dynamics. While allowing for a rich specification language and guaranteeing the correctness of the solution, our approach is conservative in the sense that we might not find a solution, even if one exists. The overall amount of required computation is large. However, most of it is performed offline before the deployment. Illustrative simulations and experimental results are included.

Temporal Logic Planning and Control of Robotic Swarms by Hierarchical Abstractions

We develop a hierarchical framework for planning and control of arbitrarily large groups (swarms) of fully actuated robots with polyhedral velocity bounds moving in polygonal environments with polygonal obstacles. At the first level of hierarchy, we aggregate the high-dimensional control system of the swarm into a small-dimensional control system capturing its essential features. These features describe the position of the swarm in the world and its size. At the second level, we reduce the problem of controlling the essential features of the swarm to a model-checking problem. In the obtained hierarchical framework, high-level specifications given in natural language, such as linear temporal logic formulas over linear predicates in the essential features, are automatically mapped to provably correct robot control laws. For the particular case of an abstraction based on centroid and variance, we show that swarm cohesion, interrobot collision avoidance, and environment containment can also be specified and automatically guaranteed in our framework. The obtained communication architecture is centralized

A fully automated framework for control of linear systems from LTL specifications

We consider the following problem: given a linear system and an LTL−−X formula over a set of linear predicates in its state variables, find a feedback control law with polyhedral bounds and a set of initial states so that all trajectories of the closed loop system satisfy the formula. Our solution to this problem consists of three main steps. First, we partition the state space in accordance with the predicates in the formula and construct a transition system over the partition quotient, which captures our capability of designing controllers. Second, using model checking, we determine runs of the transition system satisfying the formula. Third, we generate the control strategy. Illustrative examples are included.

Automatic Deployment of Robotic Teams

A major goal in robot motion planning and control is to be able to specify a task in a high-level, expressive language and have the robot(s) to automatically convert the specification into a set of low-level primitives, such as feedback controllers and communication protocols, to accomplish the task. The robots can vary from manipulator arms used in manufacturing or surgery, to autonomous vehicles used in search and rescue or in planetary exploration, and to smart wheel chairs for disabled people. They are subject to mechanical constraints (e.g., a carlike robot cannot move sideways,an airplane cannot stop in place) and have limited computation, sensing, and communication capabilities. The environments can be cluttered with possibly moving and shape-changing obstacles and can con tain dynamic (moving, appearing, or disappearing) targets. One of the major challenges in this area is the development of a computationally efficient frame work accommodating both the robot constraints and the complexity of the environment, while, at the same time, allowing for a large spectrum of task specifications.

An Automated Framework for Formal Verification of Timed Continuous Petri Nets

In this paper, we develop an automated framework for formal verification of timed continuous Petri nets (ContPNs). Specifically, we consider two problems: (1) given an initial set of markings, construct a set of unreachable markings and (2) given a Linear Temporal Logic (LTL) formula over a set of linear predicates in the marking space, construct a set of initial states such that all trajectories originating there satisfy the LTL specification. The starting point for our approach is the observation that a ContPN system can be expressed as a Piecewise Affine (PWA) system with a polyhedral partition. We propose an iterative method for analysis of PWA systems from specifications given as LTL formulas over linear predicates. The computation mainly consists of polyhedral operations and searches on graphs, and the developed framework was implemented as a freely downloadable software tool. We present several illustrative numerical examples.

Dealing with Nondeterminism in Symbolic Control

Abstractions (also called symbolic models) are simple descriptions of continuous and hybrid systems that can be used in analysis and control. They are usually constructed in the form of transition systems with finitely many states. Such abstractions offer a very attractive approach to deal with complexity, while at the same time allowing for rich specification languages. Recent results show that, through the abstraction process, the resulting transition systems can be nondeterministic (i.e.,if an input is applied in a state, several next states are possible). However, the problem of controlling a nondeterministic transition system from a rich specification such as a temporal logic formula is not well understood. In this paper, we develop a control strategy for a nondeterministic transition system from a specification given as a Linear Temporal Logic formula with a deterministic Buchi generator. Our solution is inspired by LTL games on graphs, is complete, and scales polynomially with the size of the Buchi automaton. An example of controlling a linear system from a specification given as a temporal logic formula over the regions of its triangulated state space is included for illustration.

Hierarchical abstractions for robotic swarms

We develop a hierarchical framework for planning and control of arbitrarily large groups of fully actuated robots with polyhedral velocity bounds (swarm) moving in polygonal environments with polygonal obstacles. At the first level of hierarchy, we aggregate the high dimensional control system of the swarm into a small dimensional control system capturing its essential features. These features describe the position of the swarm in the world and its size. At the second level, we reduce the problem of controlling the essential features of the swarm to a model checking problem. In the obtained hierarchical framework, high level specifications given in natural language such as linear temporal logic formulas over linear predicates in the essential features are automatically mapped to probably correct robot control laws

Multi-robot deployment from LTL specifications with reduced communication

In this paper, we develop a computational framework for fully automatic deployment of a team of unicycles from a global specification given as an LTL formula over some regions of interest. Our hierarchical approach consists of four steps: (i) the construction of finite abstractions for the motions of each robot, (ii) the parallel composition of the abstractions, (iii) the generation of a satisfying motion of the team; (iv) mapping this motion to individual robot control and communication strategies. The main result of the paper is an algorithm to reduce the amount of inter-robot communication during the fourth step of the procedure.

Trajectory planning for a car-like robot by environment abstraction

This work proposes a fully automatic planning and control strategy for solving a navigation problem for a car-like robot with non-negligible size and constraint control inputs. The approach uses cell decompositions for abstracting the robot behavior to a final state description on which the planning problem is solved. As part of the solution, we obtain a ranking of different cell decomposition types that are suitable for planning the motion of a car-like robot. The originality of our method mainly comes from the iterative procedure for finding a feasible path based on cell decompositions. Although the approach is not complete, it benefits from a fully-automatic planning and control strategy and from a reduced computational complexity. The solution is implemented as a user-friendly freely-downloadable MATLAB package. This may come as a handy tool for employing the strategy for automatic planning and control of a car-like robot in a real scenario.