Mission Accomplished: An Introduction to Formal Methods in Mobile Robot Motion Planning and Control

A new trend in the robotic motion planning literature is to use formal methods, like model checking, reactive synthesis and supervisory control theory, to automatically design controllers that drive a mobile robot to accomplish some high level missions in a guaranteed manner. This is also known as the correct-by-construction method. The high level missions are usually specified as temporal logics, particularly as linear temporal logic formulas, due to their similarity to human natural languages. This paper provides a brief overview of the recent developments in this newly emerged research area. A number of fundamental topics, such as temporal logic, model checking, bisimulation quotient transition systems and reachability controller design are reviewed. Additionally, the key challenges and possible future directions in this area are briefly discussed with references given for further reading.

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The PETLON Algorithm to Plan Efficiently for Task-Level-Optimal Navigation

Journal of Artificial Intelligence Research ◽

10.1613/jair.1.12181 ◽

2020 ◽

Vol 69 ◽

pp. 471-500

Author(s):

Shih-Yun Lo ◽

Shiqi Zhang ◽

Peter Stone

Keyword(s):

Mobile Robot ◽

Motion Planning ◽

Mobile Robots ◽

Large Scale ◽

Accurate Estimate ◽

Indoor Environments ◽

Task Planning ◽

Trade Offs ◽

High Level ◽

Task Level

Intelligent mobile robots have recently become able to operate autonomously in large-scale indoor environments for extended periods of time. In this process, mobile robots need the capabilities of both task and motion planning. Task planning in such environments involves sequencing the robot’s high-level goals and subgoals, and typically requires reasoning about the locations of people, rooms, and objects in the environment, and their interactions to achieve a goal. One of the prerequisites for optimal task planning that is often overlooked is having an accurate estimate of the actual distance (or time) a robot needs to navigate from one location to another. State-of-the-art motion planning algorithms, though often computationally complex, are designed exactly for this purpose of finding routes through constrained spaces. In this article, we focus on integrating task and motion planning (TMP) to achieve task-level-optimal planning for robot navigation while maintaining manageable computational efficiency. To this end, we introduce TMP algorithm PETLON (Planning Efficiently for Task-Level-Optimal Navigation), including two configurations with different trade-offs over computational expenses between task and motion planning, for everyday service tasks using a mobile robot. Experiments have been conducted both in simulation and on a mobile robot using object delivery tasks in an indoor office environment. The key observation from the results is that PETLON is more efficient than a baseline approach that pre-computes motion costs of all possible navigation actions, while still producing plans that are optimal at the task level. We provide results with two different task planning paradigms in the implementation of PETLON, and offer TMP practitioners guidelines for the selection of task planners from an engineering perspective.

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Model Checking Temporal Logic Formulas Using Sticker Automata

BioMed Research International ◽

10.1155/2017/7941845 ◽

2017 ◽

Vol 2017 ◽

pp. 1-33 ◽

Cited By ~ 3

Author(s):

Weijun Zhu ◽

Changwei Feng ◽

Huanmei Wu

Keyword(s):

Model Checking ◽

Temporal Logic ◽

Complex Problem ◽

Finite State Automaton ◽

Dna Molecules ◽

Single Stranded Dna ◽

Finite State ◽

Input Strings ◽

Logic Model Checking ◽

The Given

As an important complex problem, the temporal logic model checking problem is still far from being fully resolved under the circumstance of DNA computing, especially Computation Tree Logic (CTL), Interval Temporal Logic (ITL), and Projection Temporal Logic (PTL), because there is still a lack of approaches for DNA model checking. To address this challenge, a model checking method is proposed for checking the basic formulas in the above three temporal logic types with DNA molecules. First, one-type single-stranded DNA molecules are employed to encode the Finite State Automaton (FSA) model of the given basic formula so that a sticker automaton is obtained. On the other hand, other single-stranded DNA molecules are employed to encode the given system model so that the input strings of the sticker automaton are obtained. Next, a series of biochemical reactions are conducted between the above two types of single-stranded DNA molecules. It can then be decided whether the system satisfies the formula or not. As a result, we have developed a DNA-based approach for checking all the basic formulas of CTL, ITL, and PTL. The simulated results demonstrate the effectiveness of the new method.

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Interval Temporal Logic Model Checking: The Border Between Good and Bad HS Fragments

Automated Reasoning - Lecture Notes in Computer Science ◽

10.1007/978-3-319-40229-1_27 ◽

2016 ◽

pp. 389-405 ◽

Cited By ~ 5

Author(s):

Laura Bozzelli ◽

Alberto Molinari ◽

Angelo Montanari ◽

Adriano Peron ◽

Pietro Sala

Keyword(s):

Model Checking ◽

Temporal Logic ◽

Logic Model ◽

Interval Temporal Logic ◽

Logic Model Checking

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Kinodynamic Motion Planning for a Two-Wheel-Drive Mobile Robot

Handbook of Research on Biomimetics and Biomedical Robotics - Advances in Computational Intelligence and Robotics ◽

10.4018/978-1-5225-2993-4.ch014 ◽

2018 ◽

pp. 332-346

Author(s):

Kimiko Motonaka

Keyword(s):

Mobile Robot ◽

Motion Planning ◽

Invariant Manifold ◽

Nonholonomic System ◽

Control Method ◽

Controller Design ◽

Dynamic Control ◽

Target Position ◽

Arbitrary Point ◽

Wheel Drive

Since a nonholonomic system such as a robot with two independent driving wheels includes complicated nonlinear terms generally, it is hard to realize a stable and tractable controller design. However, about a dynamic control method for the motion planning, it is guaranteed that a nonholonomic-controlled object can always be converged to an arbitrary point using a control method based on an invariant manifold. Based on it, the method called “kinodynamic motion planning” was proposed to converge the states of the two-wheeled mobile robot to the arbitrary target position while avoiding obstacles by combining the control based on the invariant manifold and the HPF. In this chapter, how to combine the invariant manifold control and the concept of the HPF is explained in detail, and the usefulness of the proposed approach is verified through some simulations.

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