Efficient Path Interpolation and Speed Profile Computation for Nonholonomic Mobile Robots

This paper studies path synthesis for nonholonomic mobile robots moving in two-dimensional space. We first address the problem of interpolating paths expressed as sequences of straight line segments, such as those produced by some planning algorithms, into smooth curves that can be followed without stopping. Our solution has the advantage of being simpler than other existing approaches, and has a low computational cost that allows a real-time implementation. It produces discretized paths on which curvature and variation of curvature are bounded at all points, and preserves obstacle clearance. Then, we consider the problem of computing a time-optimal speed profile for such paths. We introduce an algorithm that solves this problem in linear time, and that is able to take into account a broader class of physical constraints than other solutions. Our contributions have been implemented and evaluated in the framework of the Eurobot contest

Min Max Generalization for Two-stage Deterministic Batch Mode Reinforcement Learning: Relaxation Schemes

We study the minmax optimization problem introduced in [22] for computing policies for batch mode reinforcement learning in a deterministic setting. First, we show that this problem is NP-hard. In the two-stage case, we provide two relaxation schemes. The first relaxation scheme works by dropping some constraints in order to obtain a problem that is solvable in polynomial time. The second relaxation scheme, based on a Lagrangian relaxation where all constraints are dualized, leads to a conic quadratic programming problem. We also theoretically prove and empirically illustrate that both relaxation schemes provide better results than those given in [22]

Symbolic methods and automata

peer reviewe

Decidability of Difference Logic over the Reals with Uninterpreted Unary Predicates

First-order logic fragments mixing quantifiers, arithmetic, and uninterpreted predicates are often undecidable, as is, for instance, Presburger arithmetic extended with a single uninterpreted unary predicate. In the SMT world, difference logic is a quite popular fragment of linear arithmetic which is less expressive than Presburger arithmetic. Difference logic on integers with uninterpreted unary predicates is known to be decidable, even in the presence of quantifiers. We here show that (quantified) difference logic on real numbers with a single uninterpreted unary predicate is undecidable, quite surprisingly. Moreover, we prove that difference logic on integers, together with order on reals, combined with uninterpreted unary predicates, remains decidable.Comment: This is the preprint for the submission published in CADE-29. It also includes an additional detailed proof in the appendix. The Version of Record of this contribution will be published in CADE-2

Implicit Real Vector Automata

peer reviewedThis paper addresses the symbolic representation of non-convex real polyhedra, i.e., sets of real vectors satisfying arbitrary Boolean combinations of linear constraints. We develop an original data structure for representing such sets, based on an implicit and concise encoding of a known structure, the Real Vector Automaton. The resulting formalism provides a canonical representation of polyhedra, is closed under Boolean operators, and admits an efficient decision procedure for testing the membership of a vector

Robot weed killers - no pain more gain

Weed destruction plays a significant role in crop production, and its automation has both economic and environmental benefits by minimizing the usage of chemicals in the fields. Our aim is to design a small low-cost versatile robot allowing the destruction of weeds that lie between the crop rows by navigating in the field autonomously. Major challenges foreseen are: mapping the unknown geometry of the field, high-level planning of efficient and complete coverage of the field, and controlling the low-level operations of the robot. Traditionally, sensors like odometer have been used for localisation of robots but without much success in real-world scenarios. Specialized sensors like cameras will therefore be investigated and the plethora of image recognition algorithms will be explored and fine-tuned to enable Simultaneous Localisation And Mapping (SLAM) even on resource constrained robotic platforms. Vision-based localisation is not always viable because of the varying weather conditions of the environment and to overcome that, intelligent stochastic data fusion and machine learning algorithms will be utilized to combine data from heterogenous sensor. The image sensors for localisation will be re-used to differentiate crop rows from the weeds, which are cut when they grow. Finally, logics and reinforcement learning techniques will be explored, to exploit the generated map of the field and other sensorial information, to efficiently plan and execute weed elimination

Number-Set Representations for Infinite-State Verification

In order to compute the reachability set of infinite-state models, one needs a technique for exploring infinite sequences of transitions in finite time, as well as a symbolic representation for the finite and infinite sets of configurations that are to be handled. The representation problem can be solved by automata-based methods, which consist in representing a set by a finite-state machine recognizing its elements, suitably encoded as words over a finite alphabet. Automata-based set representations have many advantages: They are expressive, easy to manipulate, and admit a canonical form. In this survey, we describe two automata-based structures that have been developed for representing sets of numbers (or, more generally, of vectors): The Number Decision Diagram (NDD) for integer values, and the Real Vector Automaton (RVA) for real numbers. We discuss the expressiveness of these structures, present some construction algorithms, and give a brief introduction to some related acceleration techniques

Model Checking in Practice: An Analysis of the ACCESS.bus Protocol using SPIN

peer reviewedThis paper presents a case study of the use of model checking for analyzing an industrial protocol, the ACCESS.bus protocol. Our analysis of this protocol was carried out using SPIN, an automated verification system which includes an implementation of model-checking algorithms. A model of the protocol was developed, and properties expressed by linear-time temporal-logic formulas were checked on this model. This analysis revealed subtle flaws in the design of the protocol. Developers who worked on implementations of ACCESS.bus were unaware of these flaws at a very late stage of their development process. We also present suggestions for solving the detected problems

Efficient Path Planning for Nonholonomic Mobile Robots

This work addresses path planning for nonholonomic robots moving in two-dimensional space. The problem consists in computing a sequence of line segments that leads from the current configuration of the robot to a target location, while avoiding a given set of obstacles. We describe a planning algorithm that has the advantage of being very efficient, requiring less of one millisecond of CPU time for the case studies that we have considered, and produces short paths. Our method relies on a search in a Voronoi graph that characterizes the possible ways of moving around obstacles, followed by a string-pulling procedure aimed at improving the resulting path