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

Decidability of difference logics with unary predicates

peer reviewedWe investigate the decidability of a family of logics mixing difference-logic constraints and unary uninterpreted predicates. The focus is set on logics whose domain of interpretation is R, but the language has a recognizer for integer values. We first establish the decidability of the logic allowing unary uninterpreted predicates, order constraints between real and integer variables, and difference-logic constraints between integer variables. Afterwards, we prove the undecidability of the logic where unary uninterpreted predicates and difference-logic constraints between real variables are allowed

Decidability of Difference Logic over the Reals with Uninterpreted Unary Predicates

peer reviewedFirst-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

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