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Set computation methods have been widely used to compute reachable sets, design invariant sets and estimate system state for dynamic systems. The wrapping effect of such set computation methods plays an essential role in the accuracy of their solutions. This paper studies the wrapping effect of existing interval, zonotopic and polytopic set computation methods and proposes novel approaches to reduce the wrapping effect for these set computation methods based on the task of computing the dynamic evolution of a nonlinear uncertain discrete-time system with a set as the initial state. The proposed novel approaches include the partition of a polytopic set via Delaunay triangulation and also the representation of a polytopic set by the union of small zonotopes for the following set propagation. The proposed novel approaches with the reduced wrapping effect has been further applied to state estimation of a nonlinear uncertain discrete-time system with improved accuracy. Similar to bisection for interval and zonotopic sets, Delaunay triangulation has been introduced as a set partition tool for polytopic sets, which has opened new research directions in terms of novel set partition, set representation and set propagation for reducing the wrapping effect of set computation. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of platooning control for a fleet of sailboats. A quadrilateral path is proposed to avoid going into the wind. A tack strategy is defined to go front the wind, stay in a short corridor and regulate the sailboat acceleration, which is a challenging task in comparison to autonomous underwater vehicles (AUVs) or surface vehicles that can use motors for such regulation. Desired acceleration which guarantees to reach the platooning has been derived and validated. A method of regulating the sail angle using a proportional command is proposed to control the sailboat acceleration. Simulation results demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper deals with the simultaneous localization and mapping problem (SLAM) for a robot. The robot has to build a map of its environment while localizing itself using a partially built map. It is assumed that (i) the map is made of point landmarks, (ii) the landmarks are indistinguishable, (iii) the only exteroceptive measurements correspond to the distance between the robot and the landmarks. This paper shows that SLAM can be cast into a constraint network the variables of which being trajectories, digraphs and subsets of $\mathbb {R}^{n}.$ Then, we show how constraint propagation can be extended to deal with such generalized constraint networks. As a result, due to the redundancy of measurements of SLAM, we demonstrate that a constraint-based approach provides an efficient backtrack-free algorithm able to solve our SLAM problem in a guaranteed way. [ABSTRACT FROM AUTHOR]

In this paper, we consider the resolution of non-linear constraint satisfaction problems where the variables of the systems are trajectories (functions from $${\mathbb{R}}$$ to $${\mathbb{R}^{n}}$$ ). We introduce the notion of tubes as intervals of functions, for which the lower and upper bounds are trajectories with respect to the inclusion. We then define basic operators and prove propositions verified by tubes. We show the possibility to build contractors on tubes and propagate constraints to solve problems involving time-dependant functions as the unknown variables. We show that the approach is particularly powerful when inter-temporal equations (e.g. delays) are involved. Finally, in order to illustrate the principle and efficiency of the approach, several test cases are provided. [ABSTRACT FROM AUTHOR]

This paper addresses the common issue of locating an Underwater Vehicle. Usually, the positioning of a vehicle is based on the propagation of electromagnetic waves, using systems such as the Global Positioning System. However, water, and particularly salty water, makes the use of electromagnetic waves impractical due to the attenuation caused by the high conductivity of the medium. Hence, the most reliable way to transmit information underwater is by using sound waves and many technologies have emerged to solve the positioning problem in this way. Technologies such as Long BaseLine (LBL), Short BaseLine (SBL) and Ultra-Short BaseLine (USBL) are the most frequently used underwater. These technologies are based on the use of multiple emitters in the case of LBL and SBL, or multiple receivers in the case of USBL. This paper describes a way of finding a vehicle location, on-board, based on the measurement at the vehicle by a single receiver of the phase of an acoustic sine wave transmitted from a single emitter that is at a fixed and known location. The method also uses other proprioceptive measurements: vehicle's velocity and heading. An algorithm based on contractors and bisections scatters the solution space searching for all possible solutions (positions in this case) to the set of equations. Moreover, this paper introduces the Time Constraint Satisfaction Problem. Indeed, the proposed algorithm does not compute the solutions from measurements at a single point in time, rather it uses a set of measurements taken over a time window and stored in a buffer. As a result, the location is not only known at the latest instant but the past locations can be tracked back over the length of the chosen time window. [ABSTRACT FROM AUTHOR]

This paper proposes a set-membership approach to characterize the kernel of an interval-valued function. In the context of a bounded-error estimation, this formulation makes it possible to embed all uncertainties of the problem inside the interval function and thus to avoid bisections with respect to all these uncertainties. To illustrate the principle of the approach, two testcases taken from robotics will be presented. The first testcase deals with the characterization of all loops of a mobile robot from proprioceptive measurements only. The second testcase is the localization of a robot from range-only measurements. [ABSTRACT FROM AUTHOR]

This paper proposes a new set-membership state estimator for estimating the state vector of a nonlinear dynamic robot. The method combines a symbolic technique based on flatness concepts with rigorous numerical methods based on interval analysis. Two testcases related to the state estimation of a sailboat robot are proposed to illustrate the principle and the efficiency of the approach. [ABSTRACT FROM AUTHOR]

In this article we present a new approach for object recognition in a robotic underwater context. Color is an attractive feature because of its simplicity and its robustness to scale changes, object positions and partial occlusions. Unfortunately, in the underwater medium, the colors are modified by attenuation and are not constant with the distance. To perform a color-based recognition of an object, we develop an algorithm robust with respect to the attenuation which takes into account the light modification during its path between the light source and the camera. Therefore, a given underwater object can be identified in an image by detecting all the colors compatible with its prior known color. Our method is fast, robust and needs a very few computers resources. We successfully used it when experimenting in the sea using a system we built. It is suitable for robotic applications where computers resources are limited and shared between various embedded devices. This novel concept enables the use of the color in many applications such as target interception, object tracking or obstacle detection. [ABSTRACT FROM AUTHOR]

In this paper, we consider the resolution of constraint satisfaction problems in the case where the variables of the problem are subsets of $${\mathbb{R}^{n}}$$ . In order to use a constraint propagation approach, we introduce set intervals (named i-sets), which are sets of subsets of $${\mathbb{R}^{n}}$$ with a lower bound and an upper bound with respect to the inclusion. Then, we propose basic operations for i-sets. This makes possible to build contractors that are then used by the propagation to solve problem involving sets as unknown variables. In order to illustrate the principle and the efficiency of the approach, a testcase is provided. [ABSTRACT FROM AUTHOR]

The problem of characterizing in a guaranteed way the set of all feasible set-points of a control problem is known to be difficult. In the present work, the problem to be solved involves non-linear equality constraints with variables affected by logical quantifiers. This problem is not solvable by current symbolic methods like quantifier elimination, which is commonly used for solving this class of problems. We propose the utilization of guaranteed set-computation techniques based on interval analysis, in particular a solver referred to as Quantified Set Inversion (QSI). As an application example, the problem of simultaneously controlling the speed and the orientation of a sailboat is presented. For this purpose, the combination of QSI solver and feedback linearization techniques is employed. [ABSTRACT FROM AUTHOR]

In this paper, we show that the problem of computing the smallest interval submatrix of a given interval matrix [A] which contains all symmetric positive semi-definite (PSD) matrices of [A], is a linear matrix inequality (LMI) problem, a convex optimization problem over the cone of positive semidefinite matrices, that can be solved in polynomial time. From a constraint viewpoint, this problem corresponds to projecting the global constraint PSD (A) over its domain [A]. Projecting such a global constraint, in a constraint propagation process, makes it possible to avoid the decomposition of the PSD constraint into primitive constraints and thus increases the efficiency and the accuracy of the resolution. [ABSTRACT FROM AUTHOR]

This paper deals with the minimax parameter estimation of nonlinear parametric models from experimental data. Taking advantage of the special structure of the minimax problem, a new efficient and reliable algorithm based on interval constraint propagation is proposed. As an illustration, the ill-conditioned problem of estimating the parameters of a two-exponential model is considered. [ABSTRACT FROM AUTHOR]

In this paper, the problem of interest is to find a path with given endpoints such that the path lies inside a compact set S given by nonlinear inequalities. The proposed approach uses interval analysis for characterizing S by subpavings (union of boxes) and graph algorithms for finding short feasible paths. As an illustration, the problem of finding collision-free paths for a polygonal rigid object through a space that is cluttered with segment obstacles is considered. [ABSTRACT FROM AUTHOR]

This paper deals with the determination of the position and orientation of a mobile robot from distance measurements provided by a belt of onboard ultrasonic sensors. The environment is assumed to be two-dimensional, and a map of its landmarks is available to the robot. In this context, classical localization methods have three main limitations. First, each data point provided by a sensor must be associated with a given landmark. This data-association step turns out to be extremely complex and time-consuming, and its results can usually not be guaranteed. The second limitation is that these methods are based on linearization, which makes them inherently local. The third limitation is their lack of robustness to outliers due, e.g., to sensor malfunctions or outdated maps. By contrast, the method proposed here, based on interval analysis, bypasses the data-association step, handles the problem as nonlinear and in a global way and is (extraordinarily) robust to outliers. [ABSTRACT FROM AUTHOR]

Discrete-event systems are driven by events and generate events. To describe their evolution, the dater approach associate to each event a sequence of dates, namely a dater, corresponding to the dates at which the event occurs. In this paper, we show that for a large class of discrete-event systems, the dater approach makes it possible to cast the characterization of the set of all parameters that are consistent with some collected dater, in a bounded-error context, into a set-inversion framework. Set inversion consists of characterizing the reciprocal image of a given set by a known function. Provided that an inclusion function is known for the function to be inverted, the characterization can be performed by the interval-based algorithm SIVIA. A short presentation of this algorithm is recalled in this paper. The approach is illustrated through three examples. [ABSTRACT FROM AUTHOR]