Luc Jaulin’s research while affiliated with National Institute of Advanced Technologies of Brittany and other places

In this paper, we give a control approach to follow a trajectory for a Dubins car controlling the heading independently. The difficulty is that the Dubins car should have a heading corresponding to the argument of the vector speed of the vehicle. This non holonomic constraint can be relaxed thanks to a specific control which uses Lie brackets. We will show such a control will allow us, at least from a theoretical point of view, to control independently the moving position of the car and the heading.

In engineering, models are often used to represent the behavior of a system. Estimators are then needed to approximate the values of the model's parameters based on observations. This approximation implies a difference between the values predicted by the model and the observations that have been made. It creates an uncertainty that can lead to dangerous decision making. Interval analysis tools can be used to guarantee some properties of an estimator, even when the estimator itself doesn't rely on interval analysis (Adam, 2019) (Adam, 2015). This paper contributes to this dynamic by proposing an interval-based and guaranteed method to validate a nonlinear estimator. It is based on the Moore-Skelboe algorithm (van Emden, 2004). This method returns a guaranteed maximum error that the estimator will never exceed. We will show that we can guarantee properties even when working with non-guaranteed estimators such as neural networks.

This paper proposes a new interval-based contractor for nonlinear equations which is minimal when dealing with narrow boxes. The method is based on the centered form classically used by interval algorithms combined with a Gauss Jordan band diagonalization preconditioning. As an illustration in stability analysis, we propose to compute the set of all parameters of a characteristic function of linear time-delayed equations which have at least one zero in the imaginary axis. Our approach is able compute a guaranteed and accurate enclosure of the solution set faster than existing approaches.

Localization tasks, generally modeled as Constraint Satisfaction Problem (CSP), are recurring problems in mobile robotics. Known approaches rely on software libraries which all have their advantages but also their limitations, among which non-optimal computing performances. This paper proposes a different approach which consists in extending the RISC-V ISA to provide hardware support for interval primitives.

Contractor algebra is used to characterize a set defined as a composition of sets defined by inequalities. It mainly uses interval methods combined with constraint propagation. This algebra includes the classical operations we have for sets such as the intersection, the union and the inversion. Now, it does not include the complement operator. The reason for this is probably related to the interval arithmetic itself. In this paper, we show that if we change the arithmetic used for intervals adding a single flag, similar to not a number, we are able to include easily the complement in the algebra of contractors.

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.