## Section: Overall Objectives

### Overall Objectives

The COPRIN project-team
scientific objective is to develop and implement systems solving
algorithms based on constraints propagation methods, interval
analysis and symbolic computation, with interval arithmetic as the
primary tool. The academic goals of these algorithms is to provide *certified solutions* to generic problems (e.g. to calculate all solutions
of a system of
equations within a search space) or to manage the *uncertainties*
of the problems (e.g. to provide an enclosure of all solutions of a
system of equations whose coefficients are intervals). These academic
goals may also be declined in applicative goals. For example we may
determine a domain that describes
all possible dimensions of a mechanism that has to satisfy a set of
performance requirements. Given this domain it will be possible
to determine nominal dimensions for the mechanism so that even if
there are bounded variations between the real dimensions and the
nominal ones, then the real mechanism will still satisfy the
requirements: hence we will be able to manage manufacturing
uncertainties for the real process.

Our research aims to develop algorithms that can be used for any problem or are specific to a given class of problems, especially problems that are issued from application domains for which we have an internal expertise (such as mechanism theory and robotics).

A key point of these algorithms is that they rely heavily on symbolic pre-processing and formal calculation in order to improve the efficiency of the problem at hand. Our long term goal is to be able to synthesize automatically a specific solver according to the structure of the problem that has to be managed.

Implementation of the algorithms will be performed within the
framework of general purpose software such as `Scilab` , `Maple` , `Mathematica` and will be based
on the already existing library `ALIAS` , that are
still being developed mostly for internal use.

Since a theoretical complexity analysis of interval analysis based
solving algorithms is
usually extremely difficult, the efficiency of the algorithm is
systematically
experimentally evaluated
through `ALIAS` on various realistic test examples.

Dissemination is also an essential component of our activity because interval analysis based methods are not sufficiently known in the engineering and academic communities.

The study of robotics problems is a major focus point of the COPRIN project. In this field our objectives are:

to develop methods for the analysis of existing robots, taking into account uncertainties in their modeling that are inherent to such mechatronic devices

to develop a design methodology for complex robotic systems that guarantees a required level of performance for the

**real**robot. Our methodology aims at providing not a single design solution but a set of solutions offering various compromises among the performances. Furthermore the solutions will be robust with respect to errors in the realization of the real robot (e.g. due to manufacturing tolerances and control errors)

Experimental work and the development of our own prototypes (see section 6.2.1.4 ) are strategic for the project as they allow us to validate our theoretical work and to discover new problems that will feed in the long term the theoretical analysis developed by the team members.

We have started since five years a strategic move toward **assistance robots** (see section
6.2.1.3 ).
Our long term goal will be to provide
robotized devices for assistance, including smart objects, that may
help disabled,
elderly and handicapped
people in their personal life. Our goals for these devices are that

they can be adapted to the end-user and to its everyday environment

they may be controlled through a large variety of simple interfaces

they may eventually be used to monitor the health status of the end-user in order to detect emerging pathologies

As this topic is very large and cannot be managed by a single project-team COPRIN has been one of the main proponant for the creation of the "Action d'Envergure National" PAL (Personnal Assistant Living), that has been accepted in 2011 and that is coordinated by D. Daney.

In summary COPRIN has two major research axes, interval analysis and robotics. The coherence of these axis is that interval analysis is a major tool to manage the uncertainties that are inherent to a robotized device, while robotics provides realistic problems which allow us to develop, test and improve interval analysis algorithms.