Computing the Flat Outputs of Engel Di erential Systems The Case Study of the Bi - steerable Car

Flatness is an interesting structural property of many engineering systems. Typically, the knowledge of the Flat Outputs of a system allows the design of open loop control and helps the design of control loops. When the literature includes many works on nding families of at systems or proposing tools to check the atness of a system, there has been very few works on the actual computation of the Flat Outputs which remains an open practical problem. In this paper, we present a necessary condition for the at coordinates change of any system represented by two di erential 1forms in a state space of dimension 4. This condition is expressed by a partial di erential equation and implies an approach to help the computation of the at outputs. Then, we apply our approach to a speci c system, namely the Bi-steerable car for which we explicitely compute the at outputs. Hence, we solve the problem of the open loop control design for bi-steerable cars which was our initial and main motivation.