1. A method to assist in the driving of a vehicle (A) in motion moving along an initial trajectory (TI 1 , TI 2 ), in an environment containing at least one obstacle (O 1 to O 4 ) having to be avoided, whereby the following successive sequence of operations is carried out automatically and repetitively: A/ a check is carried out, while the vehicle is moving (A), to see if at least one condition for modifying the trajectory because of an obstacle (O 1 to O 4 ) is fulfilled; and B/ if such a condition is fulfilled: a) a criterion CR is calculated using the following expression: 
 CR=R 2 +a 1 .D 2 +a 2 .T 2 in which: R is an evaluation of a risk of collision with the obstacle; D is an evaluation of a deviation relative to the initial trajectory; T is the time needed to rejoin this initial trajectory; and a 1 and a 2 are weighting values; b) a value E is determined which verifies the following equation: 
 E=∂CR/∂s∂q in which: s is a curvilinear abscissa of the vehicle (A) along the initial trajectory; q represents a turn parameter of a control element of the vehicle (A) used to modify said initial trajectory so as to follow said avoidance trajectory; and E represents the derivative of the criterion CR in relation both to said curvilinear abscissa s and to said turn parameter q; and values of the turn parameter q are determined for which said value E is zero, said values being used to obtain an avoidance trajectory with which to reach the planned destination while avoiding said obstacle; and c) the duly determined values are used, in conjunction with the corresponding curvilinear abscissi, to assist in the driving of the vehicle (A).