1. A mobile apparatus system made up of a first mobile apparatus and a second mobile apparatus each comprising a control device and having an operation controlled by the control device to autonomously move along a target trajectory representing changes in a target position defined in a two-dimensional model space, the control device including a first processing unit, a second processing unit, and a third processing unit, wherein in the i-th mobile apparatus (i=1, 2), the first processing unit recognizes the i-th mobile apparatus and a trajectory representing changes in position of the i-th mobile apparatus as a first spatial element and a first trajectory representing changes in a first position, respectively, in the model space, recognizes an object and a trajectory representing changes in position of the object as a second spatial element and a second trajectory representing changes in a second position, respectively, and recognizes the second spatial element continuously or intermittently expanded in accordance with the second trajectory as an expanded second spatial element, the second processing unit determines whether a safety condition is satisfied based on a recognition result by the first processing unit, the safety condition specifying that a possibility of contact between the first spatial element and the second spatial element is low, and on a condition that the second processing unit determines that the safety condition is not satisfied, the third processing unit searches for the target trajectory based on the recognition result by the first processing unit, the target trajectory allowing the first spatial element to avoid contact with the expanded second spatial element, in the first mobile apparatus, the control device causes the second mobile apparatus to recognize a part or a whole of the target trajectory searched for and determined by the third processing unit, and in the second mobile apparatus, the control device recognizes the part or the whole of the target trajectory of the first mobile apparatus, and based on this recognition result, the first processing unit recognizes the trajectory of the first mobile apparatus as the second trajectory, with the first mobile apparatus regarded as the object.