The bringing of two rigid bodies into collision-free contact by bounded controls in a finite time

The control problem of moving a rigid body onto the surface of another rigid body in such a way that no collision occurs in investigated. For this, phase constraints must be satisfied in the sense that the surface of one body must not overlap the other, and here an important condition must be met: contact of the bodies is ensured by bounded controls and in a finite time. No impact of the rigid bodies occurs at the instant of contact because a strict rule is observed: if any point of one body lies on the surface of the other, then the velocity of the point is directed along this surface (or away from it). To observe this rule, special controls are used. These controls realize assigned accurate values of the coordinates and velocities of the mechanical system in a finite time.