Plane Motions of a Body Controlled by Means of Internal Masses in the Presence of Dry Friction Between the Body and the Plane

This chapter addresses two-dimensional motions of capsule systems along a rigid horizontal plane in the presence of Coulomb's dry friction between the plane and the housing. It is required to transfer the system from a given initial position to a given final position with a desired orientation of the housing. For the case of a rectilinear motion, it is sufficient that the capsule robot have one internal body oscillating along a straight line parallel to the line of the motion of the robot. To perform a two-dimensional motion along a plane while changing the orientation of the housing a capsule robot must have a more complex structure containing several internal bodies or one internal body capable of moving along a curved trajectory the shape of which depends on the motion to be performed. Two types of mobile capsule system are considered in this chapter. One of the systems consists of a rigid housing and two internal bodies: a point mass that can move along a rectilinear guide relative to the housing and a rotor that can rotate about a vertical axis fixed in the housing. Controlling the motion of the internal bodies, one can control linear and angular motions of the housing. The other system contains only one internal body: a point mass that moves along a curvilinear trajectory relative to the housing. It is proved that one internal point mass suffices to control completely the position and orientation of the housing of the capsule system in the plane.