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Locomotion of mobile robots over surfaces and in various media can be based upon different principles. The most widespread types of locomotion are motions using special outer devices like wheels, legs, tracks, and propellers. Also, locomotion of multibody systems can be based upon periodic change of configuration of the system. In the paper, such types of progressive motions for multibody robotic systems are discussed and illustrated. Some of these types of locomotion are similar to those used by living organisms: animals, fish, and insects. Other types have no obvious analogs in the nature. The following locomotion principles are discussed.

Progressive motion of a multibody system consisting of equal rigid bodies in a resistive medium is considered. The bodies are connected consecutively, and between each pair of bodies the actuators are installed. The actuators can exert forces upon the two neighboring bodies so that the distance between them can change within prescribed limits. It is shown that, under the influence of these internal forces produced by the actuators and external resistance of the medium, the system can move progressively with a velocity changing periodically. The algorithm of locomotion is proposed and justified. The necessary and sufficient condition is obtained that ensures the possibility of this motion. The cases of linear and quadratic isotropic/anisotropic resistance forces depending on the velocity of moving bodies and directed against this velocity, are analyzed. The locomotion described in the paper resembles the motion of worms and other biological objects.

The ellipsoidal estimation of reachable sets is an efficient technique for the set-membership modelling of uncertain dynamical systems. In this paper, the optimal outer ellipsoidal approximation of reachable sets is considered, and attention is paid to the new criterion associated with the projection of the approximating ellipsoid onto a given direction. Nonlinear differential equations governing the evolution of ellipsoids are analysed and simplified. The asymptotic behaviour of ellipsoids near the initial point and at infinity is studied. It is shown that the optimal ellipsoids under consideration touch the corresponding reachable sets at all time instants. A control problem for a system subjected to uncertain perturbations is investigated in the framework of the optimal ellipsoidal estimation of reachable sets.

In this paper, a pendulum driven cart is built using Lego robot parts. It consists of a cart with four passive wheels and a pendulum mounted on top of the cart. A DC motor is attached to the hinge joint between the cart and the pendulum which cart swing forward and backward. The cart motion is generated using its internal force and friction with the ground. A four step motion generation pattern is proposed. The motion generation results are verified experimentally. I. INTRODUCTION Quota from an encyclopedia "In physics, friction is the resistive force that occurs when two surfaces travel along each other whilst forced together. It causes physical deforma- tion and heat buildup." Both living creatures and man made systems use a lot friction for motion generation. In particular, snake type animals move without legs and driving wheels. Chernousko (2001) showed that it was possible even for a two link system with one actuator mounted on its hinge joint to move to any location on a plane (1). In order to generate net motion, a fast phase motion and a slow phase motion was introduced. In the fast phase the effects of friction forces were ignored. Hence, the moment was conserved. In the slow phase, static friction kept one link static while the other link was moved by its actuator. This paper describes a theoretical and experimental efforts concerning the motion generation of a pendulum-driven cart using internal forces and static friction only. Pendulum control is a classic control problem. Furuta (1978) is a leading researcher on this subject (3). What is original in this paper is that we drive a cart by swing a pendulum mounted on it. It is contrary to a typical pendulum control problem moving a cart to control a pendulum on top of it. The pendulum cart system is built using Lego Mindstorm 2.0 components, as shown in Figure 1. It consists of a cart with four passive wheels, a pendulum mounted on top of the cart which could move forward and backward, a DC motor is attached to the hinge joint between that pendulum and the cart, and a RCX controller connected to the motor. The RCX controller is programmed to drive the motor in this experiment.

In this paper, a capsule type robot is designed. The motion is described. The robot has no moving part outside its body, no legs, no wheel. Its motion is purely based on its internal force and friction with the environments. A four step motion pattern is proposed. A minimal energy solution is derived. A prototype capsule robot, consisting a plastic tube with a copper coil and a NiFeB magnet rod which can slide inside the tube, is built. It is essentially a motion magnet linear motor. The motion generation results are verified experimentally.

Linear elastic systems controlled by bounded distributed forces are considered. We propose a method of control based on decomposing the original system into an infinite number of subsystems with one degree of freedom each. After that, we apply the time-optimal control to each mode of oscillations. As a result, we present explicit formulae for the distributed control and upper estimates on the time of the control process. Sufficient controllability conditions are also obtained. Examples are presented.

Motions of multibody systems over a rough horizontal plane are investigated. The system under consideration is a linkage consisting of several rigid bodies connected by revolute joints with vertical axes. Control torques are created by actuators installed at the joints. Dry friction forces between the linkage and the plane act upon the system. It is shown that the multibody system can move in an arbitrary direction: lengthwise, sideways, and rotate. Different modes of motion of two-link, three-link, and multilink systems are investigated. The control laws for periodic and wave-like motions are proposed. The displacements and speed of motions are estimated, and optimal parameters are obtained which maximize the average speed. The results of computer simulation are presented. The obtained results are discussed with respect to motions of snakes and other animals, as well as to possible applications to mobile robots.