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A three-phase vibration-driven system's locomotion on an isotropic rough surface
The average velocity and the backward velocity are two critical factors to evaluate the locomotion performance of a vibration-driven robot. These two factors are often antagonistic when the ground friction is isotropic and, consequently, lead to a bi-objective optimization. The goal of this paper is to give a practicable bi-objective optimization scheme for vibration-driven locomotion robots. To this end, a generalized dynamic model of the multi-module vibration-driven locomotion robot is built by assuming that the ground friction is isotropic Coulomb type and the driving force is ideal. The non-dominated sorting genetic algorithm II (NSGA-II) is then employed to construct the optimization scheme and then obtain the Pareto front. A numerical example with a two-module vibration-driven system is provided to demonstrate the necessity and effectiveness of applying the bi-objective optimization method. A robot prototype is further designed, and a series of experimental tests are carried out. By choosing the motors’ rotary speed and phase shift as optimization parameters, the average and backward velocities are extracted to check against the Pareto front. The consistency between the theoretical predictions and the experimental results shows the practicability of the proposed bi-objective optimization scheme. Therefore, the proposed optimization scheme will provide comprehensive guidance for system design and optimization in micro-locomotion robots.
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
Vibration-driven systems can move progressively in resistive media owing to periodic motions of internal masses. In consideration of the external dry friction forces, the system is piecewise smooth and has been shown to exhibit different types of stick-slip motions. In this paper, a vibration-driven system with Coulomb dry friction is investigated in terms of sliding bifurcation. A two-parameter bifurcation problem is theoretically analyzed and the corresponding bifurcation diagram is presented, where branches of the bifurcation are derived in view of classical mechanics. The results show that these sliding bifurca-tions organize different types of transitions between slip and sticking motions in this system. The bifurcation diagram and the predicted stick-slip transitions are verified through numerical simulations. Considering the effects of physical parameters on average steady-state velocity and utilizing the sticking feature of the system, optimization of the system is performed. Better performance of the system with no backward motion and higher average steady-state velocity can be achieved, based on the proposed optimization procedures .
The controlled horizontal motion of a body in the presence of dry friction forces is investigated. Control is accomplished by means of a movable mass that can move within the body in a bounded range. Some simple modes of periodic relative motions of the movable mass, under which the entire system moves as a whole, are investigated. Constraints are imposed on the relative displacement, velocity and acceleration of the movable mass. The optimum parameters of this relative motion, under which the maximum mean velocity of the body is reached, are determined.
In the present paper, a three-module vibration-driven system moving on a rough horizontal plane is modeled to investigate the relation among the system’s steady-state motion, external Coulomb’s dry friction force and internal excitations. Each module of the system represents a vibration-driven system composed of a rigid body and a movable internal mass. Major attention is focused on the primary resonance situation that the excitation frequency is close to the first-order natural frequency of the system. In the case that the external friction is low, the internal excitation is weak and the stick–slip motion is negligible, both methods of averaging and modal superposition are employed to study the steady-state motion of the system. Through a set of algebraic equations, an approximate value of the system’s average steady-state velocity is obtained. Several numerical examples are calculated to verify the validity of the analytical results both qualitatively and quantitatively. It is seen that big quantitative errors will appear if stick–slip motions occur. Then, two mechanisms for the possible stick–slip motions are put forward, which explain the errors on the average steady-state velocity. Numerical simulations verify our analysis on the stick–slip effects and their mechanisms. Finally, to maximize the average steady-state velocity of the system, optimal control problem is studied. It is shown that, in addition to modifying the friction coefficients, the improvement of the system’s efficiency can be provided by changing the initial phase shifts among the three internal excitations.
The rectilinear motion of a vibration-driven mechanical system composed of two identical modules connected by an elastic element
is considered in this paper. Each module consists of a main body and an internal mass that can move inside the main body.
Anisotropic linear resistance is assumed to act between each module and the resistant medium. The motion of the system is
excited by two acceleration-controlled masses inside the respective main bodies. The primary resonance situation that the
excitation frequency is close to the natural frequency of the system is considered, and the steady-state motion of the system
as a whole is mainly investigated. Both the internal excitation force and the external resistance force contain non-smooth
factors and are assumed to be small quantities of the same order when compared with the maximum value of the force developed
in the elastic element during the motion. With this assumption, method of averaging can be employed and an approximate value
of the average steady-state velocity of the entire system is derived through a set of algebraic equations. The analytical
results show that the magnitude of the average steady-state velocity can be controlled by varying the time shift between the
excitations in the modules. The optimal value of the time shift that corresponds to the maximal average steady-state velocity
exists and is unchanging with the external coefficients of resistance. For a system with specific parameters, numerical simulations
are carried out to verify the correctness of the analytical results. The optimal value of the time shift is numerically obtained,
and the optimal situation is studied to show the advantages of the control.
The motion of a system consisting of a rigid body and an internal movable mass is considered. As a result of special periodic motions of the internal mass, the system as a whole can move in a resistive medium. These motions are analyzed for the cases of piecewise linear and quadratic resistance forces acting upon the body. Optimal parameters of the periodic motions are found that correspond to the maximal average speed of the system as a whole.
The dynamical system consisting of a rigid body and an internal mass is investigated in this paper. The rigid body can move along a rough horizontal plane with a piece-wise linear resistance law due to the special periodic internal motions. A three-phase control is constructed and the motion of the body relative to the environment is controlled by varying the relative acceleration of the internal mass. The relationships between the control parameters for the realization of a directed velocity-periodic motion of the rigid body are established through both theoretical and numerical methods. Optimal and practical parameters of the internal motion, at which the maximal mean velocity of the body is reached, are determined.
Progressive motions of a body containing internal moving masses are analyzed in the presence of resistance forces acting between
the body and the environment. The cases of Coulomb’s dry friction and nonlinear resistance forces are considered. The internal
masses perform periodic motions subject to constraints imposed on the displacements, velocities, and accelerations. Optimal
relative periodic motions of internal masses are determined that correspond to the maximal average speed of the system as
a whole. Experimental data confirm the obtained theoretical results.