Worm-like locomotion systems. An intermediate theoretical approach. (Q2881015)

The book under review is \textit{not} a textbook for studying mechanical worm-like robotic systems, designed for performing specified tasks. Instead, the authors concentrate on the clear presentation of the mathematical and mechanical concepts used for the study of the kinematic and dynamic behavior and the control of worm-like locomotion systems, not on the presentation of the design of models of realistic mechanisms. They start with a short introduction of the basic concepts of modeling, which are further extended in the mathematical, mechanical and control comments of the Appendix.NEWLINENEWLINE Various models of a straight worm with propulsive spikes are discussed in the first chapter. Many detailed examples show the impact of the inequality condition \(\dot x\geq 0\) on the kinematics and on the motion \(t\to x(t)\) of the artificial (unrealistic) worm, for all model points that contact a flat as well as a hilly ground. Then, the motion of the worms is studied without and with activators (external forces). In the next chapter, the authors present the theory of motion of worms with propulsive friction, first the motion on a solid ground without lubrication, following the law of Coulomb friction, then the study of motion of the worm in a fluid environment of high viscosity. Again, numerous examples illustrate the modeling and solution procedures. The last chapter is devoted to the adaptive control of worms, i.e. the problems arising in connection with unclear data of the worm system. It describes how the worm's locomotion can be controlled to stay close to an optimal pattern, gained in the kinematical theory, but disturbed by varying external forces or failing activator data.NEWLINENEWLINE The book is a valuable study guide for graduate students of mechanical engineering and/or applied mathematics. The large number of the examples with the numerical results and the detailed discussions of the insights gained will be appreciated. Sample computer programs are provided and can encourage the serious student to further experiment with newly created worm models. The style of presentation, with cartoons and an unconventional nomenclature, may also help. (For instance, the specific models of the worms have catchy names. The worm with ground control by spikes is SPIKY, with both stiction and lubrication is COULY, with lubrication only is STICKY, and with dry sliding friction only is SLIDY.) The authors also discuss how the general differential equations \(\dot x= v\) and \(\dot v= f(y,v,t)+\lambda\) can be solved, using computer programs written in MAPLE and MATLAB, when \(\lambda\) is represented by Heaviside functions. For the mechanical engineer interested in worm-like robotic systems, the bibliography will be helpful.