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The paper focusses on various gear shift patterns in an uncertain terrestrial locomotion system, i.e., in a wormlike locomotion system (WLLS). A WLLS in this theory is understood as a system living in a straight line (one dominant linear dimension) with no active (i.e., driving) legs nor wheels. A mechanical model comprises a chain of discrete mass points (1) connected by viscoelastic force actuators and (2) having ground interaction via spikes which make the velocities unidirectional. A spike means any device which realizes this restriction. The distances between two consecutive mass points are changed by an adaptive controller. In combination with the ground contact spikes, this results in an undulatory locomotion of the system. Optimal gaits which achieve a defined number and succession of resting mass points as well as the resulting velocity are developed in numerical investigations. We present a gait shifting procedure incorporating a combination of speed adjustment and gait change that enables optimal crawling for predefined limits of actuator or spike force load.

This paper deals with the (adaptive) control of mechanical systems, which are inspired by biological ideas. We introduce a certain type of mathematical models of worm-like locomotion systems and present some theoretical control investigations. Only discrete straight worms will be considered in this paper: chains of point masses moving along a straight line. We introduce locomotion systems in form of a straight chain of k=3 interconnected point masses, where we focus on interaction which emerges from a surface texture as asymmetric Coulomb friction. We consider two different types of drives: (i) The point masses are under the action of external forces, which can be regarded as external force control inputs. (ii) We deal with massless linear springs of fixed stiffnesses and controllable original spring lengths, which can be regarded as internal control inputs. The locomotion systems with these two types of drive mechanisms are described by mathe-matical models, which fall into the category of nonlinearly perturbed, multi-input, multi-output systems (MIMO-systems), where the outputs of the system are, for instance, the positions of the point masses or the displacements of the point masses. The goal is to simply control these systems in order to track given reference trajectories to achieve movement of the system. Because one cannot expect to have complete information about a sophisticated mechanical or biological system, but instead only structural properties are known, we deal with uncertain systems. Therefore, the method of adaptive control is chosen in this paper. Since we deal with nonlinearly perturbed MIMO-systems, we focus on the adaptive lambda-tracking control objective to achieve our goal. This means tracking of a given reference signal for any pre-specified accuracy lambda > 0. The objective is not to obtain information about the characteristics of the system or about system parameters, but simply to control the unknown system. This control objective allows us to design simple adaptive controllers, which achieve lambda-tracking. Numerical simulations of tracking different reference signals, for an arbitrary choice of the system parameters, will demonstrate and illustrate, that the introduced, simple adaptive controller works successfully and effectively.