Carsten Behn

Structural Characterization of the Whisker System of the Rat

Vibrissae or tactile hairs, commonly known as whiskers, are the mechanical gates of special mechano-sensitive organs. In terrestrial mammals, they carry various functions, especially object determination and texture discrimination. We hypothesise that the characteristic morphology and structure of whiskers is a primary morphological condition for their mechano-sensitive functions. To constitute mathematical models on the systematic but different mechanical behavior of the main types of whisker hairs (micro vibrissae, macro vibrissae, straddlers), information is lacking on the distribution of properties in a field of all three types of hairs, taken from one and the same animal. Referring to sets taken from five individuals, geometry data is provided as one complete set for a female rat (Rattus norvegicus). Due to measurements of diameters along the length, the shape of whiskers in rats is confirmed to resemble a cone, which may be overlaid by some convexity or concavity. Additionally, the surface and internal structure of different vibrissae were examined by scanning electron microscopy. The cuticle of the rat whisker consists of flat scales, overlapping like roofing slates. A cross section reveals up to 20 superposed layers of cuticular scales. The longitudinal dimension of one scale is shorter in whiskers compared with body hairs. A hollow medulla is observed from the base to approximately half of the overall length, which is then partially filled by compact tissue, until it disappears completely near the tip. An extraordinarily thick cortex probably rules the characteristic bending features, and the multilayer cuticle probably has a mainly protective function.

Gait generation considering dynamics for artificial segmented worms

This paper deals with terrestrial worm-like locomotion systems living in a straight line. They are modeled as chains of mass points having ground interaction via spikes which make the velocities unidirectional. A method is presented to construct gaits with any desired time pattern of resting mass points (which are acted on by the propulsive forces). Taking the dynamics into consideration, conclusions about the choice and shift of gaits in connection with actuator data are given.

Adaptive λ-tracking for locomotion systems

Abstract 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 the 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 mathematical 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 λ -tracking control objective to achieve our goal. This means tracking of a given reference signal for any pre-specified accuracy λ > 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 λ -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.

ADAPTIVE VERSUS FUZZY CONTROL OF UNCERTAIN MECHANICAL SYSTEMS

The motivation of this work is formed by the biological behavior of a receptor cell (sensory system). It is modeled as a spring-mass-damper oscillator with a spatial disturbance signal acting on the frame and an inner active element that generates a force acting on the mass. Both the system parameters and the excitation signal are supposed to be unknown. The goal is to achieve a predefined movement of the mass, such as tracking a set point trajectory or stabilization. Thus, a controller is required to act on the system using the control force as input in such a way that the desired behavior is generated. This is done by means of high-gain-stabilization. Like its biological paradigm, the receptor is in a permanent state of adaption. This means that recurring disturbances, such as wind acting on the vibrissa, are damped in order to achieve λ-stabilization. To achieve this control goal and at the same time deal with unknown systems, adaptive controllers are introduced. These adaptive control strategies are compared with an adaptive fuzzy approach.

Animal vibrissae: modeling and adaptive control of bio-inspired sensors

The reception of vibrations is a special sense of touch, important for many insects and vertebrates. The latter realize this reception by means of hair-shaped vibrissae in the mystacial pad, to acquire tactile information about their environments. The system models have to allow for stabilizing and tracking control while nevertheless being able to detect superimposed solitary excitations. Controllers have to be adaptive in view of both the randomness of the external signals to be suppressed and the uncertainty of system data. We presents mechanical models and an improved adaptive control strategy that avoids identification but renders the system sensitive.

Worm-like robotic systems: Generation, analysis and shift of gaits using adaptive control

The starting point of this work is a biologically inspired model of a worm-like locomotion system (WLLS). The mechanical model comprises discrete mass points connected by viscoelastic force actuators. Ground contact is constituted by ideal spikes which act as constraint forces, preventing backward motion for each mass point equipped with them. The distances between each two consecutive mass points are changed by an adaptive controller in order to track a reference trajectory. In combination with the ground contact via spikes, this results in a (undulatory) locomotion of the system. After presenting the aforementioned model and the adaptive controller, the construction of specific reference functions, which result in certain gaits, is described. For this purpose an existing algorithm is used; it allows for defining the number and succession of the active spikes as well as the resulting velocity. In the following gait examination, simulations for worm systems with four mass points are carried out to find a selection of those gaits most suitable in terms of actuator and spikes load. Prior to implementing the automatic gait change, simulations are carried out to determine the criteria for shifting: actuator and spike forces. With those criteria, the choice of the optimal gait depends on both locomotion speed and ground inclination. An approximation of the forces mentioned before enables a formulation of inclination-dependent speed intervals. This leads to a combination of speed adjustment and gait change that enables optimal crawling for predefined limits of actuator or spike forces.

Worm-like Locomotion Systems (WLLS) - Theory, Control and Prototypes

Most of biologically inspired locomotion systems are dominated by walking machines pedal locomotion. A lot of biological models (bipedal up to octopedal) are studied in the literature and their constructions were transferred by engineers in different forms of realization. Non-pedal forms of locomotion show their advantages in inspection techniques or in applications to medical technology for diagnostic systems and minimally invasive surgery (endoscopy). These areas of application were considered by (Choi et al., 2002), (Mangan et al., 2002), (Menciassi & Dario, 2003). Hence, this type of locomotion and its drive mechanisms are current topics of main focus. In this chapter we discuss the problem of developing worm-like locomotion systems, which have the earthworm as a living prototype, from two points of view: • modelling and controlling in various levels of abstraction, • designing of prototypes with classical and non-classical forms of drive.

Object contour reconstruction using bio-inspired sensors

This work is inspired and motivated by the sophisticated mammals sense organ of touch: vibrissa. Mammals, especially rodents, use their vibrissae, located in the snout region - mystacial vibrissae - to determine object contacts (passive mode) or to scan object surfaces (active mode). Here, we focus on the passive mode. In order to get hints for an artificial sensing prototype, we set up a mechanical model in form of a long slim beam which is one-sided clamped. We investigate in a purely analytical way a quasi-static sweep of the beam along a given profile, where we assume that the profile boundary is strictly convex. This sweeping procedure shows up in two phases, which have to be distinguished in profile contact with the tip and tangentially contact (between tip and base). The analysis eventuates in a phase decision criterion and in a formula for the contact point. These are the main results. Moreover, based on the observables of the problem, i.e. the clamping moment and the clamping forces, which are the only information the animal relies on, a reconstruction of the profile is possible - even with added uncertainty mimicking noise in experimental data.

Towards the Development of Tactile Sensors for Determination of Static Friction Coefficient to Surfaces

Natural vibrissae fulfill a lot of functions. Next to object distance detection and object shape recognition, the surface texture can be determined. Inspired by the natural process of surface texture detection, the goal is to adapt this feature by technical concepts. Modeling the vibrissa as an Euler–Bernoulli bending beam with a quasi-statically moving support and the vibrissa–surface contact with respect to Coulomb’s Law of Friction, a first approach was formed by the group of Behn and Steigenberger. Due to the motion of the support (pushing the vibrissa) and the surface contact, the vibrissa gets deformed. Firstly, the beam tip is sticking to the surface. The acting friction force prevents a movement of the beam tip until the maximal stiction is reached. The displacement of the support corresponds to changes in the acting forces and moments. Out of these changes the coefficient of static friction can be determined. The analytical results of Steigenberger and Behn are verified and validated by numerical simulations and an experiment.

Bio-inspired Technical Vibrissae for Quasi-static Profile Scanning

A passive vibrissa (whisker) is modeled as an elastic bending rod that interacts with a rigid obstacle in the plane. Aim is to determine the obstacle’s profile by one quasi-static sweep along the obstacle. To this end, the non-linear differential equations emerging from Bernoulli’s rod theory are solved analytically followed by numerical evaluation. This generates in a first step the support reactions, which represent the only observables an animal solely relies on. In a second step, these observables (possibly made noisy) are used for a reconstruction algorithm in solving initial-value problems which yield a series of contact points (discrete profile contour).