Mathematical Problems in Engineering

Volume 2018, Article ID 1613945, 11 pages

https://doi.org/10.1155/2018/1613945

## Object Shape Recognition and Reconstruction Using Pivoted Tactile Sensors

^{1}Technical Mechanics Group, Technische Universität Ilmenau, Max-Planck-Ring 12, 98693 Ilmenau, Germany^{2}Institute of Mathematics, Technische Universität Ilmenau, Weimarer Straße 25, 98693 Ilmenau, Germany^{3}Department of Engineering and Natural Sciences, Merseburg University of Applied Sciences, Eberhard-Leibnitz-Str. 2, 06217 Merseburg, Germany

Correspondence should be addressed to L. Merker; ed.uanemli-ut@rekrem.sakul and C. Behn; ed.uanemli-ut@nheb.netsrac

Received 3 January 2018; Revised 5 April 2018; Accepted 17 April 2018; Published 26 June 2018

Academic Editor: Paolo Boscariol

Copyright © 2018 L. Merker et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Many mammals use some special tactile hairs, the so-called mystacial macrovibrissae, to acquire information about their environment. In doing so, rats and mice, e.g., are able to detect object distances, shapes, and surface textures. Inspired by the biological paradigm, we present a mechanical model for object contour scanning and shape reconstruction, considering a single vibrissa as a cylindrically shaped Euler-Bernoulli-bending rod, which is pivoted by a bearing. In doing so, we adapt our model for a rotational scanning movement, which is in contrast to many previous modeling approaches. Describing a single rotational quasi-static sweep of the vibrissa along a strict convex contour function using nonlinear Euler-Bernoulli theory, we end up in a boundary-value problem with some unknown parameters. In a first step, we use shooting methods in an algorithm to repeatedly solve this boundary-value problem (changing the vibrissa base angle) and generate the support reactions during a sweep along an object contour. Afterwards, we use these support reactions to reconstruct the object contour solving an initial-value problem. Finally, we extend the scanning process adding a second sweep of the vibrissa in opposite direction in order to enlarge the reconstructable area of the profile.

#### 1. Introduction

Tactile sensors are frequently used in uncertain (changing, dark, noisy) environments, where optical sensors reach their capability. In many areas of application, e.g., in mobile robotics, tactile sensors are designed from simple passive impact sensors all the way through to complex, integrated systems, giving more detailed contact information. Since a large number of technical implementations are inspired by nature, it is well worth taking a brief view to the biological paradigm.

Rodents like rats and mice use their mystacial macrovibrissae (prominent tactile hairs in their snout region) for exploring the environment. The facial vibrissae array (mystacial pad) consists of a variety of vibrissal systems, each consisting of a hair shaft, which is embedded in its own support—the so-called follicle-sinus complex (FSC). A vibrissa itself does not consist of any sensory components but transmits mechanical stimuli to the FSC, where the actual perception of stimuli happens. Therefore, the FSC is equipped with a variety of mechanoreceptors converting tactile information into neural impulses for the central nervous system [1]. In addition, the FSC is surrounded by an extrinsic and intrinsic musculature, which enables rats and mice to use their vibrissae in two very special modes [2, 3]:(i)a passive mode without activating the musculature, in which each vibrissa is deformed only due to external forces (e.g., wind or mechanical contacts, when the animal is passing an object)(ii)an active exploration mode whereby the vibrissae can be swept back and forth along obstacles rotationally by alternating contraction of the intrinsic and extrinsic musculature.

The active exploration mode, also known as active “whisking” is primary used to detect object surface or shape information.

Previous technical solutions of biological inspired tactile sensors are of different complexity depending on the purpose of use. In the most trivial case, an artificial vibrissa is used as a passive contact detector providing a binary contact signal. In mobile robotics, simple systems like these are already usable for obstacle collision avoidance [4] or autonomous wall following robot movements [5]. Other tactile sensor systems provide even more detailed information like object distances, shapes, or surface textures.

Works focussing the contact sensing problem from a dynamic point of view are, for instance, [6–9]. The authors in [8, 9] focus on a dynamic active antenna sensing in analyzing the natural resonance frequencies to determine the distance to an object. The dynamic approach therein is in contrast to our work, since we focus on a quasi-static movement of the support deflection angle. Further on, the boundary conditions in [8, 9] represent a bearing as a contact of the rod with an object. This contradicts the real behavior. The authors should analyze a one-sided contact restriction, but not a simple support as a contact scenario. Moreover, it seems that there are some problems in identifying the contact point in observing only the behavior of the eigenvalues and natural frequencies. Having a glance to the natural frequency plot [9, Figure 5], one can observe nearly two possibilities of a contact close to and . The authors in [7] resolve this problem in designing the sensing rod within an elastic foundation. While [8, 9] are limited to the detection of the obstacle distance in determining only one contact point, this paper furthermore presents a procedure of reconstructing a whole part of an object contour.

Scanning an object, different information at the support of the rod (e.g., reaction forces and moments) can be used to determine the contact position. The object reconstruction process is considered in [10–12] as well, neglecting all dynamic aspects, but only using linear bending theory, which is not suitable for the large deflections of the vibrissa, which actually occur in reality. Due to the limitation to small deflections, the scanning process is frequently realized by rotating the artificial vibrissa by small pushing angles against an object [12] and not by an actual scanning sweep including large deflections, as it can be observed in animal’s kingdom. A big disadvantage of using only small pushing angles is the need of changing the support position in order to scan a larger part of the object contour. In contrast, this problem does not occur within the present paper. It is shown that, considering large bending deflections described by nonlinear theory, it is possible to reconstruct a larger part of any object contour even without changing the support position.

Even though some previous publications consider large deflections as well, the scanning process is frequently realized by a translational scanning movement [13–17]. There, the authors describe a quasi-static translational sweep of a single rod, which is one-sided clamped, along a strict convex profile. Firstly, the scanning process is treated analytically as far as possible in order to generate the unknown support reactions, when the rod is swept along a profile contour. This analytical approach is in contrast to just performing experiments and measurements. Afterwards, the support reactions are used to determine a sequence of contact points, which approximate the object contour. However, compared with the biological paradigm, the considered models (translational movement) rather represent the passive mode of an operating vibrissa. The animal’s ability to actively rotate its vibrissae back and forth is not taken into account there.

Other works consider a rotatory scanning movement, but the contact sensing problem or reconstruction process is always based on measurements only. For example, in [18, 19], a single artificial vibrissa is swept along an object rotationally by a DC-motor, whereby the support reactions are measured in a load cell. At different points in time, the elastic line of the vibrissa is determined by numerically integrating the deformation equations. A variety of deformation states finally makes the object contour apparent. Nevertheless, there is no mechanical model allowing for a theoretical generation of the support reactions. For that reason, it is not possible to carry out parameter studies with regard to different geometric properties of the vibrissa without the need of performing a large number of experiments.

Although some publications take various morphological characteristics like the elasticity of the FSC [17] or the tapered and precurved geometry of a vibrissa into account [20–23], there is no mechanical model for generating the support reactions during a rotatory scanning sweep as well.

Within the present paper we limit ourselves to the main functionality of a rotatory scanning movement and the biological requirement, that only the support of the rod can be used for detecting mechanical stimuli. Thus, we focus on a kind of an active vibrissa movement behavior starting with a general modeling of a rotatory sweep along a strict convex object contour using a single technical vibrissa. A theoretical treatment of the scanning process will provide a basis for an algorithm, which is used for(i)solving a boundary-value problem to generate the support reactions during a rotatory scanning sweep,(ii)solving an initial-value problem to reconstruct the object contour only using the generated observables.

The algorithm allows the generation of the support reactions needed for the reconstruction including large bending deflections, which is new in literature. Afterwards, numerical simulations are performed to demonstrate the functional capability of the algorithm. In addition, the scanning process is extended in a further step by a second sweep in opposite direction in order to enlarge the scanning range. The governed results extend and complement the ones from [13–17, 24].

#### 2. General Modeling of a Rotational Sweep

Figure 1 shows the presented model, which is based on the following assumptions:(i)** Vibrissa:**(a)The vibrissa is modeled as a cylindrically shaped Euler-Bernoulli bending rod of length . It is assumed to have a constant second moment of area and a constant Young’s modulus —describing a linear elastic material behavior of the rod.(b)The rod undergoes large deflections which are described using nonlinear Euler-Bernoulli theory.(ii)** Support and drive:**(a)The rod is pivoted rotationally by a bearing.(b)Its base angle (drive angle) is increased incrementally in order to generate a rotational planar vibrissa movement in a mathematical positive sense with respect to the -axis. Therefore, the required holding moment is calculated.(iii)** Object and contact:**(a)The object is modeled as a rigid body with a** strict convex** contour function .(b)Due to the strict convexity, the contour function can be parameterized by means of its slope angle .(c)During scanning for each preset drive angle some point of the vibrissa undergoes a contact force due to the contact with a specific unknown profile point, which is determined by a unique .(d)The strict convex object shape ensures that for each deformation state there is only** one contact point** with the object.(e)The contact is considered as an** ideal contact**, so (ignoring friction effects) the contact force is always perpendicular to the profile tangent.