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For many practical applications it is important to determine not only a numerical approximation of one but a representation of the whole set of globally optimal solutions of a non-convex optimization problem. Then one element of this representation may be chosen based on additional information which cannot be formulated as a mathematical function or within a hierarchical problem formulation. We present such an application in the field of robotic design. This application problem can be modeled as a smooth box-constrained optimization problem. We extend the well-known alphaBB method such that it can be used to find an approximation of the set of globally optimal solutions with a predefined quality. We illustrate the properties and give a proof for the finiteness and correctness of our modified alphaBB method.

Rodents, like mice and rats, use tactile hairs in the snout region (mystacial vibrissae) to acquire information about their environment, e.g. the shape or contour of obstacles. For this, the vibrissa is used for the perception of stimuli due to an object contact. Mechanoreceptors are processing units of this stimuli measured in the compliant support (follicle sinus complex). We use this behavior from biology as an inspiration to set up a mechanical model for object contour scanning. An elastic bending rod interacts with a rigid obstacle in the plane. Analyzing only one quasi-static sweep of the rod along the obstacle (in contrast to literature), we determine a) the support reactions (the only observables of the problem), and then b) the (discrete) obstacle contour in form of a set of contact points. In doing this, we first assume a stiff support (clamping) of the vibrissa, but in a next step we increase the elasticity of the support in focussing on a bearing with a rotational spring (also to control or delimitate the bending moment at the support). Thereby, we present a fully analytical treatment of the non-linear differential equations emerging from Bernoulli's rod theory and a representation by Standard Elliptic Integrals.