Claudio Mirolo

A solid modelling system for robot action planning

The characteristics of several solid representation schemes are discussed with respect to their possible use in robot action planning systems. The World Modeler (WM), a solid modeler developed by combining the generalized cylinder approach with constructive solid geometry, is presented. An efficient algorithm for computing collision among convex polyhedrons, that utilizes the internal geometric data structure of the World Modeler is explained.<<ETX>>

Learning (through) recursion: a multidimensional analysis of the competences achieved by CS1 students

In this paper I will discuss an investigation intended to address the learning of recursion in a multidimensional perspective, where the dimensions correspond to different types of competence relevant to programming. One such dimension is the understanding of the computation model, that I have assessed under the methodology proposed by Goetschi et al. (2003). Moreover, I have tried to analyze and correlate other learning dimensions, such as the ability to establish relations in the problem domain, to deal with recursive structures, as well as to develop basic abstraction skills. One of my objectives is indeed to gain a better understanding of the major sources of difficulties that students face. In essence, my investigation lends further support to previous related findings on mental models. However, a consistent model of recursive computations, although implied by the ability to use recursion in problem-solving, does not seem to be sufficient for the achievement of higher-level skills.

Local geometric issues for spatial reasoning in robot motion planning

Starting from their (1989) past work on geometric modelling, the authors discuss various techniques for the robot motion planning problem and suggest further work in this field. The efficiency of any approach to motion planning is strongly related to the ability of getting relevant information from a small subset of the geometric items. Considering a restricted portion of the configuration space around the current configuration of the introduces some local issues. So, a spatial reasoning system is defined by the interactions between local focusing and a global view of the planning process.<<ETX>>

Is iteration really easier to learn than recursion for CS1 students

There is general consensus that recursion is difficult to learn, which may be meant to imply that novice students are more at ease with iteration --- probably a widespread perception of students themselves. However, three years of investigation in a context where recursion is introduced earlier than iteration, as well as control experiments for a standard imperative-first introduction to programming, have provided no evidence that students make more progress with iteration than they do with recursion. More specifically, by means of a pair of questionnaires devised for this purpose, two research questions have been addressed. First, do the students who learned recursion before iteration actually exhibit a stronger ability to deal with the latter? Second, do the students of the imperative-first path master iteration better than those of the recursion-earlier path?

Convex Minimization on a Grid and Applications

This article discusses a discrete version of the convex minimization problem with applications to the efficient computation of proximity measures for pairs of convex polyhedra. Given ad-variate convex function and an isothetic grid of sizeO(nd) in Rd, which is supposed to be finite but not necessarily regular, we want to find the grid cell containing the minimum point. With this aim, we identify a class of elementary subproblems, each resulting in the determination of a half-space in Rd, and show that the minimization problem can be solved by computingO(logn) half-spaces in the worst case foralmost uniformgrids of fixed dimensiondandO(logn) half-planes in the average for arbitrary planar grids. A major point is the potential of the approach to uniformly solve distance related problems for different configurations of a pair of convex bodies. In this respect, the case of a bivariate function is of particular interest and leads to a fast algorithm for detecting collisions between two convex polyhedra in three dimensions. The collision algorithm runs inO(log2n) average time for polyhedra withO(n) vertices whose boundaries are suitably represented; more specifically, the 1-skeletons can be embedded into layered Directed Acyclic Graphs which require justO(n) storage. The article ends with a brief discussion of a few experimental results.

A practical motion planning strategy based on a plane-sweep approach

We discuss a practical motion planning strategy based on a two-step approach. First, an approximation of the C-space is built by a plane-sweep algorithm. Then, the search for a solution path drives the necessary refinement steps. Our claim is that an approach based on the incremental characterization of the C-space can be competitive with the best proposed motion planning techniques. We substantiate this claim in the simple case of planning translations of a convex body in the plane. Since the shape of the free space is incrementally recognized by probing the space via collision detection, every item of geometric information is obtained from the analysis of contact configurations involving convex bodies. At any stage the probes provide a partial characterization, represented by a simple cell subdivision and a suitable set of chains approximating the boundaries of the grown obstacles. The cells and their adjacencies do not change during the refinement step, so that the search strategy is straightforward. Although the performances are not optimal in theory, the planning algorithm shows a good behaviour, as demonstrated by a few experiments where it is compared with a quadtree-based strategy.

Flexible exploitation of space coherence to detect collisions of convex polyhedra

The paper presents a fast algorithm to compute collision translations for pairs of convex polyhedra with some interesting features. From a theoretical viewpoint, besides the novelty of the approach, the polylog asymptotic trend in the average case is as good as that of the best algorithms proposed to solve the similar problems. On the other hand, the measured performances to detect possible collisions from scratch are satisfactory, and this is especially true in cases where the bodies do not collide. However, the most peculiar feature is a simple and flexible mechanism to exploit spatial coherence in a continuous range, which distinguishes this algorithm from all the other proposals we know. Furthermore, the nature of the approach is such that the self-tuning capability is attained at negligible additional costs even for unrelated collision tests. After a brief outline of the main ideas characterizing the approach, a set of numerical results are summarized. The proposed algorithm may be appropriate to plan collision-free paths, both online and off-line, on the basis of fine-grain descriptions of the objects in the workspace.

Incremental Convex Minimization for Computing Collision Translations of Convex Polyhedra

The subject of this paper is an asymptotically fast and incremental algorithm for computing collision translations of convex polyhedra, where the problem at hand is reduced to determining collision translations of pairs of planar sections and minimizing a bivariate convex function. There are two main reasons, in our view, why the algorithm is worth consideration. On the one hand, the addressed proximity measure, namely collision translation, is not as widely studied as distance. On the other, its peculiar computation strategy may be interesting in itself, being well suited to work without initialization and also endowed with an inherently embedded mechanism to exploit spatial coherence. After outlining the main ideas of this novel approach and providing an estimation of the computational costs, we summarize a broad set of numerical experiments meant to explore extensively the behavior of the algorithm, both without and with initialization. Finally, in order to assess the efficacy and the potential of the approach under analysis, the attained performances are contrasted with those of other popular algorithms designed to compute distances between polyhedra. A thorough comparison of the reported query times and, more significantly, of the corresponding trends shows that the behavior of the collision translation algorithm is quite interesting, especially when used without initialization or under variable coherence, which should encourage further work on this approach.

Fast convex minimization to detect collisions between polyhedra

The subject of the paper is a fast algorithm for detecting collisions of two convex polyhedra translating in space. A major feature is the novelty of the approach: collision detection for two convex bodies is reduced to collision detection for pairs of planar sections and minimization of a bivariate convex function; furthermore, most of the subproblems are solved using two-dimensional geometry. As proved by previous theoretical work, on this basis it is possible to design an algorithm, which runs in O(log/sup 2/n) time in the average and O(log/sup 3/n) in the worst case, where n is the total number of vertices. Here the focus is on a more practical version of the algorithm, which is particularly suited to plan collision-free paths on the basis of fine-grain descriptions of the objects in the workspace, as it is the case for the systems supported by sophisticated geometric modelers. After explaining the main ideas underlying the approach, a set of experimental results are presented and discussed in some depth.

Archaeology of information in the primary school

Informatics education at the lower school levels is customarily interpreted as dexterity with the ICTs. However, in our view the importance of such operational abilities has been overstated, whereas the underlying learning objectives and the actual impact on childrens intellectual development are still to be clarified. In this paper we consider a different educational perspective, whose primary aim is to provide children with appropriate mental scaffolding for computer science concepts and methodologies, many of which will be learned only later. Rather than exposing the pupils to a broad span of computing ideas, we essentially focus on representational codes and their potential to disclose new information by simple formal manipulations. Our approach is inspired by the early historical developments of ideas and tools, that allows us: (i) to propose engaging tasks within a background portrayed in the narrative register; (ii) to draw links with the topics of the specific history and mathematics syllabi; (iii) to reflect, at a meta-level, on the cognitive demands of relevant cultural achievements and on their pedagogical implications. After outlining our experience with pupils aged 6 and 9-10, we will briefly discuss childrens subjective perception and feedback, in particular as to the retention of the material learned.