Alessia Marigo

On the reachability of quantized control systems

In this paper, we study control systems whose input sets are quantized, i.e., finite or regularly distributed on a mesh. We specifically focus on problems relating to the structure of the reachable set of such systems, which may turn out to be either dense or discrete. We report results on the reachable set of linear quantized systems, and on a particular but interesting class of nonlinear systems, i.e., nonholonomic chained-form systems. For such systems, we provide a complete characterization of the reachable set, and, in case the set is discrete, a computable method to completely and succinctly describe its structure. Implications and open problems in the analysis and synthesis of quantized control systems are addressed.

Dexterous Grippers: Putting Nonholonomy to Work for Fine Manipulation

In this paper, we describe the realization and control of robotic end-effectors that are designed to achieve high operational versatility with limited constructive complexity. The design of such end-effectors, which can be regarded either as low-complexity robot hands or as highly versatile robot grippers, is based on the intentional exploitation of nonholonomic effects that occur in rolling. While the potential usefulness of manipulation by rolling has been theoretically established in the literature, several problems in the practical implementation of the concept remained open. In particular, manipulation of parts of complex, and a priori unknown, shape is considered in this paper. Experimental low-complexity grippers that realize dexterous manipulation by rolling are also described.

Planning Motions of Polyhedral Parts by Rolling

Abstract. The nonholonomic nature of rolling between rigid bodies can be exploited to achieve dextrous manipulation of industrial parts with minimally complex robotic effectors. While for parts with smooth surfaces a relatively well-developed theory exists, planning for parts with only piecewise smooth surfaces is largely an open problem. The problem of arbitrarily displacing and reorienting a polyhedron by means of rotations about edges belonging to a fixed plane is considered. Relevant theoretical results are reviewed, and a polynomial time algorithm is proposed that allows planning such motions. The effects of finite accuracy in representing problem data, as well as the operational and computational complexity of the method are considered in detail.

Steering driftless nonholonomic systems by control quanta

We consider the problem of steering a class of nonholonomic systems, namely systems that are feedback equivalent to a strictly triangular form, which is considerably larger than other classes for which the steering problem, has been given closed form solutions in the literature. The proposed solution consists in the application of a finite concatenation of finite-support control actions chosen among a finite set, suitable selected in the input space, each resulting in a quantum change in the system state. The method results in a closed form algorithm which is exact up to an arbitrary tolerance.

Dexterity through rolling: manipulation of unknown objects

The nonholonomy exhibited by kinematic systems consisting of bodies rolling on top of each other can be used for the purpose of building dexterous mechanisms with a minimum hardware complication. Such a desirable engineering feature can be fully exploited, however, only if the capability of planning and controlling the rolling motions of arbitrary objects is achieved. In this paper we present recent advances of both theoretical and experimental natures towards realizing a robot gripper for manipulation of objects whose shape is not known a priori, but is reconstructed as manipulation proceeds.

Manipulation of polyhedral parts by rolling

The nonholonomy exhibited by kinematic systems consisting of bodies rolling on top of each other can be used to the purpose of building dexterous mechanism with a minimum hardware complication. Previous work concentrated on manipulation of objects possessing a regular surface. On the other hand, industrial parts are most often irregular, possessing vertices and edges. In this paper we present some results on the description of the set of positions and orientations that polyhedral objects can reach when manipulated by rolling without slipping. An algorithm for planning the manipulation of a polyhedral part from a given configuration to another reachable one, is also presented.

Feedback encoding for efficient symbolic control of dynamical systems

The problem of efficiently steering dynamical systems by generating input plans is considered. Plans are considered which consist of finite-length words constructed on an alphabet of input symbols, which could be, e.g., transmitted through a limited capacity channel to a remote system, where they can be decoded in suitable control actions. Efficiency is considered in terms of the computational complexity of plans, and in terms of their description length (in number of bits). We show that, by suitable choice of the control encoding, finite plans can be efficiently built for a wide class of dynamical systems, computing arbitrarily close approximations of a desired equilibrium in polynomial time. The paper also investigates how the efficiency of planning is affected by the choice of inputs, and provides some results as to optimal performance in terms of accuracy and range.

Encoding steering control with symbols

In this paper, we consider the problem of steering complex dynamical systems among equilibria in their state space in efficient ways. Efficiency is considered as the possibility of compactly representing the (typically very large, or infinite) set of reachable equilibria and quickly computing plans to move among them. To this purpose, we consider the possibility of building lattice structures by purposefully introducing quantization of inputs. We consider different ways in which control actions can be encoded in a finite or numerable set of symbols, review different applications where symbolic encoding of control actions can be employed with success, and provide a unified framework in which to study the many different possible manifestations of the idea.

A local-local planning algorithm for rolling objects

In this paper, we consider planning motions of objects of regular shape rolling on a plane among obstacles. Theoretical foundations and applications of this type of operations in robotic manipulation and locomotion have been discussed elsewhere. In this paper, we propose a novel algorithm that improves upon existing techniques in that: i) it is finitely computable and predictable (an upper bound on the computations necessary to reach a given goal within a tolerance can be given), and ii) it possesses a topological (local-local) property which enables obstacles and workspace limitations to be dealt with in an effective way.

Reachability analysis for a class of quantized control systems

We study control systems whose input sets are quantized. We specifically focus on problems relating to the structure of the reachable set of such systems, which may turn out to be either dense or discrete. We report on some results on the reachable set of linear quantized systems, and study in detail an interesting class of nonlinear systems, forming the discrete counterpart of driftless nonholonomic continuous systems. For such systems, we provide a complete characterization of the reachable set, and, in the case the set is discrete, a computable method to describe its lattice structure.