@article {MCB04,
	title = {Reachability and Steering of Rolling Polyhedra: A Case Study in Discrete Nonholonomy},
	journal = {IEEE Trans. on Automatic Control},
	volume = {49},
	number = {5},
	year = {2004},
	month = {May},
	pages = {710-726},
	abstract = {<p>Rolling a ball on a plane is a standard example of nonholonomy reported in many textbooks, and the problem is also well understood for any smooth deformation of the surfaces. For non-smoothly deformed surfaces, however, much less is known. Although it may seem intuitive that nonholonomy is conserved (think e.g. to polyhedral approximations of smooth surfaces), current definitions of {\textquoteleft}{\textquoteleft}nonholonomy{\textquoteright}{\textquoteright} are inherently referred to systems described by ordinary differential equations, and are thus inapplicable to such systems. \{\.I}n this paper we study the set of positions and orientations that a polyhedral part can reach by rolling on a plane through sequences of adjacent faces. We provide a description of such reachable set, discuss conditions under which the set is dense, or discrete, or has a compound structure, and provide a method for steering the system to a desired reachable configuration, robustly with respect to model uncertainties. \\Based on ideas and concepts encountered in this case study, and in some other examples we provide, we turn back to the most general aspects of the problem and investigate the possible generalization of the notion of (kinematic) nonholonomy to non-smooth, discrete, and hybrid dynamical systems. To capture the essence of phenomena commonly regarded as {\textquoteleft}{\textquoteleft}nonholonomic{\textquoteright}{\textquoteright}, at least two irreducible concepts are to be defined, of {\textquoteleft}{\textquoteleft}internal{\textquoteright}{\textquoteright} and {\textquoteleft}{\textquoteleft}external{\textquoteright}{\textquoteright} nonholonomy, which may coexist in the same system. These definitions are instantiated by examples.</p>
},
	keywords = {Embedded Control, Robotics},
	author = {A. Bicchi and Y. Chitour and A. Marigo}
}
@article {BMP02,
	title = {On the reachability of quantized control systems},
	journal = {IEEE Trans. on Automatic Control},
	volume = {4},
	number = {47},
	year = {2002},
	month = {April},
	pages = {546-563},
	abstract = {<p>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 the 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.</p>
},
	keywords = {Embedded Control, Robotics},
	author = {A. Bicchi and A. Marigo and B. Piccoli}
}
@conference {MPB00-cdc,
	title = {Reachability Analysis for a Class of Quantized Control Systems},
	booktitle = {Proc. IEEE Int. Conf. on Decision and Control},
	year = {2000},
	month = {December},
	pages = {3963-3968},
	address = {Sydney, AU},
	keywords = {Hybrid and Embedded Control Systems, Nonlinear Control Systems, Quantized Control Systems},
	author = {A. Marigo and B. Piccoli and A. Bicchi}
}
@article {MB00,
	title = {Rolling Bodies with Regular Surface: Controllability Theory and Applications},
	journal = {IEEE Trans. on Automatic Control},
	volume = {45},
	number = {9},
	year = {2000},
	month = {September},
	pages = {1586-1599},
	keywords = {Nonlinear Control Systems, Robot Hands},
	author = {A. Marigo and A. Bicchi}
}
@conference {BM00,
	title = {Rolling Contacts and Dextrous Manipulation},
	booktitle = {Proc. IEEE Int. Conf. on Robotics and Automation},
	year = {2000},
	month = {May},
	pages = {282-287},
	address = {San Francisco, CA},
	keywords = {Nonholonomic Systems, Nonlinear Control Systems, Robot Hands},
	author = {A. Bicchi and A. Marigo}
}
@inbook {MB98,
	title = {Rolling bodies with regular surfaces: the holonomic case},
	booktitle = {Differential geometry and control},
	series = {Proceedings of Symposia in Pure Mathematics},
	volume = {64},
	year = {1999},
	pages = {241-256},
	publisher = {American Mathematical Society},
	organization = {American Mathematical Society},
	author = {A. Marigo and A. Bicchi},
	editor = {G. Ferreyra and R. Gardner and H. Hermes and H. Sussmann}
}
@inbook {BMP99-CPRA,
	title = {Robotic Dexterity via Nonholonomy},
	booktitle = {Control Problems in Robotics and Automation},
	series = {LNCIS 230},
	year = {1997},
	pages = {35-49},
	publisher = {Springer Verlag},
	organization = {Springer Verlag},
	address = {Berlin Heidelberg, Germany},
	keywords = {Haptics, Robotics},
	author = {A. Bicchi and A. Marigo and D Prattichizzo},
	editor = {B. Siciliano and K. Valavanis}
}
@inbook {CMPB97,
	title = {Rolling Polyhedra on a Plane: Analysis of the Reachable Set},
	booktitle = {Algorithms for Robotic Motion and Manipulation},
	year = {1997},
	pages = {277-286},
	publisher = {A. K. Peters},
	organization = {A. K. Peters},
	address = {Wellesley, MA, U.S.A.},
	keywords = {Embedded Control, Robotics},
	author = {Y. Chitour and A. Marigo and D Prattichizzo and A. Bicchi},
	editor = {J.P. Laumond and M. Overmars}
}
@inbook {CMPB96,
	title = {Reachability of Rolling Parts},
	booktitle = {Advances in Robotics: The ERNET Perspective},
	year = {1996},
	pages = {51-60},
	publisher = {World Scientific Publisher Corp.},
	organization = {World Scientific Publisher Corp.},
	address = {Singapore},
	keywords = {Haptics, Robotics},
	author = {Y. Chitour and A. Marigo and D Prattichizzo and A. Bicchi},
	editor = {C. Bonivento and C. Melchiorri and H. Tolle}
}
