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.

[1]  Vilmos Komornik,et al.  On the sequence of numbers of the form $ε₀ + ε₁q + ... + ε_nq^n$, $ε_i ∈ {0,1}$ , 1998 .

[2]  M. Kawski.  Nilpotent Lie algebras of vectorfields. , 1988 .

[3]  Magnus Egerstedt,et al.  Motion Description Languages for Multi-Modal Control in Robotics , 2003, Control Problems in Robotics.

[4]  E. Feron,et al.  Real-time motion planning for agile autonomous vehicles , 2000, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[5]  Roger W. Brockett,et al.  On the computer control of movement , 1988, Proceedings. 1988 IEEE International Conference on Robotics and Automation.

[6]  Fabio Fagnani,et al.  Stabilizing quantized feedback with minimal information flow : the scalar case , 2002 .

[7]  Antonio Bicchi,et al.  Optimal Control of Quantized Input Systems , 2002, HSCC.

[8]  Paul Erdös,et al.  Developments in Non-Integer Bases , 1998 .

[9]  Antonio Bicchi,et al.  A group-theoretic characterization of quantized control systems , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[10]  A. Marigo,et al.  Constructive necessary and sufficient conditions for strict triangularizability of driftless nonholonomic systems , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[11]  Nicola Elia,et al.  Stabilization of linear systems with limited information , 2001, IEEE Trans. Autom. Control..

[12]  Daniel Liberzon,et al.  Quantized feedback stabilization of linear systems , 2000, IEEE Trans. Autom. Control..

[13]  James A. Hendler,et al.  A motion description language and a hybrid architecture for motion planning with nonholonomic robots , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

[14]  Yoshihiko Nakamura,et al.  Polynomial Design of Dynamics-based Information Processing System , 2003, Control Problems in Robotics.

[15]  Y. Anzai.  A note on reachability of discrete-time quantized conrol systems , 1974 .

[16]  Benedetto Piccoli,et al.  Controllability for Discrete Systems with a Finite Control Set , 2001, Math. Control. Signals Syst..

[17]  Antonio Bicchi,et al.  Reachability and steering of rolling polyhedra: a case study in discrete nonholonomy , 2004, IEEE Transactions on Automatic Control.

[18]  Antonio Bicchi,et al.  Steering driftless nonholonomic systems by control quanta , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[19]  D. Delchamps.  Extracting state information form a quantized output record , 1990 .

[20]  D. Delchamps.  Stabilizing a linear system with quantized state feedback , 1990 .

[21]  Antonio Bicchi,et al.  On the reachability of quantized control systems , 2002, IEEE Trans. Autom. Control..