Motion planning through symbols and lattices

In this paper we propose a new approach to motion planning, based on the introduction of a lattice structure in the workspace of the robot, leading to efficient computations of plans for rather complex vehicles, and allowing for the implementation of optimization procedures in a rather straightforward way. The basic idea is the purposeful restriction of the set of possible input functions to the vehicle to a finite set of symbols, or control quanta, which, under suitable conditions, generate a regular lattice of reachable points. Once the lattice is generated and a convenient description computed, standard techniques in integer linear programming can be used to find a plan very efficiently. We also provide a correct and complete algorithm to the problem of finding an optimized plan (with respect e.g. to length minimization) consisting in a sequence of graph searches.

[1]  Ole Jakob Sørdalen,et al.  Conversion of the kinematics of a car with n trailers into a chained form , 1993, [1993] Proceedings IEEE International Conference on Robotics and Automation.

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

[3]  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).

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

[5]  S. Sastry,et al.  Nonholonomic motion planning: steering using sinusoids , 1993, IEEE Trans. Autom. Control..

[6]  Emilio Frazzoli,et al.  Real-Time Motion Planning for Agile Autonomous Vehicles , 2000 .

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

[8]  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.

[9]  H. Nijmeijer,et al.  Extremal controls for chained systems , 1996 .

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

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