Path-planning strategies for a point mobile automaton moving amidst unknown obstacles of arbitrary shape

The problem of path planning for an automaton moving in a two-dimensional scene filled with unknown obstacles is considered. The automaton is presented as a point; obstacles can be of an arbitrary shape, with continuous boundaries and of finite size; no restriction on the size of the scene is imposed. The information available to the automaton is limited to its own current coordinates and those of the target position. Also, when the automaton hits an obstacle, this fact is detected by the automaton's “tactile sensor.” This information is shown to be sufficient for reaching the target or concluding in finite time that the target cannot be reached. A worst-case lower bound on the length of paths generated by any algorithm operating within the framework of the accepted model is developed; the bound is expressed in terms of the perimeters of the obstacles met by the automaton in the scene. Algorithms that guarantee reaching the target (if the target is reachable), and tests for target reachability are presented. The efficiency of the algorithms is studied, and worst-case upper bounds on the length of generated paths are produced.

[1]  Henryk Wozniakowski,et al.  Information, Uncertainty, Complexity , 1982 .

[2]  Alex Meystel,et al.  Algorithm of navigation for a mobile robot , 1984, ICRA.

[3]  Rodney A. Brooks,et al.  Solving the find-path problem by good representation of free space , 1982, IEEE Transactions on Systems, Man, and Cybernetics.

[4]  Hans P. Moravec,et al.  The Stanford Cart and the CMU Rover , 1983, Proceedings of the IEEE.

[5]  John E. Hopcroft,et al.  On the movement of robot arms in 2-dimensional bounded regions , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[6]  J. Schwartz,et al.  On the “piano movers” problem. II. General techniques for computing topological properties of real algebraic manifolds , 1983 .

[7]  Manuel Blum,et al.  On the power of the compass (or, why mazes are easier to search than graphs) , 1978, 19th Annual Symposium on Foundations of Computer Science (sfcs 1978).

[8]  Vladimir Lumelsky.  Effect of robot kinematics on motion planning in unknown environment , 1985, 1985 24th IEEE Conference on Decision and Control.

[9]  D. Y. Tseng,et al.  Autonomous vehicle control: an overview of the Hughes project , 1983 .

[10]  A. J. de Zeeuw,et al.  On expectations, information and dynamic game equilibria , 1985 .

[11]  Harold Abelson,et al.  Turtle geometry : the computer as a medium for exploring mathematics , 1983 .

[12]  Alan M. Thompson.  The Navigation System of the JPL Robot , 1977, IJCAI.

[13]  Vladimir J. Lumelsky,et al.  Continuous motion planning in unknown environment for a 3D cartesian robot arm , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[14]  E. F. Moore.  Sequential Machines: Selected Papers , 1964 .

[15]  Tomás Lozano-Pérez,et al.  An algorithm for planning collision-free paths among polyhedral obstacles , 1979, CACM.

[16]  John H. Reif,et al.  Complexity of the mover's problem and generalizations , 1979, 20th Annual Symposium on Foundations of Computer Science (sfcs 1979).

[17]  E. F. Moore.  The firing squad synchronization problem , 1964 .

[18]  Richard Paul Collins Paul,et al.  Modelling, trajectory calculation and servoing of a computer controlled arm , 1972 .

[19]  Donald Lee Pieper.  The kinematics of manipulators under computer control , 1968 .

[20]  Franco P. Preparata,et al.  Segments, Rectangles, Contours , 1981, J. Algorithms.

[21]  J. Schwartz,et al.  On the “piano movers'” problem I. The case of a two‐dimensional rigid polygonal body moving amidst polygonal barriers , 1983 .

[22]  Micha Sharir,et al.  Algorithmic motion planning , 2004, Handbook of Discrete and Computational Geometry, 2nd Ed..

[23]  J. Reif.  A Survey on Advances in the Theory of Computational Robotics , 1986 .