Motion planning in the presence of movable obstacles

Motion planning algorithms have generally dealt with motion in a static environment, or more recently, with motion in an environment that changes in a known manner. We consider the problem of finding collision-free motions in a changeable environment. That is, we wish to find a motion for an object where the object is permitted to move some of the obstacles. In such an environment the final positions of the movable obstacles may or may not be part of the goal. In the case where the final positions of the obstacles are unspecified, the motion planning problem is shown to be NP-hard. An algorithm that runs in <italic>&Ogr;</italic>(<italic>n</italic><supscrpt>2</supscrpt>log<italic>n</italic>) time after <italic>&Ogr;</italic>(<italic>n</italic><supscrpt>3</supscrpt>log<supscrpt>2</supscrpt><italic>n</italic>) preprocessing time is presented when the object to be moved is polygonal and there is only one movable polygonal obstacle in a polygonal environment of complexity <italic>&Ogr;</italic>(<italic>n</italic>). In the case where the final positions of the obstacles are specified the general problem is shown to be PSPACE-hard and an algorithm is given when there is one movable obstacle with the same preprocessing time as the previous algorithm but with <italic>&Ogr;</italic>(<italic>n</italic><supscrpt>2</supscrpt>) query time.

[1]  Steven Fortune,et al.  Coordinated motion of two robot arms , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[2]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[3]  Robert E. Tarjan,et al.  Planar point location using persistent search trees , 1986, CACM.

[4]  S. Zucker,et al.  Toward Efficient Trajectory Planning: The Path-Velocity Decomposition , 1986 .

[5]  Varol Akman.  Unobstructed Shortest Paths in Polyhedral Environments , 1987, Lecture Notes in Computer Science.

[6]  Micha Sharir,et al.  On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles , 1986, Discret. Comput. Geom..

[7]  John F. Canny,et al.  New lower bound techniques for robot motion planning problems , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[8]  Chee-Keng Yap,et al.  A "Retraction" Method for Planning the Motion of a Disc , 1985, J. Algorithms.

[9]  John F. Canny,et al.  A new algebraic method for robot motion planning and real geometry , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

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

[11]  David G. Kirkpatrick,et al.  Optimal Search in Planar Subdivisions , 1983, SIAM J. Comput..

[12]  Micha Sharir,et al.  Motion Planning in the Presence of Moving Obstacles , 1985, FOCS.

[13]  Bruce Randall Donald,et al.  On the complexity of kinodynamic planning , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[14]  J. Schwartz,et al.  On the Piano Movers' Problem: III. Coordinating the Motion of Several Independent Bodies: The Special Case of Circular Bodies Moving Amidst Polygonal Barriers , 1983 .

[15]  E. J.,et al.  ON THE COMPLEXITY OF MOTION PLANNING FOR MULTIPLE INDEPENDENT OBJECTS ; PSPACE HARDNESS OF THE " WAREHOUSEMAN ' S PROBLEM " . * * ) , 2022 .

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

[17]  Micha Sharir,et al.  An efficient algorithm for planning collision-free translational motion of a convex polygonal object in 2-dimensional space amidst polygonal obstacles , 1985, SCG '85.

[18]  Gordon T. Wilfong,et al.  Planning constrained motion , 1988, STOC '88.