On Information Invariants in Robotics

We consider the problem of determining the information requirements to perform robot tasks, using the concept ofinformation invariants. This paper represents our attempt to characterize a family of complicated and subtle issues concerned with measuring robot task complexity. We also provide a first approximation to a purely operational theory that addresses a narrow but interesting special case. We discuss several measures for the information complexity of a task: (a) How much internal state should the robot retain? (b) How many cooperating agents are required, and how much communication between them is necessary? (c) How can the robot change (side-effect) the environment in order to record state or sensory information to perform a task? (d) How much information is provided by sensors? and (e) How much computation is required by the robot? We consider how one might develop a kind of ''calculus'' on (a)-(e) in order to compare the power of sensor systems analytically. To this end, we attempt to develop a notion of information invariants. We develop a theory whereby one sensor can be ''reduced'' to another (much in the spirit of computation-theoretic reductions), by adding, deleting, and reallocating (a)-(e) among collaborating autonomous agents.

[1]  Bruce Randall Donald,et al.  A provably good approximation algorithm for optimal-time trajectory planning , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

[2]  A. Tarski.  A Decision Method for Elementary Algebra and Geometry , 2023 .

[3]  Matthew T. Mason,et al.  Mechanics and Planning of Manipulator Pushing Operations , 1986 .

[4]  Bruce Randall Donald,et al.  Constructive recognizability for task-directed robot programming , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.

[5]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .

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

[7]  Jean-Claude Latombe,et al.  Robot motion planning , 1970, The Kluwer international series in engineering and computer science.

[8]  John F. Canny,et al.  On computability of fine motion plans , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

[9]  Bruce Randall Donald,et al.  Sensor interpretation and task-directed planning using perceptual equivalence classes , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[10]  B. Donald,et al.  Symbolic and Numerical Computation for Artificial Intelligence , 1997 .

[11]  Tomás Lozano-Pérez,et al.  Spatial Planning: A Configuration Space Approach , 1983, IEEE Transactions on Computers.

[12]  Patrick C. Fischer,et al.  Turing Machines with Restricted Memory Access , 1966, Inf. Control..

[13]  Bruce Randall Donald,et al.  Constructive recognizability for task-directed robot programming , 1992, Robotics Auton. Syst..

[14]  David A. Cox,et al.  Ideals, Varieties, and Algorithms , 1997 .

[15]  John H. Reif,et al.  The complexity of elementary algebra and geometry , 1984, STOC '84.

[16]  Micha Sharir,et al.  Planning, geometry, and complexity of robot motion , 1986 .

[17]  M. Minsky.  Recursive Unsolvability of Post's Problem of "Tag" and other Topics in Theory of Turing Machines , 1961 .

[18]  Dima Grigoriev,et al.  Complexity of Deciding Tarski Algebra , 1988, J. Symb. Comput..

[19]  Balas K. Natarajan,et al.  On planning assemblies , 1988, SCG '88.

[20]  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).

[21]  Ian Horswill,et al.  Analysis of Adaptation and Environment , 1995, Artif. Intell..

[22]  Michael A. Erdmann,et al.  Towards Task-Level Planning: Action-Based Sensor Design , 1992 .

[23]  Amy J. Briggs.  An efficient algorithm for one-step planar complaint motion planning with uncertainty , 1989, SCG '89.

[24]  Michael A. Erdmann,et al.  Using Backprojections for Fine Motion Planning with Uncertainty , 1985, Proceedings. 1985 IEEE International Conference on Robotics and Automation.

[25]  Daniela Rus.  Fine motion planning for dexterous manipulation , 1992 .

[26]  Stanley J. Rosenschein,et al.  Synthesizing Information-Tracking Automata from Environment Descriptions , 1989, KR.

[27]  Patrick Gordon Xavier.  Provably-good approximation algorithms for optimal kinodynamic robot motion plans , 1992 .

[28]  Michael A. Erdmann,et al.  On probabilistic strategies for robot tasks , 1989 .

[29]  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).

[30]  R. J. Schilling,et al.  Decoupling of a Two-Axis Robotic Manipulator Using Nonlinear State Feedback: A Case Study , 1984 .

[31]  John H. Reif,et al.  The complexity of elementary algebra and geometry , 1984, STOC '84.

[32]  Nancy A. Lynch,et al.  Easy impossibility proofs for distributed consensus problems , 1985, PODC '85.

[33]  Bruce Randall Donald,et al.  Program mobile robots in Scheme , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.

[34]  Russell H. Taylor,et al.  Automatic Synthesis of Fine-Motion Strategies for Robots , 1984 .

[35]  Matthew T. Mason,et al.  An exploration of sensorless manipulation , 1986, IEEE J. Robotics Autom..

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

[37]  J. Schwartz,et al.  On the Complexity of Motion Planning for Multiple Independent Objects; PSPACE- Hardness of the "Warehouseman's Problem" , 1984 .

[38]  Bruce Randall Donald,et al.  Error Detection and Recovery in Robotics , 1989, Lecture Notes in Computer Science.

[39]  Bruce Randall Donald,et al.  Towards a Theory of Information Invariants for Cooperating Autonomous Mobile Robots , 1993 .

[40]  Bruce Randall Donald,et al.  Time-safety trade-offs and a bang-bang algorithm for kinodynamic planning , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[41]  David Chapman,et al.  Planning for Conjunctive Goals , 1987, Artif. Intell..

[42]  D. Grigor'ev.  Complexity of deciding Tarski algebra , 1988 .

[43]  Michael A. Erdmann,et al.  Using Backprojections for Fine Motion Planning with Uncertainty , 1986 .

[44]  Bruce Randall Donald,et al.  Information Invariants for Distributed Manipulation , 1995, Int. J. Robotics Res..

[45]  V. Rich.  Personal communication , 1989, Nature.

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