Sloppy motors, flaky sensors, and virtual dirt: Comparing imperfect ill-informed robots

Robots must complete their tasks in spite of unreliable actuators and limited, noisy sensing. In this paper, we consider the information requirements of such tasks. What sensing and actuation abilities are needed to complete a given task? Are some robot systems provably "more powerful" than others? Can we find meaningful equivalence classes of robot systems? This line of research is inspired by the theory of computation, which has produced similar results for abstract computing machines. The basic idea is a dominance relation over robot systems that formalizes the idea that some robots are stronger than others. We show that this definition is directly related to the robots' ability to complete tasks. Our prior work in this area assumes perfect control and sensing, requires that the robot begin with a single fixed initial condition within a known environment, and models of time as a sequence of variable-length discrete stages, rather than as a continuum. In this paper, we substantially improve upon that earlier work by addressing these problems.

[1]  Jeffrey D. Ullman,et al.  Introduction to automata theory, languages, and computation, 2nd edition , 2001, SIGA.

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

[3]  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).

[4]  Antoine Girard,et al.  Approximation Metrics for Discrete and Continuous Systems , 2006, IEEE Transactions on Automatic Control.

[5]  Ronen I. Brafman,et al.  On the Knowledge Requirements of Tasks , 1998, Artif. Intell..

[6]  Kenneth Y. Goldberg,et al.  Bayesian grasping , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[7]  Steven M. LaValle,et al.  An Objective-Based Framework for Motion Planning under Sensing and Control Uncertainties , 1998, Int. J. Robotics Res..

[8]  Bruce Randall Donald,et al.  On Information Invariants in Robotics , 1995, Artif. Intell..

[9]  Michael A. Bender,et al.  The power of a pebble: exploring and mapping directed graphs , 1998, STOC '98.

[10]  Mihalis Yannakakis,et al.  Shortest Paths Without a Map , 1989, Theor. Comput. Sci..

[11]  Christos H. Papadimitriou,et al.  Games against nature , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).

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

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

[14]  Michael A. Erdmann,et al.  Randomization for robot tasks: Using dynamic programming in the space of knowledge states , 1993, Algorithmica.

[15]  Richard M. Karp,et al.  On-Line Algorithms Versus Off-Line Algorithms: How Much is it Worth to Know the Future? , 1992, IFIP Congress.

[16]  Matthew T. Mason,et al.  The mechanics of manipulation , 1985, Proceedings. 1985 IEEE International Conference on Robotics and Automation.

[17]  Michael A. Erdmann,et al.  Understanding Action and Sensing by Designing Action-Based Sensors , 1995, Int. J. Robotics Res..

[18]  Chi-Tsong Chen,et al.  Linear System Theory and Design , 1995 .

[19]  Jason M. O'Kane,et al.  On Comparing the Power of Mobile Robots , 2006, Robotics: Science and Systems.

[20]  Ricardo A. Baeza-Yates,et al.  Searching in the Plane , 1993, Inf. Comput..

[21]  Ming-Yang Kao,et al.  Searching in an unknown environment: an optimal randomized algorithm for the cow-path problem , 1996, SODA '93.

[22]  Steven M. LaValle,et al.  Planning algorithms , 2006 .

[23]  Robert E. Tarjan,et al.  Amortized efficiency of list update and paging rules , 1985, CACM.

[24]  Jérôme Barraquand,et al.  Motion planning with uncertainty: the information space approach , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

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