Using backprojections for fine motion planning with uncertainty
International Journal of Robotics Research
Mechanics and planning of manipulator pushing operations
International Journal of Robotics Research
Dynamic programming: deterministic and stochastic models
Dynamic programming: deterministic and stochastic models
Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
On the representation and estimation of spatial uncertainly
International Journal of Robotics Research
The complexity of Markov decision processes
Mathematics of Operations Research
Automatic grasp planning in the presence of uncertainty
International Journal of Robotics Research
The complexity of robot motion planning
The complexity of robot motion planning
Sensor models and multisensor integration
International Journal of Robotics Research - Special Issue on Sensor Data Fusion
Sensor-based manipulation planning as a game with nature
Proceedings of the 4th international symposium on Robotics Research
A geometric approach to error detection and recovery for robot motion planning with uncertainty
Artificial Intelligence - Special issue on geometric reasoning
Error detection and recovery in robotics
Error detection and recovery in robotics
Planning multi-step error detection and recovery strategies
International Journal of Robotics Research
International Journal of Robotics Research
Understanding action and sensing by designing action-based sensors
International Journal of Robotics Research - Special issue on integration among planning, sensing, and control
Motion planning with uncertainty: a landmark approach
Artificial Intelligence - Special volume on planning and scheduling
Geometric sensing of known planar shapes
International Journal of Robotics Research
Handbook of combinatorics (vol. 2)
The topological structure of asynchronous computability
Journal of the ACM (JACM)
SIAM Journal on Discrete Mathematics
Robot Motion Planning
Handbook of AI
Robot Motion: Planning and Control
Robot Motion: Planning and Control
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Dynamic Programming
On the undecidability of probabilistic planning and related stochastic optimization problems
Artificial Intelligence - special issue on planning with uncertainty and incomplete information
Computers, Rigidity, and Moduli: The Large-Scale Fractal Geometry of Riemannian Moduli Space
Computers, Rigidity, and Moduli: The Large-Scale Fractal Geometry of Riemannian Moduli Space
Planning Algorithms
Nonpositive Curvature and Pareto Optimal Coordination of Robots
SIAM Journal on Control and Optimization
Coordinate-free Coverage in Sensor Networks with Controlled Boundaries via Homology
International Journal of Robotics Research
International Journal of Robotics Research
On information invariants in robotics
Artificial Intelligence
Note: Combinatorial Alexander Duality—A Short and Elementary Proof
Discrete & Computational Geometry
Distance-Optimal Navigation in an Unknown Environment Without Sensing Distances
IEEE Transactions on Robotics
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In this paper we explore a topological perspective of planning in the presence of uncertainty, focusing on tasks specified by goal states in discrete spaces. We introduce strategy complexes. A strategy complex is the collection of all plans for attaining all goals in a given space. Plans are like jigsaw pieces. Understanding how the pieces fit together in a strategy complex reveals structure. That structure characterizes the inherent capabilities of an uncertain system. By adjusting the jigsaw pieces in a design loop, one can build systems with desired competencies. The paper draws on representations from combinatorial topology, Markov chains, and polyhedral cones. Triangulating between these three perspectives produces a topological language for describing concisely the capabilities of uncertain systems, analogous to the concepts of reachability and controllability in other disciplines. The major nouns in this language are topological spaces. Three key theorems illustrate the sentences in this language. (a) Goal attain-ability: There exists a strategy for attaining a particular goal from anywhere in a system if and only if the strategy complex of a slightly modified system is homotopic to a sphere. (b) Full controllability : A system can move between any two states despite control uncertainty precisely when its strategy complex is homotopic to a sphere of dimension two less than the number of states. (c) General structure: Any systemâ聙聶s strategy complex is homotopic to the product of a spherical part, modeling full controllability on subspaces, and a general part, modeling adversarial capabilities. This paper contains a number of additional results required as stepping stones, along with many examples. We provide algorithms for computing the key structures described. Finally, we show that some interesting questions are hard. For instance, it is NP-complete to determine the most precisely attainable goal of a system with perfect sensing, but uncertain control.